the radius is $\sqrt{g^2+f^2-c}$
#help-17
obtuse scroll
twin meteorBOT
diaas_(yt)
obtuse scroll
So you can just rewrite it as $(x+g)^2+(y+f)^2=r^2$
twin meteorBOT
diaas_(yt)
obtuse scroll
That's pretty much it
tepid fossil
alpine cipher
Hi, I need some help with Polynomial Vector subspaces
vocal sleetBOT
Hi, I need some help with Polynomial Vector subspaces
alpine cipher
Specifically, how you'd calculate one whose condition (I think that's the correct term?) is a differential equation
cyan talon
if you show the question sure
cyan talon
pics are fine no problem
cyan talon
yeah np
alpine cipher
I've done the existence of a zero vector part already, bc that was pretty easy, but I'm stuck on how I'd show the closure under vector addition and scalar multiplication parts
alpine cipher
in general I'd show that for any two vectors that satisfy the condition, call them x and v, the vector (x + v) also satisfies the condition
cyan talon
yea exactly
so let's do that
we have a polynomial p with p''(-8) +3p(-8) = 0, and q with q''(-8) + 3p'(-8) = 0
and we wanna show p+q also satisfies that condition i.e. (p+q)''(-8) + 3(p+q)'(-8) = 0
alpine cipher
mostly I get stuck at trying to find a way to express p" and p' in terms of p
cyan talon
yeah you don't need to
you prolly know from calculus that the derivative is a linear operator
i.e. the derivative of a sum of two functions is the sum of the derivatives
& that (c*f)' = c*f'
alpine cipher
where c is a constant?
cyan talon
you prolly know from calculus that the derivative is a linear operator
it's nice to have that in mind
alpine cipher
ok
thank you
from that, how would I word it?
like, would I just say that for some p in S, since the derivative is a linear operator, np where n is in the set of all Real numbers satisfies the condition as
(np)"(-8) - 3(np)'(-8) = 0
n(p"(-8) - 3p'(-8)) = 0
substitute p"(-8) - 3p'(-8) = 0 as p is in S
n(0) = 0
and that's scalar multiplication, and a similar wording for vector addition
cyan talon
yeah
alpine cipher
sweet
thank you so much
you just did in like 15 minutes what 2ish hours of google and rereading course notes couldn't
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
im not sure what i'm doing incorrectly. the expected final answer is 48.41
help
!status
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3. I got an answer but I was told that it's wrong.
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5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
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placid osprey
Hi there,
I have a question about vector decomposition. The vectors $u$ and $v$ are given as shown in the figure below. I need to break down vector $u$ into the sum of two components, namely $u_{|v}$ (parallel to $v$) and $u_{\perp v}$ (perpendicular to $v$).
Could someone please help me with this decomposition and provide the coordinates in the form of column vectors like $\left[\begin{array}{l}a \ b\end{array}\right]$?
twin meteorBOT
dgh
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vapid wedge
vocal sleetBOT
https://gyazo.com/652aee36f7c1c378dc893e3865b5b8d5
vapid wedge
Isn't this the same as doing 1/squareroot(3) * 1/squareroot(2) ?
flat whale
Yes
vapid wedge
so 1/squreroot(6)?
paper depot
1/sqrt(6), yes.
vapid wedge
Aah thanks was gonna ask that haha
But i have a question regarding that
This is the original question that i am on
paper depot
🙃
vapid wedge
My first guess would be to move sqrt(3) to the right hand side by dividing, right?
And then use this formula to combine sin(x) - cos(x) https://gyazo.com/f4861d7007e1b41a7e198176f3cefe40
paper depot
My first guess would be to move sqrt(3) to the right hand side by dividing, righ...
unnecessary
vapid wedge
however, my first problem comes when trying to do that since it's (-) between them, does that mean Asin(x-phi) ?
paper depot
but also you should not be describing this stuff as "moving" between sides
also no the minus sign doesnt really affect much
you just have b = -1 here
and a = sqrt(3)
vapid wedge
aaahy
OH
yeah neat
we can keep the sqrt(3)
didn't think of that
Is this correct so far?
What happens with the (-1/2)? Do i add 30* on both sides so x = 60 + n360? @paper depot
.close
hearty wigeon
Is there anything wong with my notation ?
vocal sleetBOT
Is there anything wong with my notation ?
median crane
What’s beh bew
eager elbow
hello
eager elbow
By making good use of the trigonometry form, simplifies the following expressions and gives their domains. ...
cos(Arctan(x))
need help i dont know how to start
i do this then i do what
mental falcon
so what is the domain of arctan function, and what is its range?
(starting from the inside of the nested functions, going out)
eager elbow
its R --> ]-pi/2 ; pi/2[
mental falcon
yes (-pi/2, pi/2) open interval
now cos is accepting inputs from that output of the arctan, but what is the domain of cos? it's R so it can handle any output from arctan
eager elbow
i need to restrict the cos or no ?
mental falcon
nope
eager elbow
cos is R --> [-1;1]
mental falcon
it can handle any of those inputs
spat out by the arctan
if it was something with a more restrictive domain for the outer function then you would
eager elbow
i need to do this ?
mental falcon
what is that? 🤔
eager elbow
i need to reunite the dom of arctan and the dom of cos ?
mental falcon
well both their domains are R
eager elbow
yes
mental falcon
i don't think in general you would simply take intersection of their domains...you would need to uh take the subset of the domain of arctan (inner function) such that its output is in the domain of cos (outer function) or something
like for example say you have:
$\sqrt{x-5}$
twin meteorBOT
Soosh
mental falcon
thing of sqrt as the outer function and (x-5) as the inner function
square root only accepts positive numbers, while domain of (x-5) is R
so we want domain such that x -5 > 0
i.e. the codomain of x - 5 is within the domain of square root
but honestly just thinking about it logically is easier than adding all this terminology on it, go from inside function to outeside one
you still with me? 😐
eager elbow
yes
eager elbow
i try to understand what ur writing because im not good at english
mental falcon
ah, sorry i dont know math in other languages
eager elbow
so yeah it would just be x > 5 there 🤷♂️
i understand this
but how i find the domaine of cos(arctanx) ? the domaine is just R
eager elbow
but why its R how i show it mathematicly
mental falcon
now cos is accepting inputs from that output of the arctan, but what is the doma...
^
mental falcon
there is a theorem that says (here i will copy and paste it), so you can always use that to "show it mathematically" if you are trying to prove something:
The domain of a composite function f(g(x)) is the set of those inputs x in the domain of g for which g(x) is in the domain of f.
mental falcon
hm
eager elbow
i need to use trigonometry formul
mental falcon
i think you can do with some trick but i dont remember
eager elbow
yeah trigonometry formula maybe
mental falcon
you might be able to draw a picture and think about it on the unit circle, or yeah with some trig identity playing around
mental falcon
i found this weird proof online but i never would've thought to write that first line out of thin air 😂
eager elbow
Ok
mental falcon
there is the identity 1 + tan ^ 2 = sec ^ 2
which is why theyre writing the first line, and using arctan x as the input
anyway its weird but i honestly dont know how i would do that myself
seems like a tricky proof
eager elbow
tany=x cos(arctan(x))
i will try to find
arctan(x) is an angle so to simplify i need to find the value of cos(x)
i need to use a formula with tan that gives cos
cos²(y)=1/1+tan²(y)
tan(y)=x
so cos²(x)=1/1+x²
cosx=1/sqrt(1+x²)
like that @mental falcon ?
mental falcon
why does tan x = x?
eager elbow
yeah tan(y)=x
mental falcon
i dont know you lost me
tany=x cos(arctan(x))
and also
tan y = x
?
so cos (arctan(x)) = 1 ?
mental falcon
sorry im not following but also my brain is tired rn and i need to go, maybe you can ask someone else to take a look if you arent satisfied with it
mental falcon
take care
eager elbow
yep
lime gorge
vocal sleetBOT
cyan talon
yea there's no X=0
cyan talon
yea, just those 3 cases
lime gorge
ty platypus
vocal sleetBOT
@lime gorge Has your question been resolved?
rare belfry
i need help with a problem it goes like this
Write a squared(quadratic) equation, one solution of which is the sum, and the other is the product of the solutions of the equation
3x² - 2x - 7 = 0
( i dont understand where to start or anything)
rare belfry
i dont wanna be mean but i already posted in this chanel go to avalible math help thank you mr robin
unreal pagoda
sry mb
rare belfry
im listening
slim oar
You want to find an equation with roots ab and a+b
which is: (x-ab)(x-(a+b))
expanding: x^2-x(ab+a+b)+(ab)(a+b)
ab is -7/3
a+b is 2/3
Now substitute them to get the final equation
which is x^2+5/3x-14/9
rare belfry
aight i underrstand everything but how is ab -7/3 and a+b 2/3
slim oar
This is equal to 9x^2+15x-14
rare belfry
yes thats correct that is said in my mathbook
slim oar
aight i underrstand everything but how is ab -7/3 and a+b 2/3
3(x-a)(x-b) = 3x^2-2x-7
unreal pagoda
In this exercise, we want to specify a non-Archimedean Field. To do this, we consider rational
functions. If there are polynomials (image 1)
with coefficients a0, . . . , an, b0, . . . , bm ∈ R and bm ̸= 0, we call f =p/q rational. Let f be defined on a
suitable subset of the real numbers (namely R without the zeros of q).
Let R := {f is rational function} be the set of rational functions. In the following you may use that R is a
body with respect to the following addition and multiplication: For rational functions f =p/qand g = r/s
we set
f +R g :=(ps + rq)/qs (image 2)
and f *R g := pr/qs (image 2)
On R we define an order <R by
f <R g : ⇐⇒ there exists M ∈ R with f(x) < g(x) for all x ≥ M. (image 3)
Where < is the known order on the real numbers.
I have a problem with proving that <R is an order on the field R.
Do I just need to prove that the set R is ordered and fulfills the Field axioms?
vocal sleetBOT
In this exercise, we want to specify a non-Archimedean Field. To do this, we con...
vocal sleetBOT
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tropic anchor
How do i do b
vocal sleetBOT
How do i do b
tropic anchor
.close
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warped chasm
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warped chasm
How do I do this?
hushed pewter
I would separate $\int \frac{3x+1}{1+4x^2}dx$ into $\int \frac{3x}{1+4x^2}dx+\int \frac{2}{1+4x^2}dx$
twin meteorBOT
SWR
warped chasm
then what?
vocal sleetBOT
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robust heron
could someone explain how to do this question for me
vocal sleetBOT
could someone explain how to do this question for me
robust heron
i am not entirely sure but I think this is a bernoulli trial type question
or maybe its geometric
not really sure
raven owl
or maybe its geometric
geometric distribution can be though of as how many bernoulli trials it takes until a success, so you are correct in your thinking
robust heron
ok
so i have started with defining p, q and X
but im not exactly sure how to set it up from there
raven owl
How have you defined them
robust heron
p=0.02, q=0.98, X=# of products checked
raven owl
p is good, q is good but I do not think it will be needed. For X, I would add "until a defective item is found"
robust heron
ok
raven owl
You have identified its geometric, do you know what to do next?
robust heron
thats where im a little stuck
i know im going to have to do the summation and convergence stuff
but im not sure how to get there first
oh wait isnt there a property that says P(X>=k)=(1-p)^k
robust heron
ok but in this case i need the > right?
raven owl
oh yeah true
robust heron
so should i just sub in k=85?
raven owl
yeah
raven owl
oh wait isnt there a property that says P(X>=k)=(1-p)^k
I believe this is actually 1-(1-p)^k
Nvm im looking at the reverse
robust heron
ok well it ended up being wrong so maybe it is 84?
but that doesnt make sense the way ive defined it
wait im reading that the random variable X is the number of failures UNTIL the first success
therefore i need ATLEAST 84 ?
and then maybe the 85th is defective
raven owl
I think it would be 84. Lets look at the formula P(X>=k)=(1-0.02)^k. If we atleast 1 item, we would except a 100% probability, so we would have to plug in 1-1. Following this pattern, for 85 you would plug in 85-1
raven owl
np
robust heron
.close
proper igloo
for series
vocal sleetBOT
for series
proper igloo
how do you determine what type of series they are and what style to solve them?
for example I had these two
which isnt hard in nature but finding the right method to solve is confusing to me
I solved these by trial and error, and on a test or something trial and error might not cut it lol
worthy citrus
just sort of takes practice and experience. the first one definitely looks like its in the form where you should consider doing partial fraction decomposition as the denominator is a product of two linear terms
a natural thing to do in the second one is split the fraction up into two and see what you get as a result
proper igloo
right
for the first one, I just split up A/(n+4) and b/(n+2) = 2
lemme send my work
worthy citrus
if you try a technique that doesnt work out for you, this is still useful in the long run as it lets you gather information as to why this method wasn't that good for this series
proper igloo
worthy citrus
for the first one, I just split up A/(n+4) and b/(n+2) = 2
yeah yeah this is partial fraction decomposition
proper igloo
Yea i solved it that way idk if my math was off but in the end i got like 23/84 which is wayyyy off
worthy citrus
i think your A and B are off
proper igloo
ok ill check again
livid tapir
This book looks decent though I've never read it https://link.springer.com/book/9783031375569, personally I actually dislike that the description says it's informal tho
livid tapir
But a book with proofs might be overkill for calc
proper igloo
so the issue must be when you "telescoped" the sum
is the method to take the first 3 sums and the nth sum then do limits
thats what my book says
worthy citrus
yeah i would write out a few terms and spot the pattern of cancellation
proper igloo
ok
wait are these telescopic sums just solving until the first and last sum are left? b
cuz i left like 2 terms that didnt cancel in there which might be the error now that I think about it
proper igloo
right
worthy citrus
so terms will be cancelling with things further in the series than if you just had n and n+1 appearing
as a consequence more than one term should survive
proper igloo
I see
worthy citrus
and with any luck those two terms that didnt cancel should add up to 7/12
vocal sleetBOT
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Available help channel!
frail spruce
i need help on number 88
vocal sleetBOT
i need help on number 88
frail spruce
<@&286206848099549185>
dull bear
<@&286206848099549185>
!15m please
vocal sleetBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
frail spruce
ok, sorry
frail spruce
!15m please
can u help me in 15
obtuse monolith
Do you just need to simplify
frail spruce
no it says to find the value
obtuse monolith
find the value of p? there is no = sign so there is no equation, some expressions may simplify to a number though
frail spruce
oh my textbook is weird p means pi
flat whale
wot
frail spruce
yeah it’s weird
flat whale
,tex .sum diff trig
twin meteorBOT
riemann
obtuse monolith
alright well thats just the unit circle and you square the answers u get and add them
sin(11pi/6) = -1/2 and cos(4pi/3) = -1/2
simply now that you know that calculate (sin(11pi/6))^2 + (cos(4pi/3)^2
that would be basic plugging in
@frail spruce is this resolved
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shut zinc
I am trying to find this laplace with this given f(t) but i am getting stuck. Im finding myself in a loop where i am having multiple integrations by parts. is this normal? I assume i messed up I am just lost on where
vocal sleetBOT
I am trying to find this laplace with this given f(t) but i am getting stuck. Im...
vocal sleetBOT
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Available help channel!
vast shale
silly question but is there a way for desmos to only have the grey points when the 2 functions intersect
vocal sleetBOT
silly question but is there a way for desmos to only have the grey points when t...
vast shale
im calculating tangents and im going to be zooming around so its annoying to see all the other points
formal pond
rocky valley
Hey, I need help with this question
vocal sleetBOT
Hey, I need help with this question
random shore
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
ok
rocky valley
I just don't know man!
rocky valley
?
random shore
you have x and y agree?
rocky valley
you have x and y agree?
No, not x
random shore
i meant in the question, but good catch
so we have to find x
which x do we want to find?
rocky valley
So I plug 52 in for y?
random shore
perfect
random shore
mhm
random shore
have you learnt bhaskaras?
rocky valley
No, I'm in AA2 if that helps
rocky valley
Advanced Algebra 2
rocky valley
quadratic eqution formula?
I think that's what I'm using
random shore
ok
rocky valley
bring it to other side
random shore
now to solve that you must use this formula
random shore
!
rocky valley
I think I messed up
Idk
Can you walk me through this please...
Actually brb in 5
Alright
rocky valley
Sooo
random shore
I think I messed up
why?
rocky valley
Ok, so I got x=55 and x=450
random shore
want me to check is that it?
random shore
i think you rounded wrong
rocky valley
Oh?
rocky valley
no, you're right
Ty man
Now I can go toi bed
It's in embarassing to admit
But I'm leaving school early so I don't have to take this test tommorow
I actually don't understand these concepts
random shore
youll end up having to take it anyways
rocky valley
Yeah
random shore
so study up
random shore
you got this
rocky valley
So I won't have "adequte time"
random shore
dont stress man
rocky valley
So Prolly not till next monday
rocky valley
dont stress man
I have a B+ and my parents are pissed
random shore
im not american but im sure thats not bad
rocky valley
im not american but im sure thats not bad
uhh
I have an 87
Anyway ba-bye!
.close
oblique raven
T
terse forum
!original
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
oblique raven
,rotate
twin meteorBOT
oblique raven
Ok
I need help with answering is “(x-2) a factor of x^4-3x^3+5x-10”
I think it is but my explanation is not good lol
I was going to write “yes because it multiplies”
drifting jackal
You can say that for anything, but to determine if it's a factor, when you divide and you don't have a remainder, that's when you know it's a factor
oblique raven
hmm
ok but I have a remainder?
what do u mean
did I do my math wrong I think I might’ve
polynomial divisions btw
we do synthetic and long divisions later
drifting jackal
The question asks if " (x-2) is a factor of x^4-3x^3+5x-10" and when you do the division, if you end up with a remainder, it's not a factor
drifting jackal
For it to be a factor, you should not have a remainder
oblique raven
so it’s not a factor because we have a remainder
drifting jackal
Yes
vast shale
i really need help on what exactly i'm supposed to input here. i've found that it's a geometric series where a = 1/4, r = 1/16, and sum is 4/15, does not work despite verifying on wolfram. i can use alternating series test if i rewrite using (-1)^(n+1), which eliminates the negative sign on the bottom, but it's still not correct
vocal sleetBOT
i really need help on what exactly i'm supposed to input here. i've found that i...
vast shale
at least if i simplify it, i get the form (1/4)(1/16)^n but even then it's not right unless my sum isn't correct
cobalt ocean
ah
it says 'pick the first applicable test in the list'
so it's surely meant to be geometric
and in the geometric case r should surely be negative
yeah i get a different a and r
vast shale
let me redo my work
okay this time i got -1/4 as a and -1/16 as r, but i evaluated the (-4) term with it instead of applying alternating series
i'm getting the same exact answer if i input the same number to both, with a sum of (-4/17)
still not right
calculated my infinite sum as (-1/4)/(1+1/16)
wish i got at least some partial credit to see what i'm not doing right..
boutta rip my hair out
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
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vast shale
.close
hearty crystal
Consider a sample of 8 hypertensive smoking adults. Their serum cholesterol level readings are as follows:
220, 230, 235, 225, 223, 218, 220, 233
What is the margin of error, rounded off to two decimal places, of a 99% confidence interval for the mean serum cholesterol level of hypertensive smoking adults? Use one decimal place for both sample mean and sample standard deviation.
vocal sleetBOT
Consider a sample of 8 hypertensive smoking adults. Their serum cholesterol leve...
hearty crystal
Consider a sample of 8 hypertensive smoking adults. Their serum cholesterol level readings are as follows:
220, 230, 235, 225, 223, 218, 220, 233
What is the margin of error, rounded off to two decimal places, of a 99% confidence interval for the mean serum cholesterol level of hypertensive smoking adults? Use one decimal place for both sample mean and sample standard deviation.
vocal sleetBOT
@hearty crystal Has your question been resolved?
frail lantern
the correct answer is showing as A, but i dont understand how 8 and d+2 are the solutions
vocal sleetBOT
the correct answer is showing as A, but i dont understand how 8 and d+2 are the ...
raven owl
When d=8, 2x-16=0 for left, and (x-8)=0 on right so entire right side is 0, hence they are equal
If you plug in d+2, the (x-d) term evaluates to 2, and 2x-16=2(x-8)
ivory yarrow
frail lantern
and thats why i picked C but idk it doesnt accept that
ivory yarrow
When d=8, 2x-16=0 for left, and (x-8)=0 on right so entire right side is 0, henc...
Well that's more of a hit and trial method using the options
frail lantern
oh so u expanded the right hand side
ivory yarrow
yes
frail lantern
my god
ivory yarrow
Then formed a quadratic with the x on one side
frail lantern
that makes alot of sense
yeah i got it now thanks alot @raven owl and @ivory yarrow
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Available help channel!
cloud harness
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cloud harness
how is x = 44? evaluating logarithim equations
yellow pad is what i did, i got 15 because i removed the common loga bases
ohhh
product fucking rule
omfg
hollow heron
cloud harness
i got 15, the calcu got 44
i added 4 and 11 instead of multiplying the bitch
cause product rule
slate herald
@cloud harness ?
stop swearing randomly and tell if u have any doubts regarding the question
I got 44 as well
cloud harness
stop swearing randomly and tell if u have any doubts regarding the question
I go...
i did it wrong
essentially
i added instead of multiplying
thats why i got 15 instead of 44
pallid forge
unless you have a question, you can close this now
austere lantern
Is that exercise on limits right?
finite hatch
Hey
vocal sleetBOT
@finite hatch Has your question been resolved?
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@finite hatch Has your question been resolved?
dull scaffold
pls help
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weak frigate
can someone help me why 2/15 is factored out when simplifying this?
weak frigate
im confused why 2?
whats the process to easily get 2 when factoring out these trinomials?
slim oar
whats the process to easily get 2 when factoring out these trinomials?
Factor out x^(1/2)
Then use standard factoring methods
weak frigate
Then use standard factoring methods
i dont get why 2/15 is factored out
slim oar
i dont get why 2/15 is factored out
Basically you want to get rid of fractions
Factor out 1/15 forst
Then the coefficients are 18, 20, and 30
Then factor 2 out as 2 divides all three
weak frigate
ooh okk thank youu, ill use this when simplifying integrals 🫶
this made more sense now
vocal sleetBOT
@weak frigate Has your question been resolved?
gaunt quest
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urban valley
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@gaunt quest Has your question been resolved?
dense rune
<@&286206848099549185>
vocal sleetBOT
<@&286206848099549185>
ivory yarrow
you don't need to ping helpers as soon as you post your issue
and this is pretty basic if you understand how quadrants work
in the first quadrant, your value is θ
in the second, it is π - θ
in the third, its θ - π
in the fourth, its -θ
or since you're dealing with 0,2π, just know that sin(90+θ) = -cosθ, sin(180-θ) = sinθ, cot(90+θ) = tanθ and so on
ivory yarrow
I won't spoon feed you. just know that sin 301 = sin(270 + 31)
and sin of 270 + θ = -cosθ
dense rune
what is this topic called
ivory yarrow
trigonometry
dense rune
trigonometry
more specific
ivory yarrow
I don't think trigonometry has a subtopic for this
dense rune
what is the question asking for
ivory yarrow
try figuring it out
dense rune
ok i do some u tell me if im going to the correct direction
ivory yarrow
"express whatever (...) in terms of single trigonometric functions with the range 0, 45
sure go ahead
ivory yarrow
so can i place that into the sinx cosy - siny cosx
You could have pinged me 😭
You don't need to get into sinxcosy - sinycosx
Take the hint from this
sin 320° = sin(270°+50°) = -cos50°
sin(0+-¢) or sin(π+-¢) will result in sin itself
But sin(π/2 +-¢) or sin(3π/2+-¢) would give it in terms of cos
Adjust the signs according to the quadrants
vocal sleetBOT
@dense rune Has your question been resolved?
vocal sleetBOT
any idea what am I doing wrong?
vocal sleetBOT
vocal sleetBOT
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solar forge
can somebody please tell me where did i made a mistake? there should be a + not -
vocal sleetBOT
can somebody please tell me where did i made a mistake? there should be a + not ...
solar forge
for context i am calculacting a group velocity from a dispersion relation, co cg is a group velocity and cf is a phase velocity
flat whale
not really enough context to check your entire work
solar forge
not really enough context to check your entire work
i am just pluging $c_f=\sqrt{\alpha k/\rho}$ into this: $$c_g=c_f+k\frac{\text{d}c_f}{\text{d}k}$$, so i probably made some mistake, because the right answer have +1/2 not -1/2
twin meteorBOT
marejak023
solar forge
*mistake in the derivative
flat whale
yea there's no way to tell your equation for c_g is even correct
or c_f
or if alpha and rho depend on k
solar forge
yea there's no way to tell your equation for c_g is even correct
c_f is correct, c_g is also correct, just wrong sign
flat whale
what's that supposed to say?
solar forge
this is correct answer, they just force the k into the square root but that doesnt matter, the important thing is why is there the plus sign? it just derivative so dont look for any context behind it
nvm, ill figure it out differently
.close
young cosmos
Shouldnt there be three functions inside of each other, like shouldnt 2x also be one
vocal sleetBOT
Shouldnt there be three functions inside of each other, like shouldnt 2x also be...
thick sky
just wondering if i can get some quick help on a question. I'm completely unsure how I would solve this and there really isnt anymore information added
young cosmos
.close
vocal sleetBOT
ornate ember
just wondering if i can get some quick help on a question. I'm completely unsure...
Hi this channel was already occupied. Can you make a new one?
ornate ember
vocal sleetBOT
Available help channel!
tidal surge
vocal sleetBOT
tidal surge
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
median crane
What’s the question in English
tidal surge
@median crane I need to check if f(x) etc. are solutions to dy / dx. I don't know where to go from here when solving the differential equation. Do I substitute f(x)=e^x+x+1 in y and then do: dy / dx = e^x+x+1-x etc?
median crane
When you solve an differential equation you look for a function y that satisfies the given equation
If you plug y into the equation dy/dx = y-x does the equality hold
vocal sleetBOT
median crane
You too
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Available help channel!
weak sandal
How do i get AB?
vocal sleetBOT
How do i get AB?
astral shadow
BD is 3.93?
weak sandal
yes
lean forge
If we're using frenet frame, with s being the lenght of arc, what would be (ds/dt)*ds ?
vocal sleetBOT
If we're using frenet frame, with s being the lenght of arc, what would be (ds/d...
flat whale
If we're using frenet frame, with s being the lenght of arc, what would be (ds/d...
do you know the equation of s
lean forge
We didn't do it yet
We just said it was the lenght of arc
I'm just wondering if there's some derivative identity in this instance though
flat whale
how are you supposed to find ds/dt without s?
grave mason
can somebody help me graph this?
vocal sleetBOT
can somebody help me graph this?
grave mason
they want us to solve us by finding the focus, vertex, and the p value
see the orange sheet to reference how my teacher used wants us to solve it
my main question is how do i know if it faces up or sideways?
vast shale
what are you struggling on?
grave mason
i think I can do it if I find out the direction of the graph but I don’t know if it’s up or sideways and I don’t remember how to figure out if it’s one or the other
vast shale
hmm
vocal sleetBOT
@grave mason Has your question been resolved?
vocal sleetBOT
@grave mason Has your question been resolved?
lean forge
my main question is how do i know if it faces up or sideways?
It's sideways if the square is on the y
And up if the square is on the x
grave mason
thank you!
kindred marsh
I need help with optimization. I am not sure if it wants me to add x and y.
vocal sleetBOT
I need help with optimization. I am not sure if it wants me to add x and y.
@kindred marsh Has your question been resolved?
vocal sleetBOT
@kindred marsh Has your question been resolved?
ruby vapor
I need help with optimization. I am not sure if it wants me to add x and y.
My interpretation is they want the final dimensions of the entire plot, so x+4y
vocal sleetBOT
@kindred marsh Has your question been resolved?
kindred marsh
@ruby vapor Sorry for the delay, that would get you 3600 which I don't believe is the answer (600+4(750))=3600
ruby vapor
<@780552945434755083> Sorry for the delay, that would get you 3600 which I don't...
I got a different result, the equations you posted originally weren't quite right. We have A = 6000 = x*(4y) and want to optimize perimeter, P = 5x + 4y
kindred marsh
Isn't 6000 suppose to be the perimeter?
ruby vapor
Isn't 6000 suppose to be the perimeter?
sorry, didnt see you got back. The farmer wants to fence in 6000 m^2, the square meters means it's area
and requiring the least amount of fence means perimeter
celest nacelle
Hello, currently learning about centroids.
I understand how to find the centroid of a right triangle, but what about a non right triangle?
In my book I have this, but how would you go about finding x̄?
celest nacelle
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@celest nacelle Has your question been resolved?
gleaming eagle
Thought I knew how to do this, but I ammm stuck
vocal sleetBOT
Thought I knew how to do this, but I ammm stuck
@gleaming eagle Has your question been resolved?
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@gleaming eagle Has your question been resolved?
gleaming eagle
<@&286206848099549185>
gleaming eagle
.close
hasty token
vocal sleetBOT
hasty token
how do you prove this?
astral shadow
Do you know what |z| is?
hasty token
|z| is √(x^2 + y^2) right?
ik that the left side is √(x^2 + y^2)(a^2 + b^2)
but how do you show that it equals the right side without splitting the right side into |z| x |w|
astral shadow
Well you can find the complex number zw
By multiplying
Then write it in the form x + iy
Then again find its absolute value.
But I'd recommend not doing any of this and consider:
$z = r_1 e^{i \alpha}, |z| = r_1$
Similarly for w and then prove that.
twin meteorBOT
! What the hell am I doing here?
hasty token
so zw = (ax - by) + (bx - ay)i
tulip karma
my algebra teacher says that (-125)^(2/3) is 25 (cube root of -125 is -5 squared is 25) but according to jula and wolfram alpha and my own understanding, the answer is a complex number. Am I wrong? If im right, whats a good intuitive reason why this method doesn't work in this case?
vocal sleetBOT
my algebra teacher says that (-125)^(2/3) is 25 (cube root of -125 is -5 squared...
twin meteorBOT
lovelorn math enthusiast.
grand frigate
is complex or not?
twin meteorBOT
lovelorn math enthusiast.
grand frigate
right?
tulip karma
thats my issue, it seems like it should be real based on what I'm being taught,
but based on my own intuitive understanding of complex numbers, and two math programs which I would trust with my life, the answer is complex.
try putting (-125)^(2/3) into julia or wolfram alpha
tulip karma
the important thing is that it simplifies it first to (-1)^(2/3) * (125)^(2/3)
grand frigate
so??? which one is complex?
tulip karma
-1^(2/3)
grand frigate
,,\sqrt[3]{-1}
tulip karma
it should be between -1 and i
grand frigate
this is not complex
twin meteorBOT
lovelorn math enthusiast.
tulip karma
:|
tulip karma
i never said it was -1
grand frigate
okay so... how is cube root of -1 complex?
tulip karma
-1^1 = -1 and -1^(1/2) = i so -1^(2/3) must necessarily be between -1 and i but not either of them.
which is confirmed by both julia and wolfram alpha
as expected the angle of the answer lies in the second quadrant
obviously this method is an oversimplification which does not work for negative or complex numbers
tulip karma
okay so... how is cube root of -1 complex?
again, I;m not talking about the cube root of -1. im talking about (-1)^(2/3)
which is completely different
grand frigate
why must it be between -1 and i but not either of them?
tulip karma
im saying the method you are using (that being that a ^ b/c = (c root a)^b) does not work in all cases
because 2/3 is between 1 and 1/2
and is not 1 or 1/2
grand frigate
i am not understanding it well, maybe wait for someone else tbh.
tulip karma
i am not understanding it well, maybe wait for someone else tbh.
agreed
you're extending my argument past where it makes sense, since -1^x oscilates you cannot make that argument over a range which goes up and then back down
between (-1)^1 and (-1)^(1/2) both the real and immaginary components only move in one direction
grand frigate
btw is this the plot you mean?
tulip karma
yes
the reason -1^a goes between -1 and 1 is because its actually a squished cos wave, with a sin wave which makes the complex value 0 at all integer inputs. integer inputs are therefore the only inputs which yield real numbers.
also for -1^(1/2) you can see that the real goes to 0 and the imaginary to 1
it got the graph by doing the math correctly
obviousy since the graph must be continuous it will be some complex value at x = 2/3
the right way to calculate (-1)^x where x is real is
cos(pi times x) + i times sin(pi times x)
notice how at any integer the second term becomes zero
grand frigate
@tulip karma
there are complex and real values
credit to daniStuffing
depends on which -1 you pick.
e.g. -1= e^((2npi + pi)*i)
also credit to GarlicB
frail sinew
(-1)^0.5 = i
tulip karma
its true, 25^(3/2) = 125 or -125 and also (12.5 + 21.65i)^(3/2) ≈ 125 or -125
if you are asked to either give an answer or say the answer is complex, is it expected to disregard complex answers if a real answer exists?
grand frigate
if you're interested in this stuff, you can look up "roots of unity" and "demoivre's theorem"
-daniStuffing
tulip karma
hmm, reminds me of how in the mandelbrot set it often counts while increasing the number of spokes in its patterns
regal parrot
if you are asked to either give an answer or say the answer is complex, is it ex...
It depends on your class. For an algebra class (assuming college algebra or similar, not abstract algebra), you usually disregard complex solutions
The point here is that an n degree polynomial has exactly n roots (with multiplicity) in the complex numbers
so x^2 - 1 = 0, this has two real solutions, x=1 and x=-1
x^2 + 1 = 0 has no real solutions, but it does have two complex solutions: i and -i
(This is the motivation for complex numbers, actually. It is an algebraic closure of R meaning that all roots of real polynomials lie in the complex numbers)
This is practically what asking what (-1)^(2/9) is
forgetting about the 2, its equivalent to asking
what are the roots of x^9 +1 = 0
tulip karma
ah, I should have looked at all the visualizations. look at "all values" and "plot of all roots in the complex plane"
https://www.wolframalpha.com/input?i=(-1)^(2%2F3)
regal parrot
some of them are complex numbers!
tulip karma
this is really interesting, I never thought we could both be right 😂
it seems like if i do (-1)^(a/b) as i make a and b larger to approach pi there are more and more solutions, shouldn't an irrational like (-1)^(pi) have infinite solutions?
anyway, thanks for the help, I guess I should close the issue.
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
gleaming eagle
is this just gallon ??
vocal sleetBOT
is this just gallon ??
tulip karma
rate of change is slope which means rise/run. if you imagine the graph, the rise is dollars and the run is years. therefore the unit should be dollars per year.
which makes sense intuitively also, if the price of milk is changing at some rate, that rate would be however many dollars it changes by in a year.
rose shard
I keep thinking of this as X <= 15 AND x >= 30 and so my head thinks I have to multiply them since is there any good tips on how to think of it as?
vocal sleetBOT
I keep thinking of this as X <= 15 AND x >= 30 and so my head thinks I have to m...
rose shard
Just saw this formula where he moves it to the left side and that made a lot more sense hahha
hard atlas
for what reason do you flip the inequality signs?
the picture is a pretty decent way to think about it
rose shard
Yeah, and then he just moves it to the other side
to isolate P(15<=X<=30)
and he gets P(15<=X<=30)=1- ....
So that helped a lot I guess I just had to be patient and watch the video 😂
Thanks for the help tho!
🫶
.close
winter monolith
how do I do geometry problems faster?
vocal sleetBOT
how do I do geometry problems faster?
@winter monolith Has your question been resolved?
vocal sleetBOT
@winter monolith Has your question been resolved?
left sail
@summer lichen my question from earlier expired, but I say your message
left sail
I ended up converting to polar because I couldn’t figure out my mistake but im interested to know how my bounds were incorrect if you know
The question, for reference
vocal sleetBOT
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spare portal
could anyone help me find the domain of a function?
vocal sleetBOT
could anyone help me find the domain of a function?
spare portal
I forgot how to do it because we had a 2 week school break and I just played elden ring
mental falcon
so what would prevent you from putting in any real number x for the input?
mental falcon
any places where this function would be undefined \ problematic?
mental falcon
so the inputs to avoid with a rational function like this, are ones that would make denominator be 0, because that would be division by 0 which is undefined
so to find the x values that create that problem we set the denominator equal to 0 and solve: $x^2 - x = 0$
does that make sense?
twin meteorBOT
Soosh
spare portal
oh okok
so i have to isolate the x
or am i wrong?
fk
ill stop playing elden ring'
mental falcon
... 😐
spare portal
1?
mental falcon
that's the only one?
mental falcon
yes
thats actually correct even though you seem to be half guessing 😂
if you have an equation that equals 0, always remember to factor:
$$x^2-x=0$$
$$x(x-1) = 0$$
twin meteorBOT
Soosh
mental falcon
and then you can set individual factors = 0, as in x = 0, x -1 = 0 and get the solutions: x = 0, and x = 1
mental falcon
anyway so the domain of the function is all numbers except x = 0 and x = 1, you can either write that in words or something like $x \neq 0, 1$
twin meteorBOT
Soosh
mental falcon
because all other numbers keep the equation happy, but 0 and 1 make it explode with division by 0
mental falcon
!done
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
spare portal
.close
spare portal
are the vertical Asymptotes of a function allways the same with its domain?