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#help-28
slender rose
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shadow wasp
how do i do this?
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how do i do this?
shadow wasp
<@&286206848099549185>
stiff summit
how do i do this?
Unwrap the logs by applying exponentiation on both sides
celest tapir
so that's what it is
celest tapir
hmm?
glossy valveBOT
dyxn
glossy valveBOT
dyxn
celest tapir
stupid iphone
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torn jolt
If I find and prove that the inf of a sequence such as a_n= -1+1/n is -1 and prove it using epsilon notation , do I have to prove such thing with the sup as well , or can I go with the first term , ex. a_n=-1+1/1=0 , a_2 = -1+1/2 =-0.5 , seeing this one can say that sup is 0 without epsilon proof right ?
fast peak
that argument isnt complete yet
why do you think you only need to look at the first term
torn jolt
why do you think you only need to look at the first term
So i have to prove that it doesnt take smaller values right ?
fast peak
wdym
torn jolt
wdym
I mean if , a1 is 0 and a2 is -0,5 , so I have to prove that the sequence is decreasing thus making Sup = 0 ?
fast peak
yes, decreasing is the key word
torn jolt
yes, decreasing is the key word
Can I just go with epsilon notation instead of proving its decreasing , would that do the trick ?
torn jolt
showing decreasing is much easier
I can go with a_n+1-an right ?
fast peak
yes
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ornate crown
A study reports that the 3rd quartile of the test scores for a group of 200 students is 90. If the passing score is at the 1st quartile, how many students failed the test?
A. 50 B. 75 C. 100 D. 150
plush egret
so the score at the 25th percentile is passing
ornate crown
yes
ornate crown
uhum
ornate crown
ye
plush egret
25 percent below
"a passing score is at the 1st quartile" tells us that if we plot out all the scores, and draw a line like this, we will separate the students into passing and failing groups
it means 25% failed
ornate crown
So 50?
plush egret
because by definition 25% of students are below the first quartile, where a passing score is
ornate crown
yeah
plush egret
yea, 50 failed
plush egret
ornate crown
thank youuuuuuuu
Finall questionn
Aqua Running has been promoted as a method for cardiovascular conditioning for the injured athlete as well as for others who desire a low impact aerobic workout. A study reported in the Journal of Sports Medicine investigated the relationship between exercise cadence and heart rate by measuring the heart rates of 20 healthy volunteers at a cadence of 48 cycles per minute (a cycle consisted of two steps).
The data are listed here:
87 109 79 80 96 95 90 92 96 98
91 101 78 112 94 98 94 107 81 96
- Find Q1.
A. 90
B. 91
C. 92
D. 94
oh wait
78, 79, 80, 81, 87, 90, 91, 92, 94, 94, 96, 96, 96, 96, 98, 98, 101, 107, 109, 112
This is the correct order
oh wait i think i can answer thsi one
Yeah no
i forgot
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random roost
can someome solve dis for me
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can someome solve dis for me
fast peak
get a computer
random roost
my teacher wants me to do it by hand
and it aint posisble by hand
but he says it is
wth
im losing my mind
this aint even the worse solve for x thing i gotta do
hold awn i just realized i wrote the question wrong
some einstein mf come and save me pls
i will sell u my soul
not actually but pls
fast peak
unless you want to use the quartic formula by hand (which you do not want to do) there is no way to solve this
for reference, that is the quartic formula
random roost
i cant see
😢
ig thats what my teacher wants me to do
ok ill send smth easier and if someone can help me🙏
random roost
ncm i have nothing eaisier
look at this bullshit
aint none of them doable by hand
lord
the thing is desmos alrdy gave me the intersections
so like
teacher tweaking ngl
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kindred pivot
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kindred pivot
was wondering if someone can explain me why I was incorrect in my response?
So the correct answer does not contain 8,0
robust slate
So the correct answer does not contain 8,0
y=0 -> (4x-32)/y is undefined (division by zero) -> second equation is not satisfied
robust slate
should I do that?
yeah
kindred pivot
alr thank you
robust slate
In general, you should make note of domain restrictions before you start solving
But plugging the solutions back in is always a good sanity check
kindred pivot
In general, you should make note of domain restrictions before you start solving
wdym by that
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robust slate
wdym by that
Ex. In the second equation, we know we can't have y being 0 since the fraction (4x-32)/y will be undefined
So when solving, we know to ignore solutions where y=0
kindred pivot
grea thtnaks
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grea thtnaks
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kindred pivot
.close
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livid condor
If you are done with this channel, please mark your problem as solved by typing ...
how this bot read that correctly is amusing to me
tight mortar
AI
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calm slate
Just someone prove a) i) please thank you
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Just someone prove a) i) please thank you
tight mortar
!nosols
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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
tight mortar
do you know sum of angles identity?
calm slate
Yo this is kinda cool
calm slate
do you know sum of angles identity?
Yes I do
covert heath
Just someone prove a) i) please thank you
calm slate
Bro I tried pages on pages, i played with the sum that goes cos(a+b)=cos s cosb - sin a sin b
I've wasted too many pages for it and I'm stuck on it, It's like a puzzle which I didn't get to solve, my teacher doesn't give a damn but time is limited
covert heath
Bro I tried pages on pages, i played with the sum that goes cos(a+b)=cos s cosb ...
try starting with the RHS maybe
calm slate
We can't touch RHS in the ib
But I guess that's something
But like this is the i part of the a part of a question among the hundreds, like, I just can't afford to spend this much time on it
tight mortar
I guess I should be more specific do u know sum to product formula?
tight mortar
We can't touch RHS in the ib
what rly??
covert heath
We can't touch RHS in the ib
Ah
covert heath
I guess I should be more specific do u know sum to product formula?
thats be very helpful here
calm slate
I guess I should be more specific do u know sum to product formula?
That's what chatgpt said, we don't have it in the data booklet, that's why I was kinda confused, I think I once derived it so it's not too alien, but let's say I've forgot it
calm slate
There were also power formulas and division formulas with these damn trigs but I thought I would be fine with compound angle identities and the normal stuff
calm slate
it's a bit annoying to derive
There is no way I need to do all that foe this
royal holly
you can go all out and start breaking cos3x to cosx
calm slate
Even in the worked solutions it just jumps from one form to another and I simply don't understand
tight mortar
I mean sum to product derivation isn’t like that annoying
u just add sum and diff formulas
calm slate
you can go all out and start breaking cos3x to cosx
I did that with compound angle identities, maybe it gets somewhere but it's too hopeless
royal holly
sum to product is the way yes, but if you havent been taught that/ you arent supposed to use it you can derive it first
calm slate
Let me send the worked solution
It makes it look so easy just like that
THIS IS NOT EVEN TRIG
royal holly
this is product to sum
royal holly
2sinxcos3x = sin(x+3x) + sin(x-3x)
tight mortar
It's mathematical induction
what
calm slate
this is product to sum
Sigh I don't know where
calm slate
what
The chapter is the rest of the question is about mathematical induction
It's been months since I worked with trig
tight mortar
it literally explains on the side btw but
calm slate
2sinxcos3x = sin(x+3x) + sin(x-3x)
Ohhhhhhh
royal holly
there are 8 formulas which are considered pretty elementary but help you a lot in the long run
calm slate
Mate am I supposed to have them in my head just like that when I'm studying mathematical induction, but okay sorry thank you
Thank you guys
This is a pretty nice system to be honest
calm slate
it literally explains on the side btw but
I noticed it now, it's embarrassing, I thought it was just the compound identity
Because they don't out stuff there unless it's in the booklet usually
Either way thank you I'll stop bothering you
tight mortar
in general 2cos(a)cos(b)=cos(a-b)+cos(a+b)
calm slate
Thanks bro
clever turret
What can I buy from 15 € + from Math?
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wide scaffold
A cube is sliced with a plain going through 3 distinct vertices of a cube all on different faces. What is the surface area of one of the pieces assuming the original cube had a volume of 8?
wide scaffold
I know that this means the side length is 2
and that slicing in the manner described would give a tetrahedron
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random viper
Hey im kinda stuck on this "The base of pyramid KABC is a right-angled triangle ABC, where the hypotenuse AB = 13 cm and one leg AC = 12 cm. The edge AK is perpendicular to the base plane and is 16 cm long. Calculate the total surface area of the pyramid."
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crimson sphinx
Hi i got a quesfion abt ref angles
When getting ref angle for sec and third quadrant, can i subtract 180 from theta and take the abs value of the answer?
I mean it’s theoretically right, not sure if it’d cause problems.
crimson sphinx
Hi i got a quesfion abt ref angles
When getting ref angle for sec and third quad...
In the second quadrant its
180-theta
In the third its
Theta-180
I mean it makes sense if i take thr abs value
Sec quad example:
110= abs(180-110) =70
Third quad example:
230: abs(180-230)=50
onyx glen
oh, you used sec to mean second...
yes, sure. you can think of it as |θ - 180| if you want.
a more general way of thinking about it is that the reference angle of θ is the distance between θ and the closest multiple of 180°.
(wherever that may be.)
crimson sphinx
oh, you used `sec` to mean _second_...
Yeah
crimson sphinx
a more general way of thinking about it is that the reference angle of θ is the ...
I dont understand
onyx glen
in the first quadrant (from 0 to 90°), the reference angle for θ is just θ itself, yes?
crimson sphinx
in the first quadrant (from 0 to 90°), the reference angle for θ is just θ itsel...
Yea
onyx glen
and in quadrants 2 and 3, the reference angle is indeed |θ - 180°| as you yourself came to realize
crimson sphinx
and in quadrants 2 and 3, the reference angle is indeed |θ - 180°| as you yourse...
Yeah
onyx glen
in quadrant 4, the reference angle is 360° - θ, but this can also be seen as |θ - 360°|
and the "just θ" rule for quadrant 1 can also be seen as |θ - 0°|
so in all cases the reference angle for θ is the absolute difference between θ and a multiple of 180° (0, 180 or 360 in these cases)
crimson sphinx
Ohhh
onyx glen
and in fact the multiple that's taken is always the closest one to θ
crimson sphinx
and in fact the multiple that's taken is always the _closest one_ to θ
I understand now
thx
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solid junco
Hi, I'm struggling with exponents in alg 2 rn and for questions like these, what would be my first step?
I turned the numerator to x^4 then the denom to x^3 times x^-4
I made the numerator to x^5 then multiplied it by 12 to get x^60
Apparrently i went wrong somewhere and the ansewr key says its x^9
solid junco
glossy valveBOT
Ann
onyx glen
that's where you messed up
when you have a power tower like this you go through it top to bottom
note also $(a^b)^c \neq a^{(b^c)}$ generally!
glossy valveBOT
Ann
onyx glen
but un-bracketed $a^{b^c}$ is always meant as the latter of those two
glossy valveBOT
Ann
onyx glen
so $x^{2^{-2}} = x^{(2^{-2})} = x^{\frac14}$
glossy valveBOT
Ann
onyx glen
does this make sense to you @solid junco
solid junco
yes ty i understand that part but now what do i do from x^4/x^4(x^1/4)
also how do i get the bot to visualize like that
onyx glen
also how do i get the bot to visualize like that
the bot uses a markup language called LaTeX, you can look it up and/or look at the cheat sheet in #latex-help
onyx glen
yes ty i understand that part but now what do i do from x^4/x^4(x^1/4)
x^4/(x^3 * x^(1/4)) you mean?
you typoed
solid junco
yes
onyx glen
you proceed pretty much the same way you would otherwise
simplify the big fraction inside the twelfth power all the way down to x^(something)
and then raise it to the 12th power
the fact that you've got fractional exponents does not really change this logic, only that you will obviously have a bit of fraction arithmetic to deal with
do you understand what to do now
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potent iris
Hi, I was hoping someone could help me with this. I've got some working out but I'm not really sure where to go from here. Thanks!
robust slate
Hi, I was hoping someone could help me with this. I've got some working out but ...
You should observe that $P(X \geq 1), P(X \geq 2), \cdots$ is an infinite geometric sequence
glossy valveBOT
Civil Service Pigeon
potent iris
You should observe that $P(X \geq 1), P(X \geq 2), \cdots$ is an infinite geomet...
Ah okay, I have worked a bit with infinite geometric sequences stuff before but honestly it's definitely not my strong suit. Could you please expand on this a bit more, that would be great. Thank you so much for replying though.
robust slate
Ah okay, I have worked a bit with infinite geometric sequences stuff before but ...
Did you start by finding the first few terms of said sequence?
Finding the few terms of a sequence is always a good way to wrap your ahead around what's going on
@potent iris Hello?
potent iris
Did you start by finding the first few terms of said sequence?
Hi, so sorry about that I'm back now. Honestly it's been a while since I've done that geometric stuff. I need to refresh myself on it a bit. I remember something like the sequence goes a0,ra0,r^2a0,...
Something like that right
robust slate
Hi, so sorry about that I'm back now. Honestly it's been a while since I've done...
Yes
But did you actually calculate the terms for yourself here
Because there's a specific value for $a_0$ in this case
glossy valveBOT
Civil Service Pigeon
potent iris
But did you actually calculate the terms for yourself here
I didn't do that to be honest
I'm not really sure how to exactly do that
robust slate
I'm not really sure how to exactly do that
Use the given ratio
$\frac{P(X \geq k+1)}{P(X \geq k)}=\gamma$
glossy valveBOT
Civil Service Pigeon
robust slate
If we set $k=1$, then $$\frac{P(X \geq 2)}{P(X \geq 1)}=\gamma$$
glossy valveBOT
Civil Service Pigeon
robust slate
If we set $k=2$, then $$\frac{P(X \geq 3)}{P(X \geq 2)}=\gamma$$
glossy valveBOT
Civil Service Pigeon
robust slate
and so on
potent iris
Ah okay, I'll try this and then get back to you
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robust slate
welp imma dip then ig - cya
potent iris
Hey, so sorry about that I just had to do something for someone else. I'm working on it now still
potent iris
<@446920351356813312> Are you there?
I'm trying to do this but I'm not really getting anywhere to be honest
I think it's because the geometric sequence is usually like an+1/an=r so it's like individual terms or something
But this one is like multiple terms
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waxen drum
Hiya, I was wondering how at the bottom they found the solution to be x = pi- pi/3
hot herald
supplementary identity for sine
waxen drum
supplementary identity for sine
what does this mean 😿
hot herald
look it up
waxen drum
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slate shuttle
The total values that f(2025) can take?
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The total values that f(2025) can take?
slate shuttle
Help
amber robin
By comparing the degree, we get that it's linear
Substitute ax + b and you'll get it
celest tapir
why are you assuming that it's a polynomial though 
I mean it probably works but he could lose points on an exam
celest tapir
you could have some sort of combination
onyx glen
By comparing the degree, we get that it's linear
do we even know that f is a polynomial at all?
amber robin
Still
amber robin
do we even know that f is a polynomial at all?
There is the term xy
celest tapir
your argument is on the absence of evidence, not it's existence
amber robin
Okay
glossy valveBOT
dyxn
glossy valveBOT
dyxn
glossy valveBOT
dyxn
slate shuttle
<@973300663524147230> do you know how to solce one of these
İ know
celest tapir
give it a shot then
celest tapir
we're recovering the function f
slate shuttle
I mean it probably works but he could lose points on an exam
Btw its a test we xan solve it with any way❤️
robust fox
i think we need atleat some other info
slate shuttle
we also got f(2025) = 0
🤔🤔🤔how
robust fox
to tell all the sols
amber robin
I got $f(x) = -\frac{ax+1}{a^2}+c\cdot e^{ax}$
glossy valveBOT
Suika
amber robin
Not sure whether it's right though
Where a = f'(0)
And c turns out to be (1/a²) + 1
slate shuttle
🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔🤔
celest tapir
$\dv{x}(ye^{-xf'(0)}) = -xe^{-xf'(0)}$
glossy valveBOT
dyxn
glossy valveBOT
celest tapir
$y = \frac xa + \frac 1{a^2} + Ce^{ax}$
glossy valveBOT
dyxn
amber robin
Ah, it gets cancelled out
celest tapir
for the special case of C = 0 we get the linear polynomial
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uncut badge
how did they get the numerator
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how did they get the numerator
onyx glen
black magic
uncut badge
knew it
onyx glen
but in all seriousness, this is a partial fraction decomposition in all but name
only perhaps they for some reason wanted to avoid mentioning those dirty words.
somber niche
black magic
Fifth tier magic : Divine seperation
uncut badge
but idk how they got the numerator
somber niche
Do you know how to simplify quadratic expressions?
onyx glen
yeah the non-WTF way to do it is to write $\frac{37x+1}{(5x-1)(x+1)} = \frac{A}{5x-1} + \frac{B}{x+1}$, add the fractions on the RHS, then equate coefficients
glossy valveBOT
Ann
uncut badge
Do you know how to simplify quadratic expressions?
well yeah
uncut badge
**Ann**
i got A and B
but
this is for combining power series so idk what to do with the 37x+1 after i get those
uncut badge
onyx glen
it does not disappear...
uncut badge
yeah
onyx glen
you rewrite the entire fraction into a different form.
in which its numerator of 37x+1 is not visible nor should it be.
onyx glen
,w partial fractions (37x+1)/((5x-1)(x+1))
glossy valveBOT
onyx glen
you now have $-\frac{7}{1-5x} + \frac{6}{1+x}$ as your function.
glossy valveBOT
Ann
uncut badge
onyx glen
down to whichever degree you need
oh you dont actually want the power series itself
only its interval of convergence
in which case there is even less computational hassle
frigid smelt
For this question, how do I prove that the limit does not exist?
frigid smelt
I can check either x=0 or y=0, right?
frigid smelt
Why y = x?
real barn
"identify a path along which the limit is different from the limits along x = 0 and y = 0 if the limit does not exist"
try plugging in for x = 0
and y = 0
seperately
you should get that the limit = 0
and when you're checking at y = x, approximate the sinx - x using taylor series expansion of sinx
to get everything in terms of x
when i did it, i got that the limit = 1
which is different than the two limits where x = 0 and y = 0
hence why limit DNE
pure flare
A bag contains 5 white and 5 black balls. A draws 5 balls, retains any that are white and returns any black ones to the bag. B then draws 5 balls, retains any that are white and returns any black ones to the bag. Now there are 6 balls in the bag. Find the probability that A drew exactly 2 white balls.
pure flare
is this just 25/63
onyx glen
is this just 25/63
how did you get that
onyx glen
hm
pure flare
i just calculated probability of picking 2 white balls for A
onyx glen
well, A and B together took out a total of 4 balls between them.
pure flare
yes
onyx glen
i think you might need to make a tree diagram here
which is gonna be slightly annoying but i see no way to streamline these calculations
covert heath
A bag contains 5 white and 5 black balls. A draws 5 balls, retains any that are ...
Ah I hate these
@pure flare do you have the answer
ah jee ka hai i can just google
i dont like the bayes expression
pure flare
<@771079399897956352> do you have the answer
no
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amber robin
Oh
covert heath
def have seen it before tho
amber robin
It might be a dumb question,
If we picked all black in the first try,
The probability would be 5C5/10C5
Is that right?
random roost
can someone help me calculate the area under the curve for this
amber robin
If you're not expected to do it by hand, just use wolframalpha
random roost
i am expected to do it by hand
viral jasper
Yuck
By hand, or can you at least use a calculator?
Do you know about definite integrals?
random roost
well i can make sure that my answer is corrct by using calc yea
random roost
Do you know about definite integrals?
yea
viral jasper
And do you know integrals of polynomials?
gritty rose
,tex .int rules
glossy valveBOT
riemann
gritty rose
$\int_a^b x^n dx = \frac{x^{n+1}}{n+1} \big\rvert^b_a = \frac{b^{n+1}}{n+1} - \frac{a^{n+1}}{n+1}$
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riemann
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sly prairie
I couldn't find an answer to my question on the internet so I'll ask it here : is a bilinear form positive definite if the determinant of its matrix is positive?
umbral dome
I couldn't find an answer to my question on the internet so I'll ask it here : i...
if it is positive definite then the determinant is positive, but if the determinant is positive it may or may not be positive definite
kindred grove
e.g. [[-1 0] [0 -1]]
sly prairie
if it is positive definite then the determinant is positive, but if the determin...
Okay, I see, thank you!
kindred grove
det is 1, but it's negative definite
umbral dome
you can see this by considering that the determinant is the product of eigenvalues and using the eigenvalue criterion for positive-definiteness
sly prairie
you can see this by considering that the determinant is the product of eigenvalu...
So all of the eigenvalues are positive?
umbral dome
yes, it's positive definite if and only if all of the eigenvalues are positive
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magic obsidian
my calculus 3 textbook doesnt mention torsion/encapsulation, is this normal? it does mention curvature as |r''(s)|, |T'(s)|, |T'(t)|/|r'(t)|, and |r' x r''|/|r'|^3
plush egret
looks like thats a geometry thing?
i wouldnt expect it to be in a calc 3 book personally
maybe analysis
magic obsidian
i wouldnt expect it to be in a calc 3 book personally
alright cool
wait dyk if my textbook is like "standard"
i just found it online
gimme a sec
plush egret
calc 1 - 2 - 3 usually have a standard set of topics
magic obsidian
just wanna make sure im not using a textbook that will give me incomplete knowledge of calc 3
magic obsidian
this looks like a list of topics through calc 1 - 2 - 3
i skipped calc 1-2
plush egret
plush egret
normal calc 3 class would probably be around here
youd anticipate covering some linear algebra topics if students havent already taken it
magic obsidian
i saw a lot of overlap in chapter 12 with linalg
plush egret
and then theres a large portion of the class dedicated to curl, gradient, divergence at the end
magic obsidian
yeep alr
plush egret
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torn jolt
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atomic hare
a quadrilateral inscribed in a circle has a special property. what is it?
atomic hare
I dont know we never talked about inscribed quadrilaterals
use the inscribed angle theorem
torn jolt
My honors geo teacher just gave us this over break and I’m so close to giving up on this and a lot more and I don’t know
torn jolt
use the inscribed angle theorem
what the hell is that 😭
Is that where the angle is half of the arc it intercepts
or smth
girl get your goofy ass ad out of here
and they have an of 😭
torn jolt
I was gonna guess that she makes us show work though
It’s very obviously not 21 or not really 87 i don’t think
torn jolt
we didn’t learn that 😭
candid herald
oh
torn jolt
yeah I’m in hs
I love math usually but i don’t love anything at this point in my life
Parent figure is just yelling at me to do this 😭
atomic hare
ABC is half of AOC from inscribed angle theorem
likewise ADC is half of COA
since AOC + COA is 360 then ABC + ADC is 180
torn jolt
So abc is 97
atomic hare
atomic hare
it looks weird since the angle is nearly 180 but it's still just the inscribed angle theorem
atomic hare
<@&268886789983436800> guys free gift
lucid flower
you can type .close
atomic hare
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torn jolt
.close
rapid bolt
Opposite angles in cycles quadraterial add up to 180 so
180-83
=97
rapid bolt
@torn jolt
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umbral dome
that channel was already closed, so any message once the channel reopened is considered opening the channel for your own question
if you don't have a question i would recommend you close the channel
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zenith ivy
Hi👋 Im struggling to understand this subject. I got this answer for the first part of the question. Does it look right? I would also appreciate some tips on how to approach the convergence question. Thanks😊
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zenith ivy
<@&286206848099549185>
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amber robin
Hi👋 Im struggling to understand this subject. I got this answer for the first p...
Which part were u stuck on?
Did u get it?
zenith ivy
Im stuck on the convergence part. After some research I think it would converge to e, but im struggling to understand why?
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gritty rose
Im stuck on the convergence part. After some research I think it would converge ...
What is "it"
zenith ivy
The fourier series
gritty rose
Hi👋 Im struggling to understand this subject. I got this answer for the first p...
Just plug in t=1 to the series then
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stuck loom
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onyx glen
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onyx glen
@stuck loom interesting that you took the time to click ❌ on the bot prompt but have decided not to share any of your progress, nor to say that you have no clue where to start (if that is indeed the case).
spiral vigil
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crude kayak
a general advice: in tests/exams, when you've nobody aside to answer your question, you may check your work by substituting the result into the conditions to see whether your result is correct
here your result is supposed to hold for ALL values of x, so it should hold for a particular value of x
you can choose any particular value of x, substitute back and identify the line from which things start to go wrong
to identify such line, you may use the bisection method to increase the search efficiency
sturdy valve
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celest tapir
,w factorize z^6 + z^4 + z^3 + z^2 + 1 = 0
glossy valveBOT
slate violet
oh lmao
celest tapir
thought so
slate violet
yeah that makes sense, so that means that either z + 1 or z^2 - z + 1 is a factor due to the condition
sturdy valve
okay so how do i solve it further?
celest tapir
(z^2 - z + 1)'s roots are the cube roots of -1
slate violet
if z^4 + z^3 + z^2 + z + 1 = 0, make the connection to roots of unity
celest tapir
so that's off the table
sturdy valve
(z^2 - z + 1)'s roots are the cube roots of -1
so z=-w,-w^2?
slate violet
if z^4 + z^3 + z^2 + z + 1 = 0, make the connection to roots of unity
it's a geometric sum if you're really stuck
celest tapir
(z_r)^5 will be 1
celest tapir
so z=-w,-w^2?
it's explicitly stated that that's not the case
sturdy valve
right
glossy valveBOT
dyxn
celest tapir
you are supposed to use their properties here
you can arbitrarily assign z_i to
any power z^k
slate violet
yeah so I'll leave it to you to verify that given $\omega^5 = 1$
if you have $\omega^{99}, (\omega^2)^{99}, (\omega^3)^{99}, (\omega^4)^{99}$, you will get $\omega, \omega^2, \omega^3, \omega^4$ in a different order
glossy valveBOT
south
slate violet
start with w^99 for example, is that w^1, w^2, w^3, or w^4?
slate violet
ohk thank you guys
np!!
sturdy valve
start with w^99 for example, is that w^1, w^2, w^3, or w^4?
w^4?
wait
so i actually have to find the roots?
slate violet
so i actually have to find the roots?
nope
celest tapir
it will reduce to the same polynomial
slate violet
the idea is that you can choose any root and the rest will be w^2, w^3, w^4
sturdy valve
it will reduce to the same polynomial
i dont think so
celest tapir
or probably something workable
the only thing you need to know is that they all have unit moduli
sturdy valve
or probably something workable
no 😭 the theta values are weird eg 72 and 36 degrees
celest tapir
trust the process
sturdy valve
im getting 2 sin 72
as my final answer
what an ugly question
cant they atleast give options
<@&286206848099549185>
ill open a new one
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slate shuttle
A polynomial P(x) whose coefficients are elements of the set A={0,1,2,3}
If it is
P(1)=?
knotty grail
A polynomial P(x) whose coefficients are elements of the set A={0,1,2,3}
If it...
write 2025 in base 4
onyx glen
do that, then P(1) will be the sum of the digits
slate shuttle
write 2025 in base 4
Wdym by base
knotty grail
Wdym by base
basically
do you know how to write numbers like 30 in binary?
you can write it as 16 + 8 + 4 + 2
similarly
check all the powers of four
and start with the largest power that is smaller than 2025
its largest multiple can also be smaller than 2025
for example
take 4^5 = 1024
onyx glen
hold on
slate shuttle
And 4^6?
slate shuttle
Ah okey
knotty grail
so it must have 0 as a coefficient
slate shuttle
Ok 4^4 768
knotty grail
now the largest multiple of 1024 fitting in 2025 is 1024 * 1
onyx glen
this is what "base" means in @knotty grail's usage
knotty grail
this is what "base" means in <@702550180154834984>'s usage
i meant it like the normal base system though
is there a context
idk
onyx glen
the word "base" on its own can mean many things
onyx glen
yes sure
onyx glen
,w 2025 in base 4
glossy valveBOT
slate shuttle
Okay soo then p(1)=1+3+3+2+2+1
İs this true?
12
🤯
Cuz P(x)=1.x^5+3.x^4+3.x^3+2.x^2+2.x^1+1
Thx
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small trout
unsure how to do this using a series
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unsure how to do this using a series
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spark adder
Hello guys can anyone help me with a few tasks in call right now or in about one hour please. Its mostly quadratic formula and other i will send pictures.
torn jolt
Hello guys can anyone help me with a few tasks in call right now or in about one...
I can help you
Pls text in dm
spark adder
Pls text in dm
Check dm pls
tired lion
Hey, could someone please walk me through this proof? It's proving that if A is a box, f, g : A -> R are Riemann integrable, then h = f^2: A → R (that is, h(x) := f(x)^2) is Riemann integrable
tired lion
So many things seem so arbitrary. Why are they letting M be a bound? Why are they calculating |f^2(x) - f^2(y)|?
It all just seems so arbitrary to me
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<@&286206848099549185>
tired lion
Hey, could someone please walk me through this proof? It's proving that if A is ...
oh wait, accidentally copied too much, ignore the (iii) part at the bottom
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jovial willow
How do I find the range of a function
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How do I find the range of a function
jovial willow
Like why is the range for these 2 functions different
honest hill
the range is the y values
jovial willow
jovial willow
the range is the y values
Ye
honest hill
,rccw
glossy valveBOT
weak bolt
I think find maximal and minimal
honest hill
the difference here is that y-2 and x^2-4 needs to be nonnegative
jovial willow
That give us real numbers as a outcome
weak bolt
Owh
weak bolt
Root must be positive
Denominator mustn't equal 0
honest hill
what exactly is the function?
jovial willow
These 2
honest hill
$\frac{\sqrt{x^2-4}}{\sqrt{x-2}}$ or $\frac{\sqrt{x^2-y}}{\sqrt{y-2}}$?
weak bolt
$\frac{\sqrt{x^2-4}}{x-2}$ or $\frac{\sqrt{x^2-y}{y-2}$
glossy valveBOT
Bonk
honest hill
$\frac{\sqrt{x^2-4}}{x-2}$ or $\frac{\sqrt{x^2-y}{y-2}$
do you have anything to add other than repeat my messages?
weak bolt
do you have anything to add other than repeat my messages?
Tried to fix it
honest hill
Tried to fix it
you just copy and pasted it
weak bolt
you just copy and pasted it
For latex*
weak bolt
Owh
honest hill
,rccw
glossy valveBOT
weak bolt
$\sqrt{x^2 - 4} = \sqrt{x - 2} \cdot \sqrt{x+2}$
honest hill
on the left, you need $\frac{x^2-4}{x-2}\geq 0$
honest hill
on the right you need $x^2-4\geq 0$ and $x-2\geq 0$
glossy valveBOT
Bonk
glossy valveBOT
honest hill
these show the domain
weak bolt
x² - 4 >=0
x - 2 >0
honest hill
do you know that if you have $\sqrt{x}$ that $x\geq 0$?
glossy valveBOT
Bonk
jovial willow
Ik
honest hill
no negative in the root
jovial willow
But the other one had x>= -2
honest hill
its because you can write x^2-4 as (x-2)(x+2)
so if its in one whole root, the x-2's cancel out
jovial willow
Then what are the 2 number lines
honest hill
$\sqrt{\frac{x^2-4}{x-2}}=\sqrt{x+2},x\neq 2$
glossy valveBOT
Bonk
honest hill
but never in the questions youve asked of photos youve posted has it been about the range
jovial willow
I meant the domain
Ik there's a way to caculate the domain by adding the domains of both the numerator and denominator but idk how
jovial willow
<@&268886789983436800>
@hardy leaf was scamming
honest hill
all you need to remember is that $\sqrt{x}$ means $x\geq 0$
glossy valveBOT
Bonk
jovial willow
Okay
honest hill
so $\sqrt{\frac{x^2-4}{x-2}}$ means $\frac{x^2-4}{x-2}\geq 0$
glossy valveBOT
Bonk
honest hill
and $\frac{\sqrt{x^2-4}}{\sqrt{x-2}}$ means $x^2-4\geq 0$ , $x-2\geq 0$ and $\sqrt{x-2}\neq 0$
glossy valveBOT
Bonk
frank smelt
x in IR
you need to find the values in which you can replace in the function
here you have a function with a square root so whats inside of it must be positive
if its squareroot(a) then must be positive, if its square root(ab) then ab must be positive
for ab to be positive: either (a > 0 and b>0) or (a<0 and b<0)
to find that first specifiy your variable : its x in IR
then for each a and b you must find where each of them is positive and negative, to do that you find where a=0 and b =0
now the problem is you gotta study their signs together
to make it easy for you draw a table having all values possible for x and the sign in each interval
the final results will show when ab is positive and when is it negative
the function exists when its positive so you cancel out the other interval where its negative
jovial willow
x in IR
you need to find the values in which you can replace in the function
her...
How come for sqrt(x²-4) ÷ sqrt(x-2) we didn't take the are inbetween 2 and -2
It's possitive when u study their signs together
frank smelt
oh right my bad
frank smelt
How come for sqrt(x²-4) ÷ sqrt(x-2) we didn't take the are inbetween 2 and -2
what do you mean ?
jovial willow
Yea see
frank smelt
How come for sqrt(x²-4) ÷ sqrt(x-2) we didn't take the are inbetween 2 and -2
because here you don't need to do that
jovial willow
frank smelt
the function exists if each is positive so no need to study their signs together
its like you're doing a different table for each of them
jovial willow
So u take both domains separately and then add the ones that are the same?
If it's split apart?
frank smelt
no problem
jovial willow
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lime ether
<@&268886789983436800>
round turret
I don't understand how the polar equation r=asec(theta) is a vertical line.
round turret
Suppose a = 1. That would yield r=sec(theta)
If I test values, 0, pi/6, pi/4, I would get --> (0, 1), (pi/6, sqrt(3)/2), (pi/4, sqt(2)/2)
zealous geode
I don't understand how the polar equation r=asec(theta) is a vertical line.
do you understand the algebraic manipulation to convert it to cartesian?
round turret
But ... it was graphed within the polar coordinate system.
zealous geode
x = a
zealous geode
oh, im a yellow helpful now, looks classy
what a nerd
glacial pasture
ill take that as a compliment
round turret
r=asec(theta), rcos(theta)=a
I don't understand why rcos(theta)=a was brought
glacial pasture
what is sec
zealous geode
well sec(theta) is equivalent to 1/cos(theta)
zealous geode
if we multiply both sides by cos(theta), we get rcos(theta) = a
round turret
i apologize
zealous geode
we can say x = rcos(theta) as long as you understand how polar coordinates compare to cartesian coordinates
so x = a
round turret
ohh i see
so rcos(theta)=a is just a vertical line
so like no matter the angle or radius measure it will be that constant "a"
zealous geode
and so similarly, r = acosec(theta) would be just a horizontal line, y = a
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round turret
I can't seem to wrap my head around why r=acos(theta) is a circle in the polar coordinate system.
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I can't seem to wrap my head around why r=acos(theta) is a circle in the polar c...
@round turret Has your question been resolved?
round turret
<@&286206848099549185>
gritty rose
I can't seem to wrap my head around why r=acos(theta) is a circle in the polar c...
Convert the equation to Cartesian coordinates
round turret
Convert the equation to Cartesian coordinates
Would I simply manipulate the equation?
soft dew
Would I simply manipulate the equation?
Yeah
So typical Cartesian conversion
You can multiply the entire thing by are
R
round turret
Would it just be sqrt (x^2+y^2)
round turret
Hold on
soft dew
Okay
celest tapir
although if you want to get comfortable in polar coordinates, you should try graphing the function in polar coordinates
round turret
i got x^2 + y^2 = x
celest tapir
ax
round turret
oh yeah, plotting it, it is correct
round turret
although if you want to get comfortable in polar coordinates, you should try gra...
thing is
when i try random coordinates, i just dont get a circle
round turret
let me see
soft dew
when i try random coordinates, i just dont get a circle
Wait you are trying to graph in polar form