👀
#help-0
remote heron
rugged bough
how do i do that😭
lone heartBOT
lone heartBOT
Available help channel!
bold token
am I tripping? I checked all integrals, it is all correct except the literal last line where I do y=Yp+Yc. Im confused to why the calculator(symbolab) did not include 2/3e^x
lone heartBOT
am I tripping? I checked all integrals, it is all correct except the literal las...
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bold token
.reopen
lone heartBOT
✅
bold token
am I tripping? I checked all integrals, it is all correct except the literal las...
<@&286206848099549185>
lone heartBOT
@bold token Has your question been resolved?
bold token
am I tripping? I checked all integrals, it is all correct except the literal las...
<@&286206848099549185>
sharp raven
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paper terrace
lone heartBOT
paper terrace
really don't understand how this is getting marked as wrong
also the software my uni uses is really terrible so it could just be that
nvm i figured it out
never ever use gradarius in your life
.close
dim terrace
lone heartBOT
dim terrace
how do i do this
jagged cobalt
,rccw
ocean sealBOT
dim terrace
yeah
wet linden
dim terrace
dim terrace
3?
lone heartBOT
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nocturne iris
hello again
lone heartBOT
hello again
lone heartBOT
@nocturne iris Has your question been resolved?
nocturne iris
<@&286206848099549185>
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@nocturne iris Has your question been resolved?
nimble marlin
A cube is being heated and the volume is expanding at the rate of 6 cm^3 per hour. At what rate per house is an edge of the cube increasing when the volume is 1000 cm^3.
nimble marlin
calculus ab - related rates
jagged imp
What have you done so far?
jagged imp
And what is the derivative that you're interesting in for the question?
nimble marlin
dx/dt
jagged imp
yup, so can you express dx/dt in terms of dx/dV and dV/dt?
nimble marlin
im pretty sure its
dx/dt = dx/dV * dV/dt
nimble marlin
plug in values
jagged imp
go ahead and do that then
nimble marlin
so its 3x^2 * 6 = 18x^2
jagged imp
Oh wait, so lets correct a small error here I didnt pick up on]
are you sure that dx/dV is 3x^2?
cause V=x^3, right? so that would instead give dV/dx=x^3
nimble marlin
OHHH
jagged imp
Can you get dx/dV from that? If so, it should be smooth sailing from there
jagged imp
Reciprocal is probably a better word, but yeah, 1/(3x^2)!
nimble marlin
okok thats why i was wrong
wait how do u know how like
which way it is
like if its dV/dx or dx/dV
jagged imp
Well the equation you started with was V=x^3
jagged imp
yeah
nimble marlin
okok thanks sm
jagged imp
no worries
nimble marlin
also i got one more question
its ab like smth i was reading on pauls online math notes
why do we need to find this if we dont use it
jagged imp
You don't. he found it to demonstrate that finding it won't help
His point is like "oh finding V' this way doesn't do too much for us, since it has these quantities we can't really find very easily, so I suggest doing this other thing instead"
nimble marlin
oh
is there anyway to know that u dont need to find it before u attempt it or do you just find it first
jagged imp
You should always just try to have your rates in terms of just one variable at once
so differentiating V=4/3pi*r^2h (if im remembering the correct formula) as is introduces a bunch of variables since the RHS is in terms of both r and h, but if you first find r in terms of h, you can write the formula in terms of one variable (h) and write the formula for V in terms of only h
jagged imp
no worries!
nimble marlin
i got one more question before i gotta go to practice could u help me out w it
jagged imp
sure
nimble marlin
The area of a rectangle is increasing at the rate of 20 ft^2 per minute. At a particular instant, one side is 8 ft and increasing at the rate of 4 ft. per minute. The other side is 9 ft. How fast is the second side changing at that instant?
all i got is that dA/dt = 20
jagged imp
Uh so I would say like, let l be the first side and w the second. Then trying to express what you want (dw/dt) in terms of what you have, you can at least start with dw/dt=dA/dt*dl/dA. Then, it comes down to finding dl/dA. It might be easier to first find dA/dl, so lets see that A=lw, and use product rule to get dA/dl = w+ldw/dt, so that dl/dA=1/(w+ldw/dt)
and I think from there its just plugging numbers in?
this is like hard to see though, the reason I thought to differentiate even though theres still multiple variables, which contradicts what pauls notes just said, is that we are given useful information about both sides basically
wait nevermind this is wrong
yeah i have no clue haha sorry
disregard what I just said, maybe someone else can help zz
lone heartBOT
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lone heartBOT
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inland fable
Hi i need help on a question that relates to series and parallel circuits
jagged cobalt
feel free to ask, but the physics server in #old-network may be more helpful
inland fable
it's a question about like
what happens when a 1 of many resistors is shorted out in a circuit
does the current change or voltage or resistance
would you know?
jagged cobalt
depends on the configuration
but the one that shorts out essentially just becomes like a piece of wire with essentially no resistance
inland fable
can i draw it out for you?
jagged cobalt
sure
inland fable
my question is what happens when r3 shorts out?
would the current change and will the voltage go up and resistance?
jagged cobalt
the total resistance drops by 12.5Ohms (roughly anyway)
that will certainly change the current - increasing
as for V, the total voltage shouldnt change, but each remaining resistor will have more voltage across them
inland fable
the total resistance drops by 12.5Ohms (roughly anyway)
that will certainly chan...
how would you calculate the new Current for R4?
how would you calculate the new Voltage across the resistors?
jagged cobalt
they all have the same resistance, so V divides equally
originally V=V1+V2+V3+V4=100
now its V=V1+V2+V4=100 and its divided equally, so about 33.3V each
as for the new current
just use I=V/R
V=100, R=whatever it was before - 12.5
R=50-12.5
jagged cobalt
sure
inland fable
for series circuits could you tell me what would happen if you double a voltage would it effect current and resistance?
jagged cobalt
what does V=IR tell you
inland fable
Volts is equal to Current times Resistance
jagged cobalt
yeah, but in this scenario, what does it tell you
may help to establish - does voltage affect resistance (we'll ignore stuff that happens in the real world like heating)
jagged cobalt
yup
inland fable
oh ok
jagged cobalt
so If I=V/R what happens if you double V
inland fable
The current will change
jagged cobalt
how much
inland fable
so it will go up
inland fable
so If I=V/R what happens if you double V
can you ask me a few more for practice
please and thank you :))
jagged cobalt
google ohms law questions, youll probably find a library of them
inland fable
okay i'll try thank you for your time
lone heartBOT
@inland fable Has your question been resolved?
alpine valve
did I do something wrong?
lone heartBOT
did I do something wrong?
alpine valve
is my a value right
sour dove
not quite.
Remember to multiply by the reciprocal. So you'd have (21/2)(2/7), which simplifies
also, 2 * 21 = 42, not 41
sour dove
wait 21x2 isn't 41
yep!
alpine valve
a = 3
alpine valve
B?
also, for ln expressions, when can I get rid of the absolute value and use parenthesis instead
is it only when the inside of the natural log is guaranteed positive no matter what value x is like ln|x^2|?
sour dove
is it only when the inside of the natural log is guaranteed positive no matter w...
yeah exactly
alpine valve
if it is asking for values of p where graph is inc dec is that concavity or slope
because if slope then P is always increasing right?
.close
stoic mirage
stoic mirage
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timber jasper
lone heartBOT
Available help channel!
long solstice
,, n \equiv r_1 \pmod {a_1} \\
n \equiv r_2 \pmod {a_2}
lone heartBOT
,, n \equiv r_1 \pmod {a_1} \\\\
n \equiv r_2 \pmod {a_2}
ocean sealBOT
hiii
long solstice
assuming i have a system like this
is there a way to know whether this system will "converge" or not?
like is it guaranteed to have a "first hit" and then every consecutive "hit" would be either lcm(a_1,a_2) or prod(a_1,a_2)
is there a way to know if there isn't going to be a "first hit"?
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long solstice
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fallow solar
$\lim_{x→\infty}$ $e^{-2x}$
lone heartBOT
$\lim_{x→\infty}$ $e^{-2x}$
ocean sealBOT
Hamdy Hisham
fallow solar
If I say that the power of e here approaches -$\infty$ then the limit would be -$\infty$ but if moved $e^{2x}$ to the denominator it will be $\frac{1}{\infty}$ which is zero
vale wigeon
\e doesn't exist, by the way. it is just e.
fallow solar
From the graph
vale wigeon
can you show us what you think the graph of y = e^(-2x) looks like?
ocean sealBOT
Hamdy Hisham
vale wigeon
can you show us what you think the graph of y = e^(-2x) looks like?
fallow solar
vale wigeon
yeah... and what does this go to as x goes off to the right?
fallow solar
Oh ok it goes to positive infinity but the same problem here if i move it to the denominator the limit would be zero
vale wigeon
no, it does not go to positive infinity
x = +infty is off to the right.
-2x itself does approach -infty, you're right about that. however that does NOT mean e^(-2x) also approaches -infty.
it should be clear as day from the graph
that the limit is 0
bold torrent
how do i solve 2x-2=x-1
lone heartBOT
how do i solve 2x-2=x-1
twin vale
how do i solve 2x-2=x-1
move the like terms to the same side
so subtract x add 2
u get 2x - x = -1 + 2
x = 1
bold torrent
alr thx
vale wigeon
u get 2x - x = -1 + 2
!nosols
lone heartBOT
u get 2x - x = -1 + 2
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.
vale wigeon
doing the entire problem for op is not allowed
twin vale
my fault ig?
bold torrent
ok so now that i have the soulutuon as 1
how do i graph the eqution
cuz y only goes up to 10
and x goes to 5
twin vale
don't know how to help u without telling you the answer gang
just search up how to graph
bold torrent
bruuh :((((
twin vale
functions
quasi oasis
Okay, so this is the question: Let X be the random variable representing the number of times you flip a coin until you receive two tails in a row. Determine the probability distribution by finding the probability of each possible outcome.
quasi oasis
So far I've manually calculated the percentages for p(x), with p(2) = 1/4 p(3) = 1/8 p(4) = 2/16 p(5) = 3/32 and so on where it follows a pattern of the fibonacci sequence over 2^n (for whatever reason I don't know.) My first attempt was p(x) = .25*(.5)^(x-2)
prime badge
okay
quasi oasis
I know that the success probability for the first two tails in a row will be .25, so at least p(x) will have that constant at the beginning. I'm not sure how to calculate the probability of previous failures, since for example flipping a coin 5 times and getting TTHHT would not be counted as a success for p(5) since the game would have ended at 2
quasi oasis
I'm also stuck on writing a formula of p(x) where p(2) and p(3) are both .125? It just doesn't make any sense to me how x can increment and p(x) doesn't change.
prime badge
that's normal?
oh i get it, makes it hard to think of the formula you mean
it is fibonacci, so it would have to be like that one
quasi oasis
so if I always end on HTT, for any length of coin flips n. Would it be something like p(n)=(n-3)(.5)(.25) since the previous flips wouldnt really matter bc the game would have ended?
prime badge
no i'm saying it can't look simpler than fibonacci
oh if you make it recursive then sure
quasi oasis
I've thought about doing that, but I don't now how to get the expected value from Sum(n*p(n)) if it is written recursively
prime badge
yeah i'm confused
quasi oasis
Yeah I've done every other part of this problem for my paper except finding the formula for p(n) lol
no clue
do i ping like another helper?
im new to this sub and also desperate lol
Ah, I see my mistakke
I didnt read the whole help rules
I'll go to the proper channel
.close
real topaz
lone heartBOT
real topaz
help
real topaz
?
real topaz
its a secret glitch
Am I stupid or what?
exotic canopy
consider the fact that 1/2023 is 2023^{-1}
real topaz
and?
exotic canopy
well, calculate the value of f(1/2023) and f(2023)
i believe you'll see some cancellation
subtle birch
well, simply calculate f(1/x) and add it to f(x) to see the magic
real topaz
yes, it was in a test, I've done it. does the answer is -2022 or -2022,5?
subtle birch
well, f(2023) to f(2) all would have a reciprocal pair. Only f(1) would be not in a pair so we would add f(1) to -2022 to get -2022.5
upbeat light
Hello everyone, I have a small question about the Fourier transform. I have the representation of a signal in the frequency domain obtained through the Fourier transform, and I want to know, based on this spectrum, why the original signal is periodic.
lone heartBOT
Hello everyone, I have a small question about the Fourier transform. I have the ...
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upbeat light
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upbeat light
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lone heartBOT
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Available help channel!
merry meteor
lone heartBOT
merry meteor
could sm1 help me understand
why for #38
like i dont get what they are doing
how is u*A tranpose a 0 vector
??
lone heartBOT
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@merry meteor Has your question been resolved?
worn fox
Just calculate $A^T\vec{u}$
ocean sealBOT
ΣΑCu
worn fox
Or easier R^Tu
lone heartBOT
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gentle dove
Hi, how do I do this question?
lone heartBOT
Hi, how do I do this question?
mystic quarry
Excuse me kind fellows
I would like to inform you all
I’m Asian
I’ll teach anybody how to do multiplication
limpid spade
Hi, how do I do this question?
Ratio?
gentle dove
Ratio?
i was thinking of doing ratio on smthn else then using that with comparison but im stuck
lone heartBOT
@gentle dove Has your question been resolved?
edgy flare
Explain how you got what you got for your ratio test
I’m not getting that.
@gentle dove
I’m getting something different than what you got.
vital marten
The answer of 10.1 is somehow 0.25? How is this possible?
lone heartBOT
The answer of 10.1 is somehow 0.25? How is this possible?
vital marten
$(\frac{1}{4})^2$
prime badge
yes that times 4
ocean sealBOT
SHREK_IS_SENPAI
prime badge
same thing
(1/4)² is anna studied on tuesday and ben on wednesday
yes
that times 2
vital marten
Oooh and multiply by 2 bc it could be either or
okok i get it now
Thank you
.close
lone heartBOT
prime badge
well it's not clear that backwards counts
lone heartBOT
Available help channel!
sonic sinew
${\log_{10}\left(\ln\left(3-12,x\right)\right)}$
lone heartBOT
${\log_{10}\left(\ln\left(3-12\,x\right)\right)}$
ocean sealBOT
Bobba
sonic sinew
How do you get the domain of this function?
I would think that (3- 12x) should be positive since the ln of something doesn't exist of a negative number
alpine sable
When is log_a(b) defined in general?
sonic sinew
when x is positive too, right?
alpine sable
b>0, a in (0,1)U(1,∞)
The second condition is already satisfied
Use the first one
sonic sinew
What do you mean with a in (0,1)U(1,inf)?
daring rover
I would think that (3- 12x) should be positive since the ln of something doesn't...
That's the first thing you should do yes, tackle this layer by layer
sonic sinew
Where it should satisfy 0<a<1 or 1<a<∞
But don't those two conditions just describe 0 < a < inf
zealous lichen
basically a can't be negative and can't be 1
alpine sable
0<a<∞ and a≠1
sonic sinew
ohh okay
daring rover
If you know logs are defined only for positive input values you're good to go
sonic sinew
yes but if I work out that (3 - 12x) >= 0, then I get that x <= 3/12
but apparently that's not the answer
sonic sinew
But if the ln of something exists, doesn't that mean that it is always positive?
so why would you then need another condition
daring rover
Whats log2(1/2)
daring rover
Yep
sonic sinew
okay I see
alpine sable
Range of log is from -∞ to ∞ (bounds not inclusive)
sonic sinew
so then ln(3 - 12x) >= 0
sonic sinew
and that's only when x >= 1 right?
daring rover
Strictly larger
sonic sinew
oh
daring rover
The logarithm is not defined at 0
sonic sinew
oh yeah true
sonic sinew
and that's only when x >= 1 right?
but this is the second condition then?
daring rover
Not quite
zealous lichen
and that's only when x >= 1 right?
I think you mean 3-12x > 1
alpine sable
Don't forget to take the intersection of the solution sets in the end 👍
green knoll
workers salary is given by the following function, and represented by X (in thousands of dollars)
what is the highest salary of 75% of the workers with the lowest salaries?
i have gotten to an answer but i need help checking it. could anyone be so kind as to help 🫶🏼
lone heartBOT
workers salary is given by the following function, and represented by X (in thou...
@green knoll Has your question been resolved?
lone heartBOT
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green knoll
<@&286206848099549185>
vital marten
<@&286206848099549185>
alpine sable
What's se?
vital marten
It means "if" or "when" in this context
latent jolt
It made me weird when I read se followed by x
vital marten
<@&286206848099549185>
I really hope someone can help this poor fella they've been waiting for 2 hours
lone heartBOT
@green knoll Has your question been resolved?
alpine sable
Ok, let me try to check the question for you
alpine sable
What is the highest salary of 75% of the workers with the lowest salaries?
Can you explain further? Sorry just got the time to go through the question. At work rn.
slim pelican
It means "if" or "when" in this context
Is it a part of the question?
lone heartBOT
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mystic nebula
lone heartBOT
mystic nebula
ik its not A and C cause its not being stretched but whats the difference between B and D
prime sluice
one's negative and one isnt afaik
mystic nebula
one's negative and one isnt afaik
how do i tell
i got thats it negative
but like what makes it negative
prime sluice
substitue with x = 1 and see where y ends up
mystic nebula
why x = 1
prime sluice
just any positive number
mystic nebula
well its not intersecting with y
prime sluice
it is on B
mystic nebula
it is on D too tho
prime sluice
the value of y
mystic nebula
ok well
the only visual difference between b and d is the way the lines are heading
so i dont get it
they dont touch the x or y axis
prime sluice
if you are looking at a more elaborate explanation then i dunno
but on a surface level when you substitute with any positive number for x, you end up with a positive y value and when you sub with a negative number for x, you end up with a negative y value
which is the case for figure B
when x is positive (right side of the graph), y is positive (top part of the graph)
the opposite when x is negative
safe halo
fuck, I failed on my exam
safe halo
For compact two-dimensional surfaces without boundaries, if each loop can be continuously compressed to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré Conjecture, proven by Grigori Perelmán, states that the same is true for three-dimensional spaces.
Someone to solve it
lone heartBOT
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slow stratus
lone heartBOT
slow stratus
I don't understand what happens here
lone heartBOT
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slow stratus
What's the derivative of f?
-5x/(1+5x^2)^2
golden canyon
-10x in the numerator, but yeah
so that's a constant multiple of g
f'(x) * -1/10 = g(x)
Now find the power series for f and take its derivative
slow stratus
I'm guessing the power series for f is SUM((5x)^(k))?
Then how do you differientiate it?
I get 5k(5k)^(k-1)
I don't see how that gets you to the answer
golden canyon
Its (-5x^2)^k
lone heartBOT
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worthy saddle
I need to get a invertible matrix P that PxD is equal to the hermite form of D
i know how to do it but i cant understand why
I would use an amplied matrix (D|I) and then transform D into Hf(D) and the thing that is on I place is P
But I dont understand why
mortal trellis
you transform it by doing row operations
row operations correspond to multiplying by elementary matrices from the left
so you are multiplying by $E_1$, then $E_2$, then $E_3$ and so on until $E_k$. so $E_k\cdots E_2 E_1 D = Hf(D)$. which means that $P=E_k\cdots E_2 E_1$. and the easiest way to calculate what that product is, is to notice that it is the same as $E_k\cdots E_2 E_1 I$, but this is again the same as applying the row operations starting with the identity matrix
ocean sealBOT
Denascite
lime abyss
can someone explain wheres 51 and 10 came from?
mortal trellis
can someone explain wheres 51 and 10 came from?
!occupied
lone heartBOT
can someone explain wheres 51 and 10 came from?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
lime abyss
can anyone explaon wheres 51 and 10 came from?
can someone explain wheres 51 and 10 came from?
can anyone explaon wheres 51 and 10 came from?
lone heartBOT
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upbeat sentinel
Can someone explain optimization to me?
lone heartBOT
Can someone explain optimization to me?
red lagoon
there u go
lone heartBOT
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lone heartBOT
alpine sable
lone heartBOT
alpine sable
what is CFD, i need help
sharp thorn
Angles on a line add upto 180
timid jay
38 degrees
Make a triangle joining C and F
You already know the angle CGF which is 104 degrees
And you also know that the angles in the triangle add up to 180 degree
So with this much info
And you also know that the triangle that's been made is an isosceles triangle
Cuz the CG and GF are radius
Now you can form an equation
2x + 104 = 180
And solve for X
Which gives you your answer
😉
timid jay
What's the actual answer?
This question is asking you to work out the angle right? What does the "m" mean in front of "CFD"m
?*
timid jay
Which country are you from?
alpine sable
usa
timid jay
Well I am from UK and here the notations are different
I assumed they are asking the angle
Na mate 38 degrees is the right answer
You cannot get anything else
Apart from 38 degrees
alpine sable
timid jay
Bro the "m" means something else
alpine sable
timid jay
In this context
alpine sable
still 0.8 percent
timid jay
I have no idea what the "m" means
I can only help if I know what "m" means
How did you work out mFE?
Second part?
Tell me that and I might be able to figure something out
alpine sable
180 - 104
alpine sable
360 - 104
timid jay
Also brother how do you not know for certain the meaning of "m" you are studying there ☠️😂
alpine sable
?
timid jay
360*
alpine sable
360 degrees
timid jay
Bro
I have no idea
This question is weird
I think this question is wrong ngl
Wait let me Google the meaning of "m"
If it's the measure of angle
Then the question is wrong 100%
I don't know what maths are you being taught there buddy
But I believe this is wrong
Ask some other people for help buddy, am sorry
Got no idea
I think this is wrong 100%
alpine sable
its alg
timid jay
Or I just don't understand what the question is asking me to do
<@&286206848099549185>
I'd like to get someone else's opinion on this cuz this is interesting and something I have never seen before in maths
This is not even the standard notation
timid jay
360 - 104
Tell me why would you do "360-104" here?
Cuz DFE is an isosceles triangle
for the question unanswered you are supposed to find the value of x right?
@alpine sable
if so then the answer must be 38 degrees
if this question is asking for something else
then I got no clue
lone heartBOT
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lone heartBOT
Available help channel!
burnt pivot
would conjigate of a complex always be the sign of complex number flipped?
proven leaf
that's just the definiton of a conjugate
if we have a complex number: a+bi then its conjugate is a-bi
and the reason we multiply by a complex number's conjugate if we have something in the denom
is because $(a+bi)(a-bi)=a^2+b^2$
ocean sealBOT
PajamaMamaLlama
proven leaf
so we get no more complex business in the denom :)
burnt pivot
how not -2???
lone heartBOT
how not -2???
burnt pivot
if i^2 = -1, and this pattern repeats when i^(x*2) than why wouldn't it be -2?
i^(x*2) should always be the same number! -1 so why not correct???
or iss my logic off?
well i know it is, but why?
proven leaf
what is i^8?
oak chasm
Well, i^8 = ((i^2)^2)^2
oak chasm
It goes in a pattern like i, -1, -i, 1, then it repeats.
burnt pivot
I see it now, what's it for odd? i^(x*3)?
burnt pivot
🤔 i see. thank you. this pattern was not there before in my mind, now it is
oak chasm
No problem.
burnt pivot
would that mean that pattern repeats ? like this
int arr[4] = {i,-1,-i,1};
and index = modulo of 4
oak chasm
Almost, except the last one is 1.
Yes, when you see a 1, that's when it repeats.
Like here, i^4 = 1, so it will repeat every four.
The reason why is because i^5 = i * i^4 = i.
burnt pivot
makes sense
oak chasm
And so forth.
burnt pivot
.close
narrow vapor
how do i find the derivative
of y=tan^-1(3x)
lone heartBOT
how do i find the derivative
of y=tan^-1(3x)
narrow vapor
I thought to use derivative of quotiant
oak chasm
Do you know the derivative of arctan(x)?
narrow vapor
No
oak chasm
Do you know implicit differentiation?
narrow vapor
Yes
oak chasm
Do you know the derivative of tan(x)?
narrow vapor
=sec^2(x)
oak chasm
OK, so we can use implicit differentiation.
For the derivative of arctan(x), we have:
y = arctan(x)
tan(y) = x
Then, you can use implicit differentiation on that.
oak chasm
You're welcome.
narrow vapor
You're welcome.
If i use implicit, I will have a y value in the answer.
The question also asks me to find the slope of the eline tangent to the function.
I cannot use a calculator
x = 1
oak chasm
OK, so what do you have with y in the answer?
narrow vapor
OK, so what do you have with y in the answer?
1 = sec^2(3y)*3y'
oak chasm
Oh, OK.
OK, let's simplify that a bit by finding it for x instead of 3x.
After that, we can just use the chain rule.
So, we have y' sec^2(y) = 1.
Then, we want y', so we get y' = 1/sec^2(y)
We had tan(y) = something, so we want it in terms of tan(y).
So, we can use the Pythagorean identity.
sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)
Does it make sense how I got that from the Pythagorean identity with everything divided by cos^2(x)?
narrow vapor
yes, so that you can get tan^2(x)
oak chasm
Right, plus you get sec^2(x).
So, you can transform a sec^2(y) to a tan^2(y) expression.
tan^2(y) + 1 = sec^2(y)
So, we can replace y' = 1/sec^2(y) with something with tangent in it.
Then, we can use the fact that tan(y) = x.
So, what do you get from that?
narrow vapor
~~1/sec^2(y) = tan^2(y)
Subs
x^2 ?~~
oak chasm
Well, we have y' = 1/sec^2(y), and we know that sec^2(y) can be replaced by tan^2(y) + 1.
So, we get y' = 1/(tan^2(y) + 1).
oak chasm
Right.
So, we converted it from arctan to tan.
Then, we used implicit differentiation.
Then, we saw that it used sec(y) when we only really knew what tan(y) was in terms of x stuff.
So, we used the Pythagorean identity to figure out how to turn sec(y) into something with tan(y).
Now, we have the derivative of arctan(x), which is 1/(x^2 + 1).
,w D[ArcTan[x], x]
ocean sealBOT
oak chasm
Now, you can just use the chain rule to get the derivative of arctan(3x).
narrow vapor
by plugging 3x into x and multiplying by 3?
oak chasm
Yes, that's what you'll get.
narrow vapor
Thank you very much, I understand now. I appreciate your time in helping me :)
oak chasm
You're welcome.
narrow vapor
.close
turbid salmon
hello, I really need help with determining if what I did to show the spread of disease is correct.
turbid salmon
and with the month of march, how can I show the spread if the previous month is 0
<@&286206848099549185>
thick basalt
isn't x supposed to represent the number of months passed?
turbid salmon
isn't x supposed to represent the number of months passed?
yeah, but the data given every month has a different growth factor than the previous month. that's why I am not quite sure on how to model them...
thick basalt
usually x represents time and the growth factor is the number your raising x to
i think
turbid salmon
usually x represents time and the growth factor is the number your raising x to
so do I have to find the average growth rate of all months? in order to model the spread of the disease?
and then replace x with the number of months that has passed?
thick basalt
I think x is supposed to stay x
Maybe youre supposed to find an exponential function just based on the data for each month
the question is worded confusingly
turbid salmon
the question is worded confusingly
yeah... that's why I'm having a hard time with determining if what I did is correct. I already asked my professor about it but he hasn't responded yet...
thick basalt
I mean I would say it makes sense
turbid salmon
alright, thank you so much for the help. I'll try waiting for my professor's response for now
thick basalt
Didn't help much but you're welcome ig 😁
turbid salmon
.close
lone heartBOT
What’s this
tacit arch
So like do I do 2x4
No
alpine sable
U don’t need to teach me it’s fine
tacit arch
2 ^ 4 = 2 * 2 * 2 * 2
alpine sable
Oh
tacit arch
Notice there are four 2s on the right side
alpine sable
??
tacit arch
Did you count them?
tacit arch
2 ^ 4 = 2 * 2 * 2 * 2
How many 2s do you see
alpine sable
4
tacit arch
2 ^ 4 = 2 * 2 * 2 * 2
Do you know how to multiply?
alpine sable
+rep nice pfp
TYANKS!!
tacit arch
It’s the last one right
No
tacit arch
2 ^ 4 = 2 * 2 * 2 * 2
,calc 2 * 2* 2 * 2
ocean sealBOT
Result:
16
tacit arch
Yes
alpine sable
Yay :D
alpine sable
What’s this
tacit arch
You left out part of the question
tacit arch
Yes the left side
tacit arch
What’s the asbeer
What does asbeer mean
thick basalt
isn't the whole point of help channel to kinda teach and not give answers
lone heartBOT
@alpine sable Has your question been resolved?
tired flicker
how to find the tangente of x2+x2y+y2=3. When x=1. I have the answer but i dont know how my teacher got to that answer.
thick basalt
The slope of the tangent line is the derivative at that point
And using that try to figure out the y intercept
than you get the equation
@tired flicker
tired flicker
i have found the derivative of the function
tired flicker
i got -2 and 1
thick basalt
How did you get 2
tired flicker
-2
thick basalt
I meant how did you get 2 answers
tired flicker
after i plug in the 1 in the parent function
to find the y
when plugged it in it gave me y2+y-2=0
thick basalt
wait which one is your function
thick basalt
I mean...
Wait what were your derivatives
cause your function wasnt even a function
tired flicker
give me a sec
thick basalt
k
tired flicker
tired flicker
2d
thick basalt
REALLY?
tired flicker
yup
tired flicker
Ping helpers ig
how do i ping
thick basalt
whats that
oh
yes
I forgot to do a science project so I had to do it over the night
💀
tired flicker
so you didnt sleep at all
thick basalt
nope
tired flicker
how did you manage to stay awake
thick basalt
Im built different
lol
I dunno I just didnt feel sleepy
If im focused and actually working, I just don't feel sleepy
tired flicker
when is the helper coming
<@&286206848099549185>
How to find the tangente of x2+x2y+y2=3. When x=1. I have the answer but i dont know how my teacher got to that answer.
nimble fern
last step
tired flicker
the first thing i did is find the derivative
tired flicker
than i found the y= -2 and y= 1
nimble fern
which is correct too
nimble fern
hmmm so you used
(-2,1) for this tangent, right?
tired flicker
yes
nimble fern
hmmm
firstly
"
2(-2)+2(-2)(1)
over
(-2)²+2(1)
"
is not 2/3
tired flicker
How to find the tangente of x2+x2y+y2=3. When x=1. I have the answer but i dont ...
x=1
nimble fern
anyways, its -2/3
tired flicker
than i found the y= -2 and y= 1
y=-2
tired flicker
anyways, its -2/3
ok
nimble fern
- ( 2(1)+2(1)(-2) ) / ( 1² +2(-2) )
nimble fern
\- ( 2(1)+2(1)(-2) ) / ( 1² +2(-2) )
=-(-2/-3)
=-2/3
tired flicker
-(2x+2xy)/x2+2y
this is the tangent i found
nimble fern
=-(-2/-3)
=-2/3
.
tired flicker
what is the b
nimble fern
b?
tired flicker
tangente= ax + b
nimble fern
yes
tired flicker
because my answer doesnt seem good
nimble fern
it's -4/3
tired flicker
where did i mess up?
nimble fern
as i have just said
the slope is negative 2/3
-2/3
change that and you'll be able to find b
tired flicker
are you a graduate
nimble fern
yea, i graduated
tired flicker
from uni
nimble fern
yep
nimble fern
nah, being a student is nice
tired flicker
why do you think so
tired flicker
what did you graduate in if you dont mind me asking
nimble fern
what did you graduate in if you dont mind me asking
oh, maths
with bad grades XD
careless + lazy
tired flicker
at least you graduated
tired flicker
i am in college and trying to get into uni
nimble fern
good luck!
tired flicker
thanks
nimble fern
anymore questions about the question above?
btw, since you have 1 and -2
there should be 2 tangents
nimble fern
nah, just post a new channel for new question
tired flicker
ok
nimble fern
you can close this if you are done 🙂
tired flicker
ok
! close
!close
!close close
!-close
i think the close function just closed
nimble fern
.close
meager summit
help
meager summit
what is wrong with this step?
what can't I get change it and break up the square root between all 3 numbers?
long axle
$\sqrt {a-b} \neq \sqrt a - \sqrt b$
ocean sealBOT
Stephen
long axle
Take an educated guess
long axle
Well what’s ur ultimate goal?
long axle
Ok well u can use a calculator if u want, or u can simplify a little further
meager summit
Ok well u can use a calculator if u want, or u can simplify a little further
alr ty
long axle
Ok then yea maybe simplify a bit then calculator
meager summit
how would i simplify to this though?
@long axle
oh make 1 = 25/25
then subtract i bet
meager summit
**Stephen**
@long axle so moral of the story is this