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#help-42
gusty steeple
what is the conjugate of 1-z?
calm coralBOT
what is the conjugate of 1-z?
surreal patio
u need a imaginary number to take conjugate
gusty steeple
yeah let z be an imaginary number
hollow perch
complex or imaginary
gusty steeple
complex mb
surreal patio
then its 1+z , no?
gusty steeple
aight so if z = 2(cis theta) ur saying that the conjugate of 1-z is 1+2(cis theta)??
gusty steeple
yeah i get the conjugate of z flips the imaginary part, but what about the conjugate of 1-z i dont get this
gusty steeple
so the conjugate of 1-z is 1-z̅
pastel heart
then what was i supposed to do?
velvet osprey
you were supposed to find two points such that the value of f at one of them is positive and on the other is negative and then apply ivt to the interval between those points
pastel heart
you were supposed to find two points such that the value of f at one of them is ...
i look online and no one is showing how to find those two points
can you tell how i do it.
gusty steeple
$\frac{1-2cosθ}{5-4cosθ}$
calm coralBOT
$\frac{1-2cosθ}{5-4cosθ}$
potent lotusBOT
Galaxy
potent lotusBOT
Galaxy
gusty steeple
let z = 2(cisθ)
i have to express the imaginary part of 1/(1-z) in terms of θ
im not too sure if this is the correct expansion
gusty steeple
i have to express the imaginary part of 1/(1-z) in terms of θ
and im not sure if im overcomplicating this but is the answer just
$-\frac{sinθ}{5-4cosθ}$
potent lotusBOT
Galaxy
calm coralBOT
calm coralBOT
Available help channel!
ionic viper
yo
ionic viper
u guys seem smart right
help me w my shit
or do it for me
i aint doin alla that
calm coralBOT
@ionic viper Has your question been resolved?
ionic viper
<@712137021833084990> Has your question been resolved?
no
the shit closed anyway
wait thats a bot💀
calm coralBOT
@ionic viper Has your question been resolved?
shrewd gyro
I would like to know how do you know if a line is parallel
calm coralBOT
I would like to know how do you know if a line is parallel
shrewd gyro
Like
I’m learning coordinate geometry
and this line is parallel to another
how similar are the equations of them?
remote mural
do you have an example question
fringe reef
I’m learning coordinate geometry
if the slope is the same then they are parallel
shrewd gyro
if the slope is the same then they are parallel
Oh ok
thank you very much
I have another question though
how do you show that a point lies on the same line?
shrewd gyro
how do you show that a point lies on the same line?
as another point
fringe reef
converting to y=mx+b form makes everything easy
shrewd gyro
yes I’m doing that
fringe reef
if you sub in (x,y) into that equation and it holds, then it lies on the line
fringe reef
if the equation doesn't hold then it's not on the line
fringe reef
no problem
thorn verge
calm coralBOT
calm coralBOT
@thorn verge Has your question been resolved?
trail yarrow
How does $a_n>\delta_1$ mean that $f(\varepsilon) < \varepsilon_2$?
potent lotusBOT
Edward II
trail yarrow
and also what is $N_1$?
potent lotusBOT
Edward II
trail yarrow
@thorn verge
calm coralBOT
@thorn verge Has your question been resolved?
thorn verge
**Edward II**
because for all $x > \delta_1 $, $f(x)<\epsilon$ and im just choosing $N_1$ such that it satisfy the condition
potent lotusBOT
cheesycrunchwrap
thorn verge
is it not allowed
trail yarrow
oh I missed another error
double check the definition of a limit, because you do should not get $x>\delta_1$ means $|f(x)|<\varepsilon_1$.
potent lotusBOT
Edward II
trail yarrow
e.g. you're claiming that in the case where f(x)=x, all x greater something are also close to 0...
thorn verge
double check the definition of a limit, because you do should not get $x>\delta_...
so for the limit definition as x approach 0+ i get for $x-0 > \delta_1$ then $|f(x)-0|<\epsilon$
potent lotusBOT
cheesycrunchwrap
trail yarrow
x-0 < delta
thorn verge
oh yah sorry
thorn verge
x-0 < delta
so that's where my proof is problematic
trail yarrow
partly
thorn verge
**cheesycrunchwrap**
. is this allowed thou
trail yarrow
there's also the fact that the value of an has nothing to do with the value of f(epsilon)
thorn verge
so what im understanding from this question is that limit right hand side of f(x) =0 and if $n > N$ then $a_n -L < f(x)$ which give me nothing about how n would behave as n get bigger
trail yarrow
(you need $s, latex uses > for upside down question mark outside of math mode)
potent lotusBOT
cheesycrunchwrap
trail yarrow
now you know you can pick some specific x such that f(x) < epsilon
trail yarrow
**cheesycrunchwrap**
by using this (correcting to x<delta)
thorn verge
(you need $s, latex uses > for upside down question mark outside of math mode)
thanks
thorn verge
by using this (correcting to x<delta)
so im picking x s.t $f(x)<\epsilon_1$ then it follows $|a_n-L|<f(x)<\epsilon_1$ and i don't have to restrict n because as n gets bigger the $|a_n-L|$ condition will be satisfied am i getting this correct now?
potent lotusBOT
cheesycrunchwrap
trail yarrow
yes
thorn verge
ok thank you so much
trail yarrow
you don't even need the subscript 1s btw
thorn verge
for epsilon?
trail yarrow
mhm, because you're not using any others
thorn verge
bc i wanted to distinct between the interval and the dummy variable
thorn verge
in the question it mention $f(\epsilon)$
trail yarrow
it's notation anyway
potent lotusBOT
cheesycrunchwrap
thorn verge
ok thanks just want to be sure bc im horrible with proof
olive wigeon
cba someone just double check pls
calm coralBOT
cba someone just double check pls
remote mural
cba someone just double check pls
uh whats the y intercept for 2x-4y+8=0
remote mural
but it’s 2
yh its 2
remote mural
idk how to explain to
point where x=0
remote mural
cba someone just double check pls
and whats the y intercept for your equation
olive wigeon
and whats the y intercept for your equation
which one are u talking abt
remote mural
cba someone just double check pls
okay next one, the slope is correct here but the y intercept isnt
whats the y intercept for y=-x/2 - 3 and x+2y-5=0
olive wigeon
okay next one, the slope is correct here but the y intercept isnt
whats the y i...
uhh
Y= -x/2-5/2
remote mural
Y= -x/2-5/2
hmm? how do you find the y intercept in the first place
olive wigeon
hmm? how do you find the y intercept in the first place
cuz it’s 2y
and I only want y
so I divide by 2
remote mural
cuz it’s 2y
you find the y-intercept by letting x=0
the x-intercept by letting y=0
olive wigeon
oh
calm coralBOT
@olive wigeon Has your question been resolved?
sleek thorn
calm coralBOT
sleek thorn
I have the problem of using the Gaussian method for the first task because I can't find a solution.
For the second task I don't know how to come up with the solution, so I don't have an approach.
calm coralBOT
@sleek thorn Has your question been resolved?
calm coralBOT
@sleek thorn Has your question been resolved?
runic jewel
Fürs erste würde ich alles in die erste einsetzen und dann die 8 möglichen Gleichungen ohne Betragsstriche durchgehen die das gleiche Ergebnis haben könnten
Keine Ahnung wohin man damit kommt, aber es wäre mein Lösungansatz
tight heron
determine the equation parallel to the bisector of the second and fourth quadrants which cuts off a chord of measurement 2squareroot(6) on the parabola of equation y = x^2 -x +3
calm coralBOT
determine the equation parallel to the bisector of the second and fourth quadran...
tight heron
no one???
calm coralBOT
@tight heron Has your question been resolved?
calm coralBOT
@tight heron Has your question been resolved?
calm coralBOT
worn hedge
There’s three vectors from the question, do I just assign one of them as (0,0,0)
velvet osprey
the generalization
what is this "generalization" of which the problem speaks?
worn hedge
If there exist 3 scalars , (a x scalar ) + (b x scalar) + (c x scalar) = 0, then it asks for the generalisation for k vectors in R^ n
velvet osprey
!original
calm coralBOT
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.
velvet osprey
If there exist 3 scalars , (a x scalar ) + (b x scalar) + (c x scalar) = 0, then...
this wording is D tier
worn hedge
Scalars being alpha, beta, gamma, and a, b and c being vectors
Then ending with vector k I guess
velvet osprey
sorry, it's very hard to understand you when you try to type it out like that
orchid abyss
how do i continue / am i on the right path?
calm coralBOT
Please stick to your channel.
velvet osprey
.close
calm coralBOT
orchid abyss
and i cant use l'hopital
leaden thunder
just wanted to confirm because chatgpt says 4
Don't use chatgpt for math
pallid jasper
!nogpt
calm coralBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
fresh canopy
Don't use chatgpt for math
I usually just use it to make sure I’m not missing anything because it is right sometimes
leaden thunder
That's bad
leaden thunder
Write it out and show it here
fresh canopy
@leaden thunder is this correct
calm coralBOT
@fresh canopy Has your question been resolved?
zinc pelican
Let ABC be a right triangle in B with AB=5 and BC=4. Hb is the intersection of AC with the height originating from B. AE is the symmedian originating from A. AE and BHb intersect at P. Find the area of triangle APB.
zinc pelican
I tried to add new perpendicular lines coming from P on AB and BC and think about the problem in terms of the pedal triangle HaHbHc but that didn’t really help
calm coralBOT
@zinc pelican Has your question been resolved?
zinc pelican
<@&286206848099549185>
junior fern
@zinc pelican start by finding information you already know how to find
like angle C
and angle A
calm coralBOT
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calm coralBOT
strange lichen
Breh
Why didn’t u just combine the terms
5^x * (e^6.5)^x
Becomes
(5e^6.5)^x
No need for product rule
@glossy crown
U found f’ to be 5 which is wrong
f’ = 5^x * ln5
calm coralBOT
@glossy crown Has your question been resolved?
remote mural
so just checking
calm coralBOT
so just checking
remote mural
we are going to need 3 terms
our phi values are going to be interscetions
our rho values are obv going to differ from 0 to something each time
and theta will always be 0 to 2pi?
right?
this is a past quiz i found but no answers are linked lol
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
austere moth
2-x-x^2
How do i factorise this?
calm coralBOT
2-x-x^2
How do i factorise this?
austere moth
My guess would be to use this ?
remote mural
no
thin tendon
2-x-x^2
How do i factorise this?
to factorize a polynomial, find a root
austere moth
and that means?
remote mural
2-x-x^2
How do i factorise this?
for factoring a quadratic of the form $\m fx = ax^2 + bx +c$, try to find two integers $u,v$ that satisfy the equations [
u\cdot v =a\cdot c \
u + v = b
]
potent lotusBOT
thin tendon
a root is a value x such that P(x) = 0
remote mural
and then you can substitute [
\m fx = ax^2 + vx + ux + c
]
and factor normally
potent lotusBOT
austere moth
a root is a value x such that P(x) = 0
So when y = 0 ?
thin tendon
whats y?
thin tendon
do you know how to solve a quadratic?
austere moth
I can do that but
how does that help me knowing that
Or rather, what is the next step after figuring that out
thin tendon
if you know the roots of a polynomial
then you know the polynomial can be written as a factor of a(x-r1)(x-r2).....(x-rn)
austere moth
oh ok
thin tendon
thats a theorem on polynomials
austere moth
So how would i go about finding the roots out?
thin tendon
solve the quadratic
like thats what solving a quadratic means
its litteraly the same as finding the two roots
its the definition of solving it even
austere moth
I'm not sure how to solve it
because i've done it using pq formula
but i'm not allowed to use a calculator
so i can't utilize it
austere moth
solve the quadratic
i assume i have to use square completion ?
austere moth
I have no idea what to do
potent lotusBOT
nadav
swift wyvern
uhh
swift wyvern
how do you even solve these without calculator
rough tl : Every year in a city, there's a 2% increasement of the citizen amount.
in 2010 they had 900k citizen, how much citizien in 2020
velvet osprey
well
the population increases by 2%
this is the same as being multiplied by 1.02
do you see why
swift wyvern
yes
swift wyvern
so uhh theres a formula right
swift wyvern
yeah im just saying theres a formula for it
velvet osprey
you know that from year to year the population multiplies by 1.02
how many years passed from 2010 to 2020
swift wyvern
i can instantly count the next year will be 918000
velvet osprey
no need
swift wyvern
how many years passed from 2010 to 2020
10
velvet osprey
right
swift wyvern
so 1.02^9?
swift wyvern
900,000 * 1.02^10
how do i count them then
velvet osprey
do you have a calculator?
swift wyvern
so yeah we need a calculator in the end
uhh yeah i got one
its midnight here
i think this is jsut a bad question
swift wyvern
900,000 * 1.02^10
wanna leave it at that or you can count it
velvet osprey
why is it a bad question?
just put this into your calculator.
you are expected to do that, no doubt.
swift wyvern
why is it a bad question?
cuz its gonna take a long time without calculator?
okay then
here?
velvet osprey
i mean you could do the long and painful calculation of 1.02^10
there are some tricks you can use to make your life easier
calm coralBOT
calm coralBOT
Available help channel!
summer dune
im trying to figure out the question, what it wants from me?
vagrant oak
im trying to figure out the question, what it wants from me?
It shows a system of 2 linear equations written in augmented matrix, and it wants you to solve it
summer dune
It shows a system of 2 linear equations written in augmented matrix, and it want...
i still dont get it, its probably because i dont know what to do(?)
like , x-3z=5 ?
summer dune
yeah
vagrant oak
note that this system doesnt have a unique solution
in fact, it has infinitely many solutions
The best thing you can do, is given an arbitary choice of x, find the form of y and z such that they give a solution to the system
summer dune
so i can choose any value for z and then use the equations to find x and y?
vagrant oak
hmm you will miss infinitely many solutions by doing so
Instead try working with x, and expressing the values of y and z using x
You could probably do it with z as well for simplicity, but the convention is to use x I guess
summer dune
Instead try working with x, and expressing the values of y and z using x
so i need to give any value to x?
thorny stump
You could probably do it with z as well for simplicity, but the convention is to...
This might be what he meant?
You already have z in both equations so...
vagrant oak
Nope, you dont give it any value. You just let it as a letter x
So in the first equation you have x - 3z = 5
Try solving for z
summer dune
yeah
vagrant oak
now the second equation is y + 2z = 4
can you express y using x?
note that you might need the solution of first equation to do this
summer dune
y = -2/3 x + 10/3 i think
thorny stump
You forgot the 4
thorny stump
4+10/3 = 22/3 but yeah
vagrant oak
4+10/3 = 22/3 but yeah
You sure?
oh alr
Ic what you did
Yeah so y = -2x/3 + 22/3
thorny stump
Though like I said, z is already in both, so I would've done it like
x = 3z+5
y = -2z+4
z is whatever
vagrant oak
I would think so
this is a general form of solution
there are infinitely many solutions, so giving just 1 or 2 would be absurd
vagrant oak
So the solution vector would be [x, -2x/3 + 22/3, x/3 - 5/3]
This tells you that given arbitary x, the solution is of this form
remote mural
Hi, can someone recommend a detailed, slow paced resource resource for stats. From which I can learn measures of central tendency and dispersions
remote mural
Please ping me if someone replies
calm coralBOT
@remote mural Has your question been resolved?
remote mural
like at what level?
Well I’m in highschool, maybe a little deeper than that. I just want a really good understanding
remote mural
how much probabilities do you know?
The basics
thin tendon
idk too much then but for hs math try basic resources
remote mural
idk too much then but for hs math try basic resources
Can you then recommend me some resources to that would help me understand the concepts better?
Because teachers lectures and the reference books I’m given are really basic, they don’t make any attempts at improving understanding, just formula bashing
calm coralBOT
@remote mural Has your question been resolved?
stiff ingot
how should I approach finding a solution for the second linear equation since i cant factorize 3m^2 - 6m + 6?
stiff ingot
should I treat it as non-homegenous put -1 on the other side?
pure kayak
quadratic formula
remote mural
How would you go about solving for the area that encapsulates both 8sinϴ and 8cosϴ?
remote mural
i cant wrap my head around the explanation my friend is providing so id like someone more adept to explain it please :)
balmy yew
if sorry if im not understanding the question but do you want the area of this?
because you could just integrate 8sin(x) from 0 to pi/4 and multiply by 2 to get that
remote mural
if sorry if im not understanding the question but do you want the area of this?
oops i meant r=8cosϴ and r=8sinϴ
im sorry!!
polar is beyond me
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
wet falcon
calm coralBOT
wet falcon
if the sum of the roots = 0, how do you know that the sum of the real part of the roots also equal to 0
does the imaginary parts of the roots cancel out?
old falcon
if the sum of the roots = 0, how do you know that the sum of the real part of th...
because thats the only way for it to zero
the real part and imaginary part cant interfere
wet falcon
oh
old falcon
so they need to zero independently
calm coralBOT
mellow crater
just comparing both sides
what is next to sin(x) on the left side should be also on the right side next to sin(x)
on the left we have 3sin(x) ---> so "3" is next to the sin(x)
on the right we have Rsin(x)cos(a) ---> so "Rcos(a)" is next to the sin(x)
it implies 3 = Rcos(a)
R * cos(a) is a number, constant
if R * cos(a) = 3 then you have:
3sin(x) + 4cos(x) = 3sin(x) + Rcos(x)sin(a)
in other words equation holds when both sides are exactly same
nothing, it stays
thing is we only look at the coeffcients
ugh, yea it may be said this way
okay, but lemme show you a simpler example
when 5x = a * x
what is a in this scenario
and if 5x^2 + x = a * x^2 + b * x?
a = 5 and b = 1, right
thing is you just compare what stands next to x^2 and x
you don't care about x^2 and x
how? it's not
it's a conclusion
in the equation you'll still have sin(x)
like 5x = a * x and we say a = 5
in a = 5 there is no x anymore, but in the equation it is
5x = 5x
that's it
thing is here that "a" is made of two factors
R and cos(a)
but logic is same
stark cloak
does anyone know if this a^k , so the k in the exponent is a common notation ? I have never seen that , therefore I dont know what it is supposed to mean and it isnt defined anywhere.
stark cloak
lol I see, but its very confusing that it wasnt set in the first occurrence of aij
calm coralBOT
stark cloak
.reopen
calm coralBOT
✅
stark cloak
entry u,v of the matrix A^k
wait just to be sure
sorry
because you said A^k , you meant A in {0,1}^k by that right ?
.close
west ermine
How do i determine if a function is odd or even, i forgot how to do this
shadow tendon
Definition of odd is f(x)=-f(-x). This means you want to show x^2=-(-x)^2.
Also the first one is even not odd
so is the 2nd one lol
west ermine
mb
shadow tendon
For first one, use (-1)^2=1
calm coralBOT
calm coralBOT
Available help channel!
noble cedar
calm coralBOT
noble cedar
0.000000000000011409999999999998458
diagonal method to solve?
lmao, my calculator would explode
thorny stump
You can transform the matrix and get some easy zeroes in there
thorny stump
Adding a row to another row does not change the determinant
noble cedar
so I should probably work my way from bottom to top
R4 - R3 -> R3
or would you recommend top to bottom
thorny stump
Doesn't matter
noble cedar
R1 - R2 -> R2
I will be stuck with a shitty large number tho, for R1 if I keep subtracting from R1
torn gorge
its zero
thorny stump
I will be stuck with a shitty large number tho, for R1 if I keep subtracting fro...
No?
Try it
torn gorge
determinant
thorny stump
Actually it's even easier with columns if you want to do it that way
noble cedar
how do you recommend tackling it?
I was thinking diagonal would be fastest for 4x4
but not this guy
thorny stump
You want the solution?
noble cedar
OK
torn gorge
thorny stump
Column 2 is all 1000 so you can subtract any value from all elements of any column
velvet osprey
are we sure that no precision issues are at hand her
noble cedar
thorny stump
So subtract 1202 from the first column and 49 from the 4th
velvet osprey
yeah you want to do this with columns not rows
if you insist on rows only it will be difficult and hard and a AEM
thorny stump
Then subtract the 4th from the 1st
thorny stump
if you insist on rows only it will be difficult and hard and a AEM
You can still get a row of zeroes pretty easily
noble cedar
oh this answer is for different question but same idea
thorny stump
Exactly the same process
thorny stump
Subtract 1303 from the 1st column, and 39 from the 4th
noble cedar
C2 = 1/100 C2
i didn't know you could do column operations too
I thought it was only row operations
multiplying row by scalar
multiplying column by scalar
both of these are allowed when finding RREF?
thorny stump
It's similar to Gaussian elimination
Not identical because swapping rows or columns can change the sign and stuff
velvet osprey
i didn't know you could do column operations too
you are finding a determinant.
noble cedar
not RCEF
velvet osprey
it'd be RCEF
noble cedar
right
velvet osprey
reduced column echeelon form
also this is not necessarily a goal
we do not achieve it here
noble cedar
so if I wanna avoid RCEF here, what's the option?
i don't necessarily like or follow the way this has been solved, is there another way to do it?
column 0 makes sense, it means if you multiply the diagonal you will always get 0, so the determinant = 0
why does the 1/100 C2 now become a scalar of 100 to the entire matrix?
that doesn't make sense to me
stoic oyster
the det of the new matrix = 1/100 the det of the first matrix (cause we divided a row by 100)
thorny stump
If you want a row of zeroes you can do R1 - R2 - R3 + R4
stoic oyster
the det of the new matrix = 1/100 the det of the first matrix (cause we divided ...
so det of first matrix = 100 det of new matrix
that's the most favorable interpretation I can see
@noble cedar
calm coralBOT
@noble cedar Has your question been resolved?
thorny stump
why does the 1/100 C2 now become a scalar of 100 to the entire matrix?
If you multiply a matrix A by a diagonal matrix D where d11 = 1, d22 = 100, d33 = 1, d44 = 1, then the result B has all the same columns as A except the 2nd column got multiplied by 100.
The determinant of AD is equal to the determinant of A multiplied by the determinant of D.
In your example the matrix on the left is B, the matrix on the right is A, and so the determinant of B is 100 times the determinant of A.
graceful crow
so this is my problem and i know the head director is male because it is myself in this case
graceful crow
this is my work i have but dont know if im doing it correctly
<@&286206848099549185>
calm coralBOT
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calm coralBOT
@graceful crow Has your question been resolved?
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@graceful crow Has your question been resolved?
cyan fox
calm coralBOT
cyan fox
Is a correct?
strange lichen
,w differentiate x^0.25 (x^(4/7) + x^(1/3))
potent lotusBOT
strange lichen
Not the one u chose
lethal ice
Just do it like that:
f(x)=x^(1/4+4/7)+x^(1/4+1/3)=x^(7/28+16/28)+x^(7/12)=x^(23/28)+x^(7/12)
Now use that (x^n)'=n*x^(n-1) --> f'(x)=23/28*x^(23/28-1)+7/12*x^(7/12-1)
I leave the rest to you
cyan fox
I leave the rest to you
I still think its c
this is what I got
23/28x^-5/28 + 7/12x^-5/12
lethal ice
correct
cyan fox
so c?
lethal ice
yeah
cyan fox
ok can you help me with another
lethal ice
If its a lot harder, sure. But if its almost the same, im sure youll get it by yourself 😄
lethal ice
yeah it is
lethal ice
Sure. Just calc it. You can easily calc the derivative of all 4 functions at 1 and eliminate 2 of them with just the slope. Then you need to calc f(1) and use the definition of the slope to see which of those possible two tangents contains (0,11)
calm coralBOT
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cyan fox
<@&286206848099549185>
remote mural
hi
lethal ice
Sorry, was afk. No, its not c. If you check f(1) of c, youll get -3+2+12=11. But your linear equation should contain (0,11). If its slope is -4 and it contains (1,11) (cause it hits the c) there), it cant contain (0,11).
cyan fox
Sorry, was afk. No, its not c. If you check f(1) of c, youll get -3+2+12=11. But...
s does that mean its a
because it has -4 slope and its f(1) is not 11
lethal ice
yeah
cyan fox
.close
royal smelt
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stoic oyster
that's fine yes
@heavy snow
p_0 sends everything to 0
yup
sure
it's completely fine
not everything has to be hard yk
I mean that's what you do for subspace proofs
they're not sophisticated at all
if you have a polynomial P with P(8) = P(-5)
then lP satisfies (lP)(8) = (lP)(-5)
it is yup eat cake
(at least for freebie subspaces like this)
intro linalg is more getting used to a new language than interesting proofs most of the time
weak rapids
nice profile dude
stoic oyster
I mean it's nice if they feel like common sense to you, you'll crush that exam
try and find another subject to read about if you're really bored
weak rapids
oh thats my college entrance exam date
weak rapids
yea
stoic oyster
#calculus is the gen chat
idk I mostly just lurk there
depends how serious the thing you're talking about is
calm coralBOT
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teal rapids
teal rapids
im so bad at proofs
yall have no idea
if yall can help with this and help me understand it so i can do the rest on the assignment that would be great
teal rapids
...
coarse bolt
It’s my brothers h.w but I’m a little confused
teal rapids
just name 3 things that take a minute or just a few minutes
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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).
coarse bolt
I think it can be rays of light, blinking
teal rapids
what no
velvet osprey
!occupied
calm coralBOT
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).
coarse bolt
I’m saying for 1
burnt phoenix
@coarse bolt please go to a different channel. This channel is already occupied.
teal rapids
yeah
velvet osprey
im gonna be a hardass about this but one person per channel
teal rapids
yeah i know i was confused 💀
she just asked in my channel
its a really simple question though so its fine i guess
coarse bolt
Oh I’m new so I am a little confused
teal rapids
yeah its okay just type in one of the available help channels
velvet osprey
#❓how-to-get-help for instructions
teal rapids
anytways can someone help me with this
im really bad at these
i just need help understanding how and stuff
so i can do the rest
coarse bolt
Srry don’t know
fringe pumice
How would I set up the equations for this
calm coralBOT
How would I set up the equations for this
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fringe pumice
.reopen
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fringe pumice
<@&286206848099549185>
remote mural
3x+2+(x^2)+(2y^2)-x = 180
2x+2+(x^2)+(2y^2) = 180
2x+x^2+2y^2 = 178
Good luck soldier
fringe pumice
Thanks
calm coralBOT
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fringe pumice
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fringe pumice
How would I find BC
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
solid skiff
fringe pumice
Idk how to do sin yet our teacher didn't teach us that
@solid skiff
<@&286206848099549185>
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nimble bloom
ohkk
oblique current
pins your first message which is supposed to be your question
nimble bloom
i needed help btw
pure kayak
past tense?
nimble bloom
need*
pure kayak
ask away
rose fox
i cant help, but what class is that for? just curious
nimble bloom
precal
rose fox
ohok
weary wyvern
if i remember my statistics right this is an underestimate. y-y^. positive residual is the prediction (y^) was too low. negative means the prediction was too high.
nimble bloom
if i remember my statistics right this is an underestimate. y-y^. positive resid...
oh so its an underestimate?
weary wyvern
residual = observed value - predicted value
nimble bloom
residual = observed value - predicted value
what is the observed value in this case?
nimble bloom
we only know the residual
23.4?
weary wyvern
right
weary wyvern
not given
weary wyvern
we don't, this is testing your interpretation of a plot of residuals
nimble bloom
we don't, this is testing your interpretation of a plot of residuals
huh
weary wyvern
in the context of the problem, its asking what does the point (175, 23.4) mean
nimble bloom
i mean how do we find out if its an underestimate or overestimate
weary wyvern
by knowing the definition of a residual.... observed value - predicted value
nimble bloom
by knowing the definition of a residual.... observed value - predicted value
ohkk
but like
how wud we know if its an overestimate or underestimate
bonglord
dont give up on me pls
weary wyvern
if we predict a value of 10, and the observed value is 15, then the residual is 15-10 = 5. which means the prediction was too low
when a residual is positive it must mean the same, that the prediction was an underestimate.
there is some estimate for a height of 175cm where the observed value was 23.4.
$$r_i=y_i-\hat{y}_i$$
$$23.4=y_i-\hat{y}_i$$
$$\Rightarrow y_i \geq \hat{y}_i$$
potent lotusBOT
b0ngl0rd
weary wyvern
$y_i$ being the observed value and $\hat{y}_i$ the predicted value.
potent lotusBOT
b0ngl0rd
weary wyvern
idk how much clearer i can make it
calm coralBOT
@nimble bloom Has your question been resolved?
safe flax
i cant figure this otu
calm coralBOT
i cant figure this otu
safe flax
.close
calm coralBOT
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safe flax
round parrot
b prime cant be found with the given information
the trick is to substitute b for h
remote mural
how does this make sense
calm coralBOT
how does this make sense
tidal grotto
Does the denominator effect whether or not the left hand side would be 0?
you can also think of it as multiplying both sides by the denominator
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sudden nebula
calm coralBOT
sudden nebula
They didn't explain the reasoning behind setting the interval p >= -1/2.
I understand that this says as long as p is either -1/2 or any number that's larger than -1/2, the lim as n approch infin will not be 0.
But did they get that from just thinking about the function given? Calculator?
calm coralBOT
@sudden nebula Has your question been resolved?
leaden thunder
They didn't explain the reasoning behind setting the interval p >= -1/2.
You just multiply (n^2)^p with n
What's the exponent after multiplying?
sudden nebula
You just multiply (n^2)^p with n
huh? My question is about the choice of -1/2. I'm not sure I follow your response.
sudden nebula
What's the exponent after multiplying?
after multiplying where?
leaden thunder
You just multiply (n^2)^p with n
Multiplying this
For large n, what's 1+n^2 approximately equal to?
sudden nebula
okay one sec
sudden nebula
For large n, what's 1+n^2 approximately equal to?
for any large n? hmmm. Some large number haha..
leaden thunder
No
sudden nebula
So this section is on series. I'm not sure if you question involves me looking for a pattern or.
leaden thunder
1 + n^2 is approximately n^2
sudden nebula
oh sure
leaden thunder
Hence why you can drop the 1
sudden nebula
yes the 1 would make a very small diff. I would agree with that.
leaden thunder
You just multiply (n^2)^p with n
Hence why you do this calculation
sudden nebula
can I do this -> n^(2 * n)
n^1 * n^(2*p) = n^(1 +(2 times p)) ?
I double checked on symbolab.
It's goochi
leaden thunder
If you say so
leaden thunder
you think it's wrong?
Yes. Why is there a 2n in the exponent
leaden thunder
playing games with me I see
Nobody is playing games
You just said you've convinced yourself that you're right
sudden nebula
Yes. Why is there a 2n in the exponent
n^1 * n^2*n = n^( 1 + (2 times n) )
because:
Exponent Properties: a^n * a^m = a^ (n+m)
sudden nebula
You just multiply (n^2)^p with n
the 2 comes from:
(n^2)^p = n^2p
because,
Exponent Prop: (a^n)^m = a^nm
leaden thunder
No idea where you're getting n^(1+2n) from
Multiplication is *
Exponentiation is ^
calm coralBOT
@sudden nebula Has your question been resolved?
sudden nebula
No idea where you're getting n^(1+2n) from
I showed each step.
I'm trying to get help rn 😦
You can open a channel still bud
Do you see the math help (available) section
molten crest
leaden thunder
Yes. Why is there a 2n in the exponent
Well you ignored this first question
sudden nebula
I gave my explanation for why I had the 2n in the exponent though.
leaden thunder
the 2 comes from:
(n^2)^p = n^2p
because,
Exponent Prop: (a^n)^m = a^nm
You explained why 2p should be in the exponent
p and n are different variables
smoky crypt
yo
topaz raft
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fallen bison
so Im having issues with this problem here
calm coralBOT
so Im having issues with this problem here
devout marsh
what do we have to find?
fallen bison
I keep trying it, and get the same answer of y=5, but the book has the answers in the back, and says its 1 but i cant seem to get that
fallen bison
what do we have to find?
the x, y, and z
remote mural
so Im having issues with this problem here
solving for x,y,z?
devout marsh
oof i am stil at 2 variable idk 3 variable
fallen bison
solving for x,y,z?
right
fallen bison
oof i am stil at 2 variable idk 3 variable
alr
devout marsh
you can find x from 3rd eqation i think
wait its ezy
u find x
then put value of x in 1 and 2
then apply elimination or substituion method to find value of y and z
wait i wil be back
fallen bison
ah shit i think i know the issue. thats a 6z not 62
i didnt make the zs stand out from 2s
here
so like, the back of the book says x is 2, y is 1, and z is -2, but when I try to show my work (required) I keep getting y=5 every time
devout marsh
srry i cant i am stil at 2 variable
lemme see if i can kinda learn it from google
fallen bison
alr its fine
devout marsh
Decide which variable you will eliminate.
Work with a pair of equations to eliminate the chosen variable.
Multiply one or both equations so that the coefficients of that variable are opposites.
Add the equations resulting from Step 2 to eliminate one variable.
google * - *
lol
fallen bison
lol
devout marsh
i am kinda understand
fallen bison
im just stumped since I watched 2 tutorials, looked at my teachers slides, and did it multiple ways, yet I still get 5 and not 1 for Y
devout marsh
is the book right :>
remote mural
I keep trying it, and get the same answer of y=5, but the book has the answers i...
can i see your work
fallen bison
hold on
wait I had to do it again and with the correct way of doing stuff I get 3.5=y (the numbers in top left are book's numbers)
devout marsh
why r u getting y=3.5 here
fallen bison
idk man
devout marsh
lel
devout marsh
did u got it?
fallen bison
I GOT 5 AGAIN
devout marsh
omg what r u doing wrong
fallen bison
fallen bison
which one?