I'd ignore it and solve the 2 x,y equations you got
#help-42
hollow totem
median schooner
oh ok
well just thinking about it
if we let lambda take 0 for example, the solution would be (4,2, 0)
but if lambda isnt 0 we have
i think two linear equations that are parallel
no tahts not true
ok ill just ignore it
thank you
hollow totem
you're welcome
median schooner
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remote mural
How would I do 9
remote mural
<@&286206848099549185>
remote mural
Sorry for pinging but I have no idea what to do for question 9
tropic fiber
Oh you have to find a two plolynomeials, where when you plug in 0 and 2 for each of the variables, you get the same output
Like x squared+15 and 8y+15
When you replace both x and y with 0, the result is 15
remote mural
Ohh
tropic fiber
Except it’s also supposed to work with 2
remote mural
So would something like 4n + 2=8f +2 work?
tropic fiber
?
You are creating two different functions
They will be f(x)=4n+2 and the other one
I’ll give you an example
f(x)=x squared+4 could be considered as one polynomial
f(x)=2x+4 could be another polynomial
What is happening is that f(0) and f(2) will be plugged in to both equations. 8n this case the outputs are the same
f(x)=2x+4 would become f(0)=2(0)+4
remote mural
Ohhh right
remote mural
Oh our teacher gave us the pdf of our whole textbook
calm coralBOT
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mild glen
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remote mural
Hello
remote mural
Can anyone help me with this question
I’ve been stuck on it for too long
And all the aid they have does not work and won’t help
Here it is
velvet osprey
do you know how to find the slope of a line?
velvet osprey
ok, do you know how to find the gradient of a line?
remote mural
Not necessarily
remote mural
No
velvet osprey
gradient = Δy/Δx = rise/run = (y_2 - y_1)/(x_2 - x_1)
any of these sound familiar?
velvet osprey
And all the aid they have does not work and won’t help
what kind of aid were you given?
remote mural
The aid doesn’t load
The videos
Also we did this bs last year
So I don’t remember it
And I tried online
velvet osprey
remote mural
I have 24 mins to get it
But ok
Yeah I’m lost
Good video but
I did everything he did in the question for my answer
But somehow it was incorrect
calm coralBOT
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weak rapids
$\sum_{r=1}^n (2r-1)=n^2$ from this, can we write $$\sum_{r=1}^n (2n-1)^3=(n^2)^3$$?
potent lotusBOT
yajatk07
potent lotusBOT
Ann
calm coralBOT
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south mist
Ive got no idea how to do q13
calm coralBOT
Ive got no idea how to do q13
primal crescent
Put x + 10 in y
south mist
got it, but how do i show that point C lies on x + y = 11?
primal crescent
did you find out A and B
calm coralBOT
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spiral forum
calm coralBOT
spiral forum
clear sapphire
You made a mistake in the transition from line 2 to 3
hollow totem
,rotate
potent lotusBOT
spiral forum
split ferry
potent lotusBOT
spiral forum
Because I don't think so, due to the y
calm coralBOT
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meager dome
Confused with this
calm coralBOT
Confused with this
meager dome
$f_x = e^y - \frac{1}{x}, f_y = xe^y$ is my derivative
potent lotusBOT
accialto
meager dome
plugging in (2,0), wouldn't it be $\frac{1}{2}, 2$?
potent lotusBOT
accialto
native seal
Just a really quick one bc im having a brain fart, 75cars/km, 80km/hr how many cars/hr?
native seal
on a 12km road if thats relevant
meager dome
the d in dx/dy/dz etc can just be substituted with a delta and two values showing a change?
calm coralBOT
the d in dx/dy/dz etc can just be substituted with a delta and two values showin...
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halcyon rock
hmm
potent lotusBOT
nosqldb
halcyon rock
$AA\vec{v}$ = $(Aa_1)v_1 + ... + (Aa_n)v_n$
potent lotusBOT
nosqldb
boreal temple
with my limited linear algebra knowledge
halcyon rock
with my limited linear algebra knowledge
yes hi
$A^{n}\vec{v} = (A^{n-1}a_1)v_1 + ... + (A^{n-1}a_n)v_n$
potent lotusBOT
nosqldb
halcyon rock
A is a n x n matrix btw
halcyon rock
oh okay, I don't know matrixes at all <:happy_cry_cat:636407813144576010>
it's okay fam
just gotta finish this problem
and back to the swe internship grind
rigid mortar
how many vectors are in the list v, Av, A^2 v, ... , A^n v? (hint)
halcyon rock
how many vectors are in the list v, Av, A^2 v, ... , A^n v? (hint)
oh shit
okay yeah
there are n+1
rigid mortar
rigid mortar
yeah, they cannot be linearly independent
halcyon rock
yeah, they cannot be linearly independent
but how do I know that none of the vectors are the same
oh wait nvm
it doesn't matter
if any one of them are redundant
rigid mortar
yeah 
young pilot
Alright here’s my problem. It’s probably not too hard though.
Suppose I have 3 points at random coordinates. Each have circles around them of equal radius. How would I find the position and radius of the smallest circle that contains all points inside all three circles?
young pilot
What that kinda solution would look like:
I feel like this question is kinda elementary though
supple needle
You have a probability zero of getting three points with the exact same coordinates, in which case the radius would just be the radius of the circles surrounding the points
young pilot
What?
I don’t get what you’re saying
In the case above the outer circle is clearly bigger
Wait I think I know how ti do it
Yeah I just have to find the circumcenter
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calm coralBOT
remote mural
Alright here’s my problem. It’s probably not too hard though.
Suppose I have 3 ...
find the center of all those three shapes
the radius would be the distance to the furthest circle + it's radius
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remote mural
A is a variable point belonging to P, where P is defined by (x-1)^2 = 8(y+1), with abscissa λ, λ belonging to real numbers. Line S is parallel to the x-axis through point A, and line T is defined as x = λ-1. The intersection between T and S is M. Find the locus (geometric locus) of M."
remote mural
I am trying to solve this problem
but I fail
everytime
I start doing this but I don`t know if y = λ is correct, I thought it because y = mx +n and would have to be λ
Please
calm coralBOT
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remote mural
Somebody?
cunning veldt
Let's call xM and yM the coordinates of M
M belongs to T, so xM = λ-1
And then since M belongs to S, yM = (λ-1)²/8 - 1
so yM = (xM)²/8 - 1
calm coralBOT
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remote mural
so yM = (xM)²/8 - 1
why /8?
cunning veldt
S is the line of points that have same ordinate as A, and T the line of the point that have λ-1 as abscissa
Since M belongs to both, M has λ-1 as abscissa, and the ordinate of A
Let's find the ordinate of A
A belongs to P and has abscissa λ, so the ordinate of A is solution the y solution of (λ-1)² = 8(y+1)
So y = (λ-1)²/8 - 1
Which is, remember, also the ordinate of M (cf line 1 to 3)
So the coordinates of M are (λ-1, (λ-1)²/8 - 1)
xM = λ-1
yM = (λ-1)²/8 - 1
So yM = (xM)²/8 - 1
remote mural
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calm coralBOT
wanton wave
Do you understand what it's saying? are you able to translate it into plain english?
yeah, but not necessarily just one x
there exists some x with that property. Maybe just a single x, or maybe infinitely many
Well yeah, I was just clarifying that x doesn't have to be unique
because you said "there exists one x"
but the statement doesn't say there has to be exactly one
∀ means "for all", it's true for ALL x
∃ means "there exists", it's true for at least one x, but maybe more
it does, one is true and the other is not
as stated here, do you think this statement is true?
Is there a number x in R, such that x is also in N?
yes, you're right. For example 2 is in R, and 2 is in N
yes
but it is not true that ALL numbers in R are also in N
for example 2.5 is in R, but 2.5 is not in N
right. That says ALL numbers in R are not in N
which is not true
certainly some real numbers are naturals
sorry, I had an extra "not" in there, just fixed it lol
$\N \subseteq \R$ means $\forall x \in \N, x \in \R$. It doesn't mean $\forall x \in \R, x \in \N$.
potent lotusBOT
tatpoj
wanton wave
no problem 👍
eager acorn
calm coralBOT
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clever nymph
Hi could someone tell me what 1N means here?f and g are bothe defined on Z
velvet osprey
probably the identity function on N
clever nymph
so how does that translate into this problem?
clever nymph
so the function is always 1 for natural numbers?
this?
velvet osprey
no
the identity function is the function whose output equals its input
it is not the constant function that always returns 1
clever nymph
oh
so the function in this case is supposed to be equal to g,right?
since that is the input
vague marlin
For heat value problems, how can we tell which boundary conditions we use when finding the transient? (Dirichilet, Neuman, mixed) Course: applied real analysis.
hushed sequoia
vague marlin
For heat value problems, how can we tell which boundary conditions we use when f...
For instance, how do we know which boundary condition we are supposed to use to determine w(x,t)?
According to the solution sheet, we would use the Dirichilet formula and I'm assuming it's because the initial condition u(1, t) is not zero?
calm coralBOT
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gritty moss
I'm not sure where to begin here.... anyone know what to do?
calm coralBOT
@gritty moss Has your question been resolved?
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@gritty moss Has your question been resolved?
gritty moss
Any <@&286206848099549185> know multivariable calc here?
red parcel
What’s ur question
halcyon robin
Shoot your problem
red parcel
I may be of some help
I TAd for I last year
Though u could ask in #multivariable-calculus
gritty moss
What’s ur question
it's above
gritty moss
Shoot your problem
it's above
red parcel
Do u know what gradient is
gritty moss
I'm hella confused. Am I dumb or is it rlly this easy?
the slope is given by f(x,y) = -x^2 - y^2
fx = -2x
fy = -2y
∇f (a) = (fx(a), fy(a))
here a is the point (1,0)
So the gradient = (-2(1), -2(0)) = (-2, 0) ?
red parcel
Seems right to me
gritty moss
damn
red parcel
Lol na man I just happened to have taught it last fall
gritty moss
I had a couple follow up questions if u don't mind
red parcel
Shoot tho I’m about to b on the go it’s my girls bday
gritty moss
i'm confused as to what they want here...
I know that the answer here should be a vector of two values...
gritty moss
I’m confused about the multiplication in the numerator. We r multiplying -g with the gradient of f. But the gradient of f is the collection of partial derivatives, which can be considered as a vector.
red parcel
I don’t see the full equation
But if f is a function it’s acceleration is f’’
The motion of a particle say
gritty moss
the equation is here.
I think I just have to rearrange for a but
how do I get a in vector form...
red parcel
I don’t see any equation
It just said force equation
And force is mass time acceleration
Times*
calm coralBOT
@gritty moss Has your question been resolved?
slim marlin
untold marlin
how do i show a set of scalars exist in a field in set logic
untold marlin
so i wanna say there exists {a_1, . . . , a_n} where each a_i in the set is an element of $C$
$\exists a_1, \dots, a_n \in \mathbb{C}$ does that work?
potent lotusBOT
omgatriple
untold marlin
i was thinking if i should have brackets around it or not, but if i have brackets, then it is a set and then it must be a subset of C, which I think unnecessarily confuses the original intension
rigid mortar
that seems good. you could also say exists (a_1,...,a_n) \in C^n, but i would do what you wrote personally
calm coralBOT
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marsh forge
i have a question of why the derivative of $sqrt(2x-2)=sqrt(2)/2(sqrt(x-1)$
marsh forge
pallid halo
,rotate
potent lotusBOT
pallid halo
well that's a sqrt(x-1) in the denominator, not sqrt(2x-2)
potent lotusBOT
prime
pallid halo
it's because:
$$\frac{1}{\sqrt{2x-2}} = \frac{1}{\sqrt{2}\sqrt{x-1}} = \frac{\sqrt{2}}{2\sqrt{x-1}}$$
potent lotusBOT
Bungo
pallid halo
in the first step i factored out a sqrt(2)
and in the second step i recognized that
$$\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$$
potent lotusBOT
Bungo
pallid halo
well, it's just a factor
which you can choose to pull out if you want
in my opinion the form 1/sqrt(2x-2) is less messy and i personally would have left it that way
but calculators gonna do what calculators gonna do
flint socket
i am still very confused about this sat math problem
calm coralBOT
i am still very confused about this sat math problem
flint socket
can someone please explain to me how to do this in a simple way
ik that the slopes have to be diff to have one solution so why isn't the answer D
the answer is A but i am getting D rn
rigid mortar
ik that the slopes have to be diff to have one solution so why isn't the answer ...
Because if a = -1, both lines have a slope of -1/2
i think you had good reasoning, maybe a computation error? 
or maybe you’re confused about how the slope is determined?
how did you get D :o
rigid mortar
Because if a = -1, both lines have a slope of -1/2
I probably gave away too much here 
prisma mango
No, because a = -1
prisma mango
If a = -1, to find the slope, you can just divide by the coefficient in front of y
prisma mango
No the question is asking what value can NOT be a
Not need all of the options but one of them can't be the value for a
Because the slopes are the same that means the system has no solution
And the only option that makes the slope the same is choice A
calm coralBOT
@flint socket Has your question been resolved?
summer herald
What do I do after?
calm coralBOT
What do I do after?
wanton wave
Well, you solved for y. According to the directions, next you're supposed to differentiate to find dy/dx
Are you confused about how to find the derivative?
summer herald
yeah bc the answer is -2x/9sqrt(81-x^2)
i dont unnderstand how I would get that from the derivative
wanton wave
did you try differentiating it yet?
summer herald
yeah and i got 0
wanton wave
You took the derivative of $\frac{2}{9}\sqrt{81-x^2}$ and got 0?
potent lotusBOT
tatpoj
wanton wave
just to clarify, you're finding the derivative of the expression there at the end of your work in the picture
summer herald
cuz 2/9 is a constant and the derivative of a constant is 0
wanton wave
yes but 2/9 sqrt(81-x^2) is not a constant
you can just take the constant multiple out. Find the derivative of sqrt(81-x^2) and then just multiply the 2/9 back in at the end
summer herald
then would i apply the chain rule
wanton wave
yep
wanton wave
no problem 👍
calm coralBOT
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quiet jetty
calm coralBOT
grand glacier
and what's the full question?
quiet jetty
and what's the full question?
just simplify
grand glacier
okay, well you should use the fact that $\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$
potent lotusBOT
τγρθ
quiet jetty
i tried to, but I got $\frac{3^{x+1}}{2\times3^x}+\frac{1}{2}$
potent lotusBOT
neon
quiet jetty
and that's not the solution
grand glacier
yeah that simplifies further
grand glacier
exponent rules
quiet jetty
okay I simplified it further to $\frac{3^{2x+1}}{2\times3^x}$
potent lotusBOT
neon
grand glacier
uhm, no:\
grand glacier
$\frac{a^b}{a^c} = a^{b-c}$
potent lotusBOT
τγρθ
quiet jetty
but the bases are not same (3 and 2×3), can I still do that?
grand glacier
you can bring the 1/2 out front if you really want to
quiet jetty
ohh I got it, I change only the 3, and leave the 2 as the denominator,
$\frac{3^{x+1}}{2\times3^x}+\frac{1}{2} = \frac{3^{x+1-x}}{2}+\frac{1}{2}$
potent lotusBOT
neon
calm coralBOT
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eager acorn
calm coralBOT
eager acorn
Can anyone explain this line?
What is this theorem
I tried to check it by taking prime 3
X3={1,2}
pure kayak
whats your confusion exactly
pure kayak
its abelian since the order of multiplication doesnt matter 1x2=2=2x1
1x1=1, 1x2=2, 2x1=2, 2x2=1 so its closed
and each element here is self inverse so we have inverses
its obviously commutative since theres only 2 elements
and the identity is just 1
it fulfills the properties of an abelian group
eager acorn
Yes it is abelian but i am not checking this
I meant is this little part of wilson theorem?
@pure kayak
Sry for this ping
velvet halo
It’s not a theorem
It’s just an example of an abelian group
The numbers 1, …, p-1 under the operation multiplication modulo p form an abelian group
That’s all the “theorem” is saying
calm coralBOT
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topaz badge
calm coralBOT
calm coralBOT
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cursive gorge
What specifically is confusing
calm coralBOT
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tawny hill
in the class 60% were boys, 1/5 part of the boys transferred classes, girls remained the same. what % are the boys now?
tawny hill
l feel so fucking dumb that l cant solve this
patent pawn
Hi think about it this way - the total class is made of X members thus .6X = number of boys. but we have 4/5 the number of boys now that 1/5 left so multiply both sides of the equation by 4/5
tawny hill
do you mean the equation x=0.6x+0.4x?
0.6x being boys and 0.4x being girls
wait
GOT DAMN
thx
.close
burnt cobalt
is the dot product -15?
calm coralBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
prisma mango
is the dot product -15?
Do not open multiple channels, you already have #help-35
burnt cobalt
Do not open multiple channels, you already have <#908075993779011615>
sorry, i closed the other one
<@&286206848099549185>
worldly bolt
<@&286206848099549185> i need help please i cant make a ticket its easy 8th grade work
i need help with this
burnt cobalt
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worldly bolt
just the first 2, maybe the third
adi what about this one ?
calm coralBOT
adi what about this one ?
worldly bolt
and thank you
weak rapids
do you know what vertically opposite angles mean?
calm coralBOT
just the first 2, maybe the third
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.
worldly bolt
.
weak rapids
?
forest walrus
adi what about this one ?
So far, which of the options do you think is correct?
calm coralBOT
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brittle gate
how would i do L
calm coralBOT
how would i do L
hard trout
You can compute them separately, then add
brittle gate
so 0 + 1
hard trout
careful, the second limit is $\lim_{t \to 3} 2f(t)$
potent lotusBOT
@hard trout
calm coralBOT
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hollow sphinx
calm coralBOT
foggy vessel
(Topic: Abstract Algebra)
I'm not sure what the question demands.
foggy vessel
I found that d_n will always have 2n elements and that half of those will be rotations and the other half reflections.
Not sure what the hint is about/
Surely I must be missing something.
calm coralBOT
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calm coralBOT
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clear delta
you invented a square angle
the angle in the bottom left isn't marked square
oh yeah it does mb
where do you get d = c + x?
ok where does "2d + 180 - d + d = 360" come from?
math often benefits from a pile of scrap paper hidden behind a few lines of solution
but i don't see where that came from hold on
you should write your logic out from start to finish and it'll be much easier to spot the error
calm coralBOT
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Available help channel!
rugged monolith
calm coralBOT
rugged monolith
@bronze adder What did you mean by just sub x = -t?
Sorry missed out the top of the image
potent lotusBOT
NEON
rugged monolith
Oh so when you integrate in the negative direction you get a negative value because dx is differentiating in respect to an infitesimmally small value of negative x?
I didn't know that
rugged monolith
Thank you
sorry yeah I worded it wrong
so the area between the curve and the x axis in y = |x| in the negative x direction
when you integrate it it is actually a negative value you get back
But since you have the limits the other way round
It becomes positive again
bronze adder
$\int_{-1}^0 |x|\dd x$
potent lotusBOT
NEON
rugged monolith
Yeah but when you calculate it
bronze adder
But since you have the limits the other way round
Ah I think I get what you mean
rugged monolith
and put the lower limit in, you get a negative value
rather than a positive value
bronze adder
and put the lower limit in, you get a negative value
Hmm?
rugged monolith
so when you take the negative value away you get a positive
rugged monolith
Sorry my internet on my pc just cut out
So with an integral of say just x
With upper limit 2 lower limit 1
When you calculate it by doing the antiderivative and plugging in 2-1
The 1 value is positive
but on the negative side, the 1 value is negative despite the area under 1 to 0 being positive
Did I explain that well?
rugged monolith
to calculate the area between -2 and -1 for the integral you do R1 - (R2+R1)
which would give you -R2 even though the area is +R2
but because of the dx being negative (the width) the negative negative R2 becomes positive
That is what I was confused about because I hadn't been taught it yet (only in year 1 a level maths) and it was on the cambridge admissions test
but your explanation was really helpful thank you
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ripe spade
you might need to reclaim a new channel
marsh bronze
accidentally closed, might want to open a new one- none is left
gaunt lichen
.reopen
ripe spade
no like send it in a new channel
calm coralBOT
Available help channel!
quiet island
Let n∈ℕ, prove that
calm coralBOT
Let n∈ℕ, prove that
quiet island
I think this problem requires to use the The Supremum Approximation Theorem and Archimedean Principle
If somebody could explain me how to use them it would be cool
ocean cypress
Expand both with binomial
agile shard
I would probably attempt to use induction
ocean cypress
Then most of the terms should cancel
quiet island
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@quiet island Has your question been resolved?
foggy elbow
Im trying to rearange this equation
calm coralBOT
Im trying to rearange this equation
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foggy elbow
<@&286206848099549185>
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foggy elbow
<@&286206848099549185>
if u have any questions that could ghelp u answer please dont hesitate
proper echo
from these two
youre asking how did we go from the first line to the second line in this picture?
foggy elbow
youre asking how did we go from the first line to the second line in this pictur...
yes
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subtle prism
Help
primal bear
,status
potent lotusBOT
subtle prism
yes I got x ≥ 7
calm coralBOT
.status
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Oh
subtle prism
subtle prism
This is the way I was taught
primal bear
that's perfect
subtle prism
do not trust chat gpt 💀
real
subtle prism
huh
potent lotusBOT
primal bear
oh fuck no equality?
subtle prism
maybe
subtle prism
I think it's tru
primal bear
no equality
subtle prism
yes yes
subtle prism
the vertical asymptote is at 4
primal bear
mhmm
subtle prism
ty
primal bear
yay
subtle prism
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calm coralBOT
primal bear
good luck with your sheet 🫡
subtle prism
I'm done 🫡
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remote mural
can someone help me solve 51? I got to graphing f and f', but I can't figure out how to solve for t.
primal bear
can someone help me solve 51? I got to graphing f and f', but I can't figure out...
uhh im not sure what you want
remote mural
uhh im not sure what you want
sorry i need help with (c)
finding the critical numbers of f in the open interval
of [0, 2pi]
for 51
primal bear
wait uh if memory serves me correctly
critical numbers are x for f'(x) =0 ?
so just take the derivative? with product rule and chain rule
and set it equal to zero
remote mural
and set it equal to zero
i did do that but i kind of got stuck
idk how to solve for t where -2 = t cot t
primal bear
uhhh im rusty with this stuff
hold on
i mean uhhh
actually beyong my paygrade maybe
im still gonna try though
well could you just write $\arccot(-2/t)$?
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Percy
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sterile mulch
Can someone explain me what highlighted in green?
calm coralBOT
Can someone explain me what highlighted in green?
sterile mulch
velvet osprey
oh this looks like bad typesetting
the top highlight is
[-2x_1 + x_2 , x_1 - 2x_2 , -2x_3]
sterile mulch
so why there are 2 of the green ones?
Because I’m trying to solve for this one
Would this be correct?
.close
karmic ridge
yo can someone help me find the second derivative?
calm coralBOT
yo can someone help me find the second derivative?
karmic ridge
i keep getting it wrong
velvet osprey
it doesn't like how unsimplified your thing is, probably
karmic ridge
with using reguar quotient rule i get this but its also wrong
karmic ridge
it doesn't like how unsimplified your thing is, *probably*
im not sure what it wants
clear delta
it wants you to not have complex fractions
protip everything in that fraction is even, as a first step
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karmic ridge
protip everything in that fraction is even, as a first step
simplified it to this, but its still giving me wrong
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karmic ridge
anyone?
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@karmic ridge Has your question been resolved?
karmic ridge
anyone
north plover
how to solve tan 2x = 1, 0<x<pi
calm coralBOT
how to solve tan 2x = 1, 0<x<pi
narrow ocean
Need help in these two questions idk what I’m doing wrong
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remote mural
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remote mural
$$a = \sqrt{3}(4-a)$$
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remote mural
shadow tendon
How did you get B
Also you dont seem to be solving for the correct region
If you want to do it with the region your solving for, I believe the actual answer would be 4-your a
remote mural
If you want to do it with the region your solving for, I believe the actual answ...
?
shadow tendon
?
It is the region bounded by the equations, which would be the upper left triangle
Seems like you are doing the lower right
remote mural
$$\frac{1}{2}a^2 = 8 - \frac{1}{2}a^2 ?$$
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shadow tendon
Yeah that should lead you to the right answer
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misty fern
help
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quartz breach
hi
quartz breach
$\frac{16\sin^{6}{x}-24\sin^{4}{x}+9\sin^2{x}}{16\cos^{6}{x}-24\cos^{4}{x}+9\cos^2{x}}$
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JoeTheLazy1
quartz breach
can we say its equal to tan^6 x or tan^4 x or tan^2 x?
velvet osprey
that does not look equal to any of those three powers of tan.
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eager jackal
Find the values of a and b such that when f(x) = x^4 − ax^2 − bx + 2 is divided by (x + 1)(x + 2) the remainder
is 0.
can someone help me with this?
fathom shuttle
if they can be divided with remainder 0, they are roots of the equation
Plug in the value of x and set the polynomial equal to 0
eager jackal
so -1 and -2 are the roots of the polynomial?
zealous spear
so -1 and -2 are the roots of the polynomial?
yes
hearty magnet
Hi could somebody help me out and check if my calculations are right?
calm coralBOT
Hi could somebody help me out and check if my calculations are right?
@hearty magnet Has your question been resolved?
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astral coyote
You seem to arrive at the correct answer
But I think you did way more then necessary, in fact you did something I cannot really follow, kind of surprised you end up with the correct thing
for instance, what are you doinh right here
I hope its clear what I mean, you just eliminate the denominator seemingoy arbitrarly, aswell as the limit
Then, you reintroduce the limit again, further down
Heres what I wouldve done (I think your calculation is correct apart from those things on the second line which idk what you were trying to do there), this is pretty much your thing but more concise:
$lim_{h \to 0^+} \frac{\sqrt{2h^2r-h^2}}h = lim_{h \to 0^+} \frac{h}{h} \sqrt{2r-1} = \sqrt{2r-1}$
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MTBO
hearty magnet
Okay thanks alot!
hearty magnet
@astral coyote could you check this out too?, i need to find the The defining quantity for f(xy)
<@&286206848099549185>
and f(xy) = \sqrt{2xy − x^2}
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hearty magnet
i need to find the The defining quantity for f(xy) = \sqrt{2xy − x^2}
, have i done it right
<@&286206848099549185>
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hearty magnet
i need to find the The defining quantity for f(xy) = \sqrt{2xy − x^2} have i done it right
?
calm coralBOT
i need to find the The defining quantity for f(xy) = \sqrt{2xy − x^2} have i don...
@hearty magnet Has your question been resolved?
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ionic cipher
is this correct ?
calm coralBOT
is this correct ?
hollow mural
is this correct ?
what are the chords or P and Q?
hollow mural
is this correct ?
mistake: your gradient of PQ. double check it
is m the gradient of PQ or the bisector?
you seem to have found PQ gradient as 1 and the bisectors gradient as -1
your method is all correct, i think your mistake was your gradient
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ionic cipher
you seem to have found PQ gradient as 1 and the bisectors gradient as -1
don't u have to flip it
as I got 1 before
but I did
-1 (1)
hollow mural
don't u have to flip it
yes, negative reciprocal
hollow mural
as I got 1 before
double check that
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graceful kelp
HELP ME PLEASEEEEEEEEEEE
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hollow mural
HELP ME PLEASEEEEEEEEEEE
you good?
graceful kelp
NO
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graceful kelp
PLS HELP ME
hollow mural
you seem a little stressed ngl
hollow mural
PLS HELP ME
tell me what it is
hollow mural
thank youuu
gradient is 1 for the bisector btw
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junior fern
tell me what it is
they need help in #help-39
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remote mural
i need help
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i need help
remote mural
what is 1+2
i know what 1+1 is but this is a whole other level of difficult
<@&286206848099549185>
pls help its 107% of my brade
*grade
glass heart
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nimble badge
Once you’ve established the successor function, 1+2 becomes a trivial extension of addition
But also quit trolling
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whole hinge
Also stop commenting in other people's help channels if you have nothing to contribute
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green steppe
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green steppe
why is this transformation not linear
glass heart
have you tried an example
green steppe
have you tried an example
wdym by an example
glass heart
the same thing I meant last time
green steppe
as in sub in arbitrary values?
glass heart
yes
glass heart
what is 3^2 -1
glass heart
ok, now what is (x,y)+(z,w)
green steppe
(4,6)?
glass heart
what is T(4,6) ?
glass heart
6^2-1 = ?
glass heart
fuck sry
ok
so T((1,2)+(3,4)) is (2,10,15)
and T(1,2) + T(3,4) is (0,3,0)+(2,7,8) = (2,10,8)
we notice that they are not equal
so T is not linear
green steppe
ooohhhhh
so if a transformation is linear then it should statisify T((x,y) + (z,w)) = T(x,y) + T(z,w)
right? @glass heart
glass heart
yes
green steppe
@glass heart
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green steppe
how can i show a matrix is a lin transformation
no wait
i worded it badly
part ii where it asks if T is a linear transformation
glass heart
check that T(S+U)=T(S)+T(U) and T(cS)=c T(S) for matrices S,U in V and scalars c
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distant hinge
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distant hinge
so uhhh, what in the world is going on here
i genuinely dont know, this is solving system of linear equations using matrices
and i know how to find the inverse of a 3 x 3, although slowly, but where does 4 2 and -3 come from
glass heart
normal matrix vector product
distant hinge
i have no idea what that is
glass heart
you know what the inverse of a matrix is but not how to multiply matrix times vector?
do you know how to multiply matrix times matrix?
kindred estuary
no way could i do it by hand
You're doing this process
Across the row, down the column
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