it’s merely coincidence that you also got dne
#help-10
oak aurora
yes would love to, do pm
oak aurora
just one last thing about why i say your final expression is about continuity of derivative is because your final expression is equivalent to this which isn’t generally true.
obtuse pebbleBOT
@thin thistle Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
why here is the remainder 2 and not 2/(x+2) ?
'synthetic division'
ahh, because its distributed in the quotient? just the way its used?
simplified?
the divisor is distributed in the quotient
to show remaineder and dividend
am i right?
er
damn i dont make sense rofl
does synthetic division method give a result where if there is a remainder it shows the result in the form of the divisor distributed across the quotient and remainder?
x - c form of divisor only right?
obtuse pebbleBOT
@timid silo Has your question been resolved?
pallid pine
where am i going wrong in solving #3
obtuse pebbleBOT
where am i going wrong in solving #3
obtuse pebbleBOT
@pallid pine Has your question been resolved?
solemn swallow
What would be the correct way of writing the fact that a Poisson distribution of parameter n is distributed like the sum of n Poisson distributions of parameter 1 ? Like what step here is wrong? I'm not sure I can write that: $$\operatorname{Poi}(n) \sim \sum_{k=0}^n \operatorname{Poi}(1) \sim n \operatorname{Poi}(1)$$
obtuse pebbleBOT
What would be the correct way of writing the fact that a Poisson distribution of...
warm shaleBOT
S
obtuse pebbleBOT
@solemn swallow Has your question been resolved?
rare root
**S**
Its better to represent it as $$Z = n_{1} + n_{2} + ... + n_{k}$$ \text{where} $n_{i}$ is $\operatorname{Poi}(1)$$
\text{ you cannot add distributions}
warm shaleBOT
peeledpotato
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
obtuse pebbleBOT
@solemn swallow Has your question been resolved?
solemn swallow
thank you
glacial bridge
Is this wrong?
obtuse pebbleBOT
Is this wrong?
daring rock
,rotate
warm shaleBOT
daring rock
@glacial bridge looks good to me
daring rock
original function was y=x^(2x) ?
glacial bridge
Yeah
daring rock
hm yeah none of those seem to be equivalent, but your derivative agrees with wolfram, and my own work
can you show the full context just to be sure?
daring rock
yes please
glacial bridge
daring rock
wait these choices are different now
glacial bridge
Oops wait
daring rock
and one of these is equivalent to what you've got
glacial bridge
The first one was from a different question, my bad
daring rock
all good
glacial bridge
and one of these is equivalent to what you've got
Which one?
I'm guessing d or e but I'm not sure 100%
daring rock
in your work, you chose to express 2ln(x) as ln(x^2)
but what if you left the 2 in front
daring rock
I mean after you differentiated
glacial bridge
2lnx^2+2?
daring rock
$$\frac{dy}{dx} = x^{2x}(\ln(x^2)+2)$$
can be instead
$$\frac{dy}{dx} = x^{2x}(2\ln(x)+2)$$
glacial bridge
Or wait 2lnx+2
warm shaleBOT
tatpoj
glacial bridge
Both 2s? The 2 in front and the +2?
daring rock
sure thing 👍
glacial bridge
So lnx^2 was wrong
daring rock
not wrong
just not the form they had as one of your choices
if this wasn't multiple choice, your original answer would do just fine
daring rock
yes
glacial bridge
🙏can't thank you enough
daring rock
no problem 👍 good work
obtuse pebbleBOT
@glacial bridge Has your question been resolved?
cobalt talon
can someone help me solving this?
obtuse pebbleBOT
can someone help me solving this?
@cobalt talon Has your question been resolved?
safe mauve
Where are you now in solving it?
sturdy barn
obtuse pebbleBOT
warm shaleBOT
G. Spark
edgy matrix
So in your problem, what is "d"?
sturdy barn
depth of the war in feet
sturdy barn
which is 32?
edgy matrix
sturdy barn
mhm
edgy matrix
$v=\sqrt(32 d) = \sqrt(32 * 8.5)$
warm shaleBOT
G. Spark
sturdy barn
hmmmm
sturdy barn
you said take the 2.5 and replace it with the d
edgy matrix
8.5?
I think it was replace "d" with the value for d, which is 8.5.
They gave you a formula with "d" in it, then they told you what value d was.
So put the value in for d and do the maths and you have your answer.
Can you do 32 times 8.5?
sturdy barn
oh
sturdy barn
yah on second
edgy matrix
geee
sturdy barn
272?
sturdy barn
how do i get that
edgy matrix
How did you get 32 * 8.5?
sturdy barn
my multiplying
sturdy barn
yah calculator
warm shaleBOT
G. Spark
sturdy barn
put 272 inside?
sturdy barn
16.4924225025?
warm shaleBOT
G. Spark
sturdy barn
so its 16.4924225025? the entire thing or just 16.4?
edgy matrix
It says to "round your answer to the nearest tenth"
So you need to shorten it a bit and round.
sturdy barn
ohh nice alright thanks
edgy matrix
Enjoy
sturdy barn
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torpid quiver
obtuse pebbleBOT
torpid quiver
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pure jungle
obtuse pebbleBOT
pure jungle
i dont get how they arrived to the end conclusion here
obtuse pebbleBOT
@pure jungle Has your question been resolved?
dapper heron
obtuse pebbleBOT
dapper heron
if the L is 2x why isnt the w =2y?
peak girder
Because x=y
And it's a half circle
If w=2y, it would either extend past the semo circle's boundary, or the circle would have to be bigger, and that would still yield a square, which is technically a rectangle but if we are going to line draw it's not a rectangle
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wide barn
Is possible to make a grafic with this?
f(x) = x² +4x -5
Because how the line can cross y at -5 if the minimum point is at (-2,1)
obtuse pebbleBOT
Is possible to make a grafic with this?
f(x) = x² +4x -5
Because how the line c...
teal turret
,w y = x^2 + 4x -5
teal turret
Min point isn’t (-2,1)
teal turret
The parabola crosses y = -5 if that’s what ur asking
wide barn
but how it can cross at -5 if the minimum is above it
steep scaffold
because -5>-9
teal turret
Min point isn’t (-2,1)
.
wide barn
oh
teal turret
Min is (-2,-9)
teal turret
Can’t rlly tell what that’s about
topaz tartan
obtuse pebbleBOT
topaz tartan
This is worded in a way where I cant understand
Ik I've probably been posting the same type of equations in but idk
opaque lily
there are 21 shots
sometimes the shots are counted as 2 points, sometimes they're counted as 3 points
those 21 shots ended up counting as 50 points
how many of those shots were 2 points and 3 points
topaz tartan
Alright
opaque lily
you can consider x as the quantity of 2 point shots and y as the quantity of 3 point shots
can you come up with any equations using those variables?
obtuse pebbleBOT
@topaz tartan Has your question been resolved?
hollow summit
hi i need help with this question
obtuse pebbleBOT
hi i need help with this question
warm shaleBOT
Stephen
teal turret
And u didn’t factor the top correctly
Find factors of -48 that add to -8
@hollow summit
obtuse pebbleBOT
@hollow summit Has your question been resolved?
west haven
obtuse pebbleBOT
west haven
Any help on this question at all would be graciously appreciated
remote skiff
Do you know what it means for a matrix to be orthogonal
west haven
yes
remote skiff
So what did you do from there
west haven
Well one of the typical methods is to multply the matrix by its transpose
as it well equal the identity
but this seemed like a hopeless indevor
remote skiff
Why is that
west haven
The resulting matrix does not appear to easily simplify to the identity
Are you maybe supposing there might be some approach to simplify it
remote skiff
Can you at least do the 1,1 entry of QQ^T
west haven
Yeah so that would be x^2+(y^T)(y^T)
remote skiff
can you simplify that further
west haven
Well I would like that to equal 1
remote skiff
Okay, so if you can do that, what is the problem for the other 3 entries?
west haven
Yeah I think that is were I am having the trouble
Part of me feels that this is the solution route but I am having trouble reducing the partitions
oh
oh
no
I was thinking I could use some form [cos, sin; sin, cos] but that would be circular reasoning
I think that the way that we derive y^T would tell us something about how we can find some (y^T)(y^T) so that x^2+(y^T)(y^T) = 1
remote skiff
I can't follow your train of thought
Your notation isn't quite right, but do you understand why the x^2 + (y^T)(y^T) you are writing equals 1
remote skiff
Using the correct notation, the 1,1 entry is the dot product of (x1, y^T) with itself, which is (x_1)^2 + <y^T, y^T> = x_1^2 + x_2^2 + x_3^2 + ... = 1
There is really nothing to this problem other than doing the matrix multiplication and being careful about what the notation means.
west haven
Okay cool! I get that!
remote skiff
The fact that you know that the 1,1 entry must equal 1, the 2,2 entry must also equal 1 etc
Is a huge hint and you only need to connect the dots
west haven
That makes sense
Let me try 2,2 real quick then
So 2,2 is <y, y> + (I - (1/(1-x_1))yy^T)^2
we know from <y^T, y^T> that <y, y> would be x_2^2 + x_3^2 + ... ?
This one seems much harder. Would I go about foiling out (I - (1/(1-x_1))yy^T)^2 or should I be approaching this differently? It feels like the ideas is that I see these parts holistically
It might be easier to do 2,1 first
x1y+y^T(I - (1/(1-x_1))yy^T)
Okay let me break this one down
yx_1 + y^T (I - ( 1 / ( 1 - x_1 ))yy^T)
yx_1 + y^T - ( 1 / ( 1 - x_1 ))yy^Ty^T
yx_1 + y^T - ((y<y^T, y^T>) / ( 1 - x_1 ))
(yx_1 - yx_1^2 + y^T + y^Tx_1 - y<y^T, y^T> )/ ( 1 - x_1 ))
`- yx^2 +yx + y^Tx + y^T - y<y^T, y^T> / (1-x)
Yeah definitely lost 😅
If I could get help on 2,1 I think I can manage the rest of this problem
If A = QQ^T, trying to find A 21
<@&286206848099549185>
obtuse pebbleBOT
@west haven Has your question been resolved?
west haven
omg I figured it out
This is the hardest questioned I have ever answered
but now I just have y^T-y
.close
midnight narwhal
obtuse pebbleBOT
west haven
the normal vector is c_1x_1 + c_2x_2 = 0 n=[c_1; c_2]
midnight narwhal
the normal vector is c_1x_1 + c_2x_2 = 0 n=[c_1; c_2]
ok so wb this
how come its not [4,-3]
i used [-4,3]
and got the same answer
west haven
idk off the top of my head the solution, but the normal vector would remain the same. In this case you would use the same strategy
obtuse pebbleBOT
@midnight narwhal Has your question been resolved?
proud belfry
how do i show these two are equal to each other
obtuse pebbleBOT
how do i show these two are equal to each other
median yacht
log(ab) = log(a) + log(b)
spark iron
obtuse pebbleBOT
spark iron
For part iv i have gotten only one condition
from the discriminant of Q(x) , also x+1/x greater than or equal to 2 for all values but i dont know what to do from there
tall wind
from the discriminant of Q(x) , also x+1/x greater than or equal to 2 for all v...
okay, are you saying that if u >= 2 then there are no real roots?
other than that, I believe you've found that if A and B satisfy A^2 - 4(B - 2) < 0 (discriminant) then R has no real roots, and hence P has no real roots
obtuse pebbleBOT
@spark iron Has your question been resolved?
tall wind
I don't have the best plan, but I'm thinking that if (A,B) is a point
and (0,-2) is a choice where there are real solutions
I'd fix B = 0, and find A such that there is only one real solution
something like that
spark iron
other than that, I believe you've found that if A and B satisfy A^2 - 4(B - 2) <...
yep
spark iron
okay, are you saying that if u >= 2 then there are no real roots?
if u is less than 2
tall wind
you can now use (0,-2) and this point you found to draw a line
then you want to find the point where the line intersects the boundary of the discriminant A^2 - 4(B-2) = 0
spark iron
cause from proofs i know x+1/x has two conditions
i think they focused on the second condition
that it is greater than or equal to -2
i can send solutions
this bit is just on the discriminant
the part i dont understand about this is why R(2) is 0
and that is how they found the line
tall wind
I believe they set u = 2 and plugged it into the line to see what happens at the boundary of the inequality u >= 2
the bit about it being equal to zero is a bit harder
obtuse pebbleBOT
spark iron
.reopen
obtuse pebbleBOT
✅
tall wind
what did they do?
spark iron
so
3 things x+1/x=-2
perfect square so double root
anything less than -2 will be not real
anything more will have double roots
so the boundry condition is -2 or 2
tall wind
yeah
spark iron
and then since the line represents the transition u could say
from real roots to double roots to complex roots
to find that transition you let R(plus minus 2) = 0
pluus 2 gives you the reflection of the line they want but they are only considering x>0
so youu find the -2 condition
so i think when A and B are on the line has double roots
cause the double roots is the minium value for it to have real roots
tall wind
so they pretty much assumed that R(2) = 0 and then solved for A and B - in which the solutions form an inequality (a line).
tall wind
it's an assumption
spark iron
yep
spark iron
alr thanks
spark iron
.close
obtuse pebbleBOT
tall wind
👍
obtuse pebbleBOT
Available help channel!
novel jewel
I need help with a numerical understanding of a problem
obtuse pebbleBOT
I need help with a numerical understanding of a problem
novel jewel
The topic is extrapolation.
We have given a dataset [xi] and [F(xi)]. We also have given that a(h) = centralised differentialquotient of F.
What we want to calculate is f(1) (the derivative at place 1). Also to be considered is that F is analytical
I am sort of lost on how to approach this
obtuse pebbleBOT
@novel jewel Has your question been resolved?
novel jewel
<@&286206848099549185>
obtuse pebbleBOT
@novel jewel Has your question been resolved?
sour ether
\frac{d}{dx}\left(\int _0^{x^2}:\left(\frac{u}{2u+3}\right)du\right)
obtuse pebbleBOT
\frac{d}{dx}\left(\int _0^{x^2}\:\left(\frac{u}{2u+3}\right)du\right)
sour ether
$\frac{d}{dx}\left(\int _0^{x^2}:\left(\frac{u}{2u+3}\right)du\right)
i hate this bot
$\frac{d}{dx}\left(\int _0^{x^2}:\left(\frac{u}{2u+3}\right)du\right)$
warm shaleBOT
HumanBot
alpine raven
skill issue
sour ether
Anyway
so i know we cant immedietley use fundamental theorem of calculus
however we can sub x^2 out for u
but when i set x^2 = u
and take derivatives of both sides
alpine raven
there is already u here, change it for smthing else
alpine raven
yes, then you have dt = 2x dx
alpine raven
replace that d/dx on the outside
hmm ?
sour ether
actually no clue if i can do that, but the syntax is right
remote skiff
You are thinking about this in the wrong direction. Do you know how to calculate $\frac{d}{dx}\left(\int _0^{x}\left(\frac{u}{2u+3}\right)du\right)$?
warm shaleBOT
JessicaK
alpine raven
You are thinking about this in the wrong direction. Do you know how to calculate...
well thats what he is asking
sour ether
well x instead
remote skiff
So call that integral $f(x) = \int _{0}^{x}\frac{u}{2u+3}du$
sour ether
but the issue for me comes because of the fact that i cant do that when the x is squared or perhaps a sin(x) instead
warm shaleBOT
JessicaK
remote skiff
Now find $\frac{d}{dx} f(x^2)$ using the chain rule
warm shaleBOT
JessicaK
sour ether
The problem is that i have 0 clue why or how we're able to do this
remote skiff
One part is the fundamental theorem of calculus, the other part is the chain rule.
sour ether
Like i know what the correct answer, but have my doubts id be able to implement it given a problem
replace u's with x^2 and multiply by derivative of the thing inside the f
remote skiff
The chain rule gives you that $\frac{d}{dx}f(x^2) = f^{\prime}(x^2) \frac{d}{dx} x^2$, the fundamental theorem of calculus tells you how to calculate $f^{\prime}(x)$ when $f(x)$ is of the form $f(x) = \int_{a}^{x} g(u)du$.
warm shaleBOT
JessicaK
sour ether
okay
okay
I think ive bruteforced my way to "understanding it"
take the x thats in some function
replace all the unknowns with it
take its derivative, multiply that by everything
.close
glass pilot
obtuse pebbleBOT
muted wraith
Using 2nd fundamental theorem what did I do wrong
should be tan - 1
muted wraith
should result in a constant
obtuse pebbleBOT
@glass pilot Has your question been resolved?
dapper verge
x^4-5x^3+8x^2-4x using this equation how would i get the complex roots because i know the real ones but dont know how to get the complex roots
obtuse pebbleBOT
x^4-5x^3+8x^2-4x using this equation how would i get the complex roots because i...
slim lake
dapper verge
i have nothing
im confused on wehre to starr
because since there is only x values i dont know how to start the equation
novel knoll
All its roots are real roots
dapper verge
but i have to find the roots
novel knoll
You said you have found the real roots
Those are all the roots, so what are you asking?
dapper verge
to find the complex roots
novel knoll
All its roots are real roots
.
novel knoll
Factor the polynomial with the roots you found then
dapper verge
actually i have a question
for rational roots theorm since my equation only has x values would i need to factor out a x in order to get my constant term?
novel knoll
Yes if you want to use that
dapper verge
but what would i do with the remaining x value afterwards?
dapper verge
ohh ok ok
so far i have 0 and 1 and 2
would it be possible to check if these are the correct answers?
i am unable to find the last real root
nimble gulch
obtuse pebbleBOT
nimble gulch
so my answer is correct i checked it. but my question is that is this series still telescopic?
because in wikipedia it says that we should have left only first and last term and all the others should cancel. but i have left here first 3 and last 3 terms
but why wikipedia says that we should have left only two terms?
after cancellation
final thunder
Idk I don’t think we really have a formal definition for telescoping series 
Terms cancel 
twin sapphire
filga any telescopic sum with cancelling terms further like cancelling every two or three terms can be re arranged
into a sum where the terms cancel with the next ones
by grouping successive terms
,w partial fraction 3/(x(x+3))
warm shaleBOT
twin sapphire
do here thats your term un
silver wolf
can anyone help me with this question
obtuse pebbleBOT
can anyone help me with this question
silver wolf
<@&286206848099549185>
astral nimbus
Range is the difference between the highest value and lowest value
Apply that logic here, and you should get 17-5=12
Answer is 12, option C
obtuse pebbleBOT
@silver wolf Has your question been resolved?
austere hound
Range is the difference between the highest value and lowest value
Apply that lo...
!nosols
obtuse pebbleBOT
Range is the difference between the highest value and lowest value
Apply that lo...
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.
Available help channel!
dreamy pulsar
obtuse pebbleBOT
silk trout
Differentiate it and plug in x = 1 and you’ll have the gradient of the tangent at that point
Gradient of the normal is the negative reciprocal of the gradient of the tangent
Plug x = 1 into the original equation for the y-coordinate and use y - y1 = m(x - x1) to get the line equation
dreamy pulsar
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rocky anvil
Can anyone explain to me that how to get this answer?
Question :(a+b)(b+c)(c+a)+abc
Answer: (a+b+c)(ab+bc+ca)
obtuse pebbleBOT
Can anyone explain to me that how to get this answer?
Question :(a+b)(b+c)(c+a)...
rocky anvil
The solving steps that given by the book
candid rock
it's just a lot of expanding brackets
the final 2 lines are factorising the polynomial ka^2 + la + m for k=b+c, l=(b+c)^2+bc, m=bc(b+c)
which is vile but
rocky anvil
i dont understand the steps
candid rock
can you expand (a+b)(c+a)
timid silo
The solving steps that given by the book
Here 1st of all they multiplied (a+b) and (c+a)
Or u can say (a+b)*(a+c)
We get: a^2+ac+ab+bc
rocky anvil
ok
timid silo
The solving steps that given by the book
Then since I din't multiply (b+c)
timid silo
We get: a^2+ac+ab+bc
In this expansion I'll try to bring in b+c
Keeping this in mind we can synonomously express it as:
rocky anvil
In this expansion I'll try to bring in b+c
oh ok. is it like (a^2+ac+ab+bc)(b+c)
ok its like take c from (ac+ab) right?
timid silo
So it's basically all like taking commons
rocky anvil
i dont understand the second =
(b+c)a²+{(b+c)²+bc}a+bc(b+c)
obtuse pebbleBOT
@rocky anvil Has your question been resolved?
rocky anvil
why suddenly have 4 (b+c) at the forth =
tawny kite
hello, to find the critical points of a two variable function, you do the partitial derivatives of fx and fy, but you would also do this for rational functions...
obtuse pebbleBOT
hello, to find the critical points of a two variable function, you do the partit...
tawny kite
Im pretty sure
I dont think it makes a difference, then you can just use quotient rule or product..
lol yes im sure thats right
im gonna stay here tho in this channnel
tardy epoch
im gonna stay here tho in this channnel
What's your question
tawny kite
nvm i can just leave
I know for sure i'll have other questions tho
for now, nothing
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lilac verge
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@lilac verge Has your question been resolved?
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@lilac verge Has your question been resolved?
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@lilac verge Has your question been resolved?
fathom flicker
obtuse pebbleBOT
fathom flicker
I was hoping someone could check my proof for this problem. There are more parts, which I will be posting below. Tag me if you have any feedback or questions or need clarification from me about any of it.
obtuse pebbleBOT
@fathom flicker Has your question been resolved?
obtuse pebbleBOT
@fathom flicker Has your question been resolved?
obtuse pebbleBOT
@fathom flicker Has your question been resolved?
obtuse pebbleBOT
@fathom flicker Has your question been resolved?
fathom flicker
<@&286206848099549185>
warm shaleBOT
Austin
fathom flicker
S is clearly a subset of Rn and f is >=0 and integrable on every compact subset of S, so I think this rewrite into an improper integral is fine, but I was wondering if I was applying this theorem correctly at that step.
Another point of contention for me was if I was applying Arzela's DCT properly.
This is a minor issue, because my professor said it could just be claimed that this is the supremum in order to apply monotone sequence theorem, but I tried showing this was the supremum and I couldn't. If anyone knows a way that is not too complicated, it might be nice to know
fathom flicker
And really, I do not need help with the integration I think. My end result was correct, so I am not that worried about it. No theorems or stuff here. Mainly I need help with what I listed above.
obtuse pebbleBOT
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dense geyser
obtuse pebbleBOT
dense geyser
Help me!
inland matrix
What have you tried?
dense geyser
What have you tried?
i replaced sin theta and cos theta by 1/root2 and tan theta by 1 in the expression
inland matrix
Ah
But why did you take the positive values for cos and tan?
The range of θ is from pi/2 to pi
i.e., second quadrant
inner stratus
Let $\varphi : \mathbb N^\longrightarrow \mathbb N^ \
\frac{\varphi(n)}{n} \to l \in \mathbb R$
Find $l$
In the first step :
Let $l<1$
Let $q = \frac {1+l}2$
Then for a certain $n_0$, $\forall n \in \mathbb{N}, \ n>n_0 \implies |\varphi (n)| < qn$
Why is that ?
obtuse pebbleBOT
Let $\varphi : \mathbb N^*\longrightarrow \mathbb N^* \\
\frac{\varphi(n)}{n} \t...
warm shaleBOT
Azenx
inner stratus
$\varphi$ is a bijection btw
warm shaleBOT
Azenx
eternal thistle
$\dfrac{\phi(n)}{n}$ is constant?
warm shaleBOT
tales
eternal thistle
Or the limit is l
inner stratus
Only the limit
But from a certain rank it would be bounded since it's convergent
by l
But since it would be bounded by l and l<1, it means that (l+1)/2 > l and so it's also an upper bound
hmmm
yea i see now
thx
.close
void sky
How do you find F and E
I have all the other letters
A= (-1,0)
B= (0,1)
C= (3,0)
D= (0,-3)
G= (1,0)
Functions:
f(x)= x^2 -2x-3
g(x)= -x^2+1
obtuse pebbleBOT
How do you find F and E
I have all the other letters
A= (-1,0)
B= (0,1)
C= (3,...
eternal thistle
Assuming they are parabolas
void sky
They are yes
void sky
Yes
eternal thistle
Intersect them to find F
void sky
I did fx=gx, still can’t find one correctly
eternal thistle
show work
void sky
You literally can’t do it, you’d have x^2-2x-3= -x^2+1
Then you’d have 2x^2-2x-2= 0
Then you’d divide by 2, so 2(x^2 - x - 1) = 0
How would you find X?
What
eternal thistle
It has solutions
void sky
How did it get that???
eternal thistle
Quadratic equation
void sky
and how do you solve that???
eternal thistle
You know the quadradic formula
void sky
I might know it in my language what is it like the formula
I don’t know what it’s called in english, but is it like x1,2= blah blah blah?
eternal thistle
show work
void sky
I didn’t get what the bot got at all
a=2
b=-2
c= -2 right?
Or is it 1 1 and -1
Ignore the other stuff
eternal thistle
Seems correct
void sky
Square root of 20 is 4.4444 🤷♂️
void sky
You still have the same thing
And I don’t think my teacher would send something this long
void sky
Made x^2 become + x^2 then turned the 1 into -1 to the other side
Oh wait
No fucking way
I’ve been wasting this much time
I forgot the -1
nvm thanks for your help
Hold on, but now how would you find E?
.close
thin thistle
can someone explain exactly what happened here
obtuse pebbleBOT
can someone explain exactly what happened here
thin thistle
heavy seal
Took log
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
h(x)=4x squared -5x +2 find the zeros of the function
obtuse pebbleBOT
h(x)=4x squared -5x +2 find the zeros of the function
empty cypress
that's a nice function!
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
timid silo
using the quadratic formula X= -b plus or minus the square root of b squared - 4ac/2A
final thunder
so do it then 
warm shaleBOT
Pure
grizzled eagle
How can I solve this system depending on the values of real values a and b? As I understand it, I first need to find the range of the coefficients matrix A, which in this case is a symmetric matrix.
obtuse pebbleBOT
How can I solve this system depending on the values of real values a and b? As I...
grizzled eagle
But I'm not sure how to solve $x^4 - 2(a^4+a^2+1)x^2 - 8a^3x + (a^8-2a^6-a^4-2a^2+1) = 0$
warm shaleBOT
Oppenjaimer
tame narwhal
how are you getting x^4 and x^2 terms?
warm shaleBOT
Oppenjaimer
grizzled eagle
Though if anyone knows of a better way of doing this, it'd be great to know.
obtuse pebbleBOT
@grizzled eagle Has your question been resolved?
obtuse pebbleBOT
@grizzled eagle Has your question been resolved?
obtuse pebbleBOT
@grizzled eagle Has your question been resolved?
grizzled eagle
<@&286206848099549185>
primal ledge
Have you tried with gaussian elimination?
However I think you should use the fact that A is symmetric in some way, but in this moment i cannot figure it out
grizzled eagle
Same here. The only thing that comes to mind is the fact that the rank of a symmetric matrix is the number of non-zero eigenvalues, but that gets me nowhere because I'm trying to solve that ugly equation in order to find said values.
primal ledge
Another thing I can see is that if you sum all the coloumns of A you obtain 1+a+a^2 is an eigenvalue
you know that the coloumns are the images of the basis
primal ledge
Another thing I can see is that if you sum all the coloumns of A you obtain 1+a+...
tell me if you didn't understand this
So you have 1 of the four solution to your weird equation, but it doesn't help that much i think
Mhh.. I'll think about it
grizzled eagle
That's something I hadn't thought of doing, but yeah, makes a lot of sense. Perhaps I can now get rid of three of those 1's and turn the thing into a 3x3 determinant, then keep going from there.
Thanks a lot, by the way.
primal ledge
You're welcome
warm shaleBOT
Oppenjaimer
grizzled eagle
Another thing I can see is that if you sum all the coloumns of A you obtain 1+a+...
This made all the difference, thanks again.
.close
buoyant lance
Question, what error did I do?
obtuse pebbleBOT
Question, what error did I do?
versed pier
,w calc integral of sin^3(2x)
warm shaleBOT
buoyant lance
inner stratus
Question, what error did I do?
you could write sin^3(2x) as a function of cos and sin
further
To get rid of the squares
buoyant lance
you could write sin^3(2x) as a function of cos and sin
Wait... I guess I could've just wrote it as sin(2x) * sin(2x) * sin(2x)
which yields us 8 ( cos(x) * sin(x))^3
because its the same as:
(2cos(x)*sin(x)) times itself three times... am I wrong?
prime magnet
any idea how to do this?
obtuse pebbleBOT
any idea how to do this?
prime magnet
i guess its not gaussian elimination
obtuse pebbleBOT
@prime magnet Has your question been resolved?
prime magnet
<@&286206848099549185>
tame narwhal
you're supposed to do it by hand???
prime magnet
i guess
tame narwhal
row reduction is probably the way to go... it'll be ugly though
tame narwhal
it is the answer
tame narwhal
ask your prof then, I dunno. it's not like inverting the matrix would be any easier
tame narwhal
should be, yeah
prime magnet
prime magnet
oh my god i thought it knows that its multiplication
yeah its good now
but still how am i supposed to write 30 lines of row operation down when other exercises are around 3-4 rows
tame narwhal
ask your prof
timid silo
Question about differential equations and undetermined coefficients
obtuse pebbleBOT
Question about differential equations and undetermined coefficients
timid silo
In here did we assume for 4e^x that its Cx^3e^x so that we dont have a repeat of Ce^x 3 times for the y' y" and y"' ?
rain forge
what do you mean by that, it's your particuliar solution ?
rain forge
so what do you mean by "we don't have to repeat 3 times" sry don't understand
timid silo
So the derivative of 6e^x would be 6e^x right?
rain forge
yes
timid silo
If we don't add the x^3 factor, then we'd have y''=y"' since the Ax term would be gone
is that why we added the x^3?
Because the general rule states that if g(x)=e^ax then we assume Yp=Ae^ax
rain forge
you want to know why there is a x^3 in the particular solution
timid silo
Yeah
rain forge
sry don't know maybe try to find a particuliar solution of this without the supposition and see if you have the x^3 at the end
compact snow
How do I do this?
obtuse pebbleBOT
How do I do this?
compact snow
How do I do this?
crisp zephyr
,rotate
warm shaleBOT
compact snow
I got y = -1 when x = -2 and x = -1 when y = 0
Then I graphed it, but I’m not sure if it’s right
novel sigil
I got y = -1 when x = -2 and x = -1 when y = 0
its better to get x = somthg, then get y
its easier
tame narwhal
that's what he's doing...
tame narwhal
I got y = -1 when x = -2 and x = -1 when y = 0
not correct
novel sigil
I got y = -1 when x = -2 and x = -1 when y = 0
u cant get y = -1
cz u have an absolute value
compact snow
Yh don’t I have to reflect it after?
tame narwhal
what do you mean "reflect" it?
novel sigil
what do you mean "reflect" it?
yea i didnt get that also
compact snow
Turn the -1 into a 1, so instead of it being (-2, -1) it turns into (-2, 1)
compact snow
-4
tame narwhal
what is |-4|
compact snow
4
tame narwhal
what is 4 + 3
compact snow
7
tame narwhal
so f(-2) = ?
compact snow
7
tame narwhal
yes
compact snow
So -2, 7 will be the first point?
tame narwhal
yes, if you're going to do it point by point in order
novel sigil
u calculate the x-2, then u make it positive cz of the absolute value
compact snow
yes, if you're going to do it point by point in order
And then how do I get the second point
novel sigil
And then how do I get the second point
u choose randomly
tame narwhal
no? why randomly?
novel sigil
for x between-2 and 4
novel sigil
no? why randomly?
he can choose whatever x between -2 and 4
tame narwhal
yes, why random? why not just move to -1
novel sigil
for x = -2, -1, 0, 1 ,2 ,3, 4
tame narwhal
or just recognize that the function is equivalent to |x| shifted to the right and up
tame narwhal
you will never have y = 0
novel sigil
So is this what it should look like
u cant have y = 0 cz u always add 3 to the function
so y = |x-2| + 3.. even if the thing in the absolute value was null, there is the +3 there
compact snow
My teacher taught me that we should first remove the modulus sticks, find x when y = 0 and y when x = 0 and that’s what we should graph, unless it’s not negative because then we have to use a x value that makes y negative
At least that’s what I understood
novel sigil
My teacher taught me that we should first remove the modulus sticks, find x when...
u cant remove then unless ur sure that the thing inside the absolute value is positive
so when x>=2, u can remove them and write |x-2|=x-2
but when x<2, |x-2| = 2-x.. cz as we know, the absolute value is always positive.. so lets take an example.. if we have x = -3 .. |-3-2| = |-5|
compact snow
For example
novel sigil
and as the absolute value make the thing inside it positive, |-5| = |5| = 5
novel sigil
For example
yes?
compact snow
tame narwhal
My teacher taught me that we should first remove the modulus sticks, find x when...
that's wrong
obtuse pebbleBOT
@compact snow Has your question been resolved?
compact snow
@tame narwhal I’m still a bit confused, can I just find two points, connect them, draw the line and then erase the part that goes under the x-axis and do the v shape?
tame narwhal
it is not a straight line, so you need more than 2 points
compact snow
He taught us that we can get the two points, draw a straight line, then the part of the straight line that goes under the x axis, we just erase and complete the V
tame narwhal
that is wrong
obtuse pebbleBOT
@compact snow Has your question been resolved?
fiery condor
Can anyone tell whether c00 is first category in l2 or not?
obtuse pebbleBOT
Can anyone tell whether c00 is first category in l2 or not?
final thunder
context?
fiery condor
I had question of true false that whether, if Y is a vector sub space of l2 then if Y isn’t same as l2 implies Y is first category subset of l2
Since as if it is not same then surely the interior is empty
final thunder
Yes it would be true i think
fiery condor
But I can’t conclude whether it is meagre or not
The question is negatively marked for wrong answer
I have exam tomorrow so I’m preparing his previous true false questions
final thunder
Why can't you conclude whetehr its meagre or not. What is your definition of first category.
fiery condor
If it can be written as countable union of nowhere dense sets (empty interior of closure)
final thunder
Yes and Y itself is nowhere dense since its a proper subset of L^2
fiery condor
No only Int(y) is empty
Can’t conclude about its closure
Actually I think my example will not work
The c00
As it is dense in l2 and so the closure is l2 itself so not nowhere dense
final thunder
Yeah I think youre right Y is not necessarily close 
fiery condor
Yeah that’s the point ai chose open subset of l2
final thunder
As it is dense in l2 and so the closure is l2 itself so not nowhere dense
wait what do you mean by this
nvm makes sense
fiery condor
Any other open subsets of l2?
obtuse pebbleBOT
@fiery condor Has your question been resolved?
obtuse pebbleBOT
@fiery condor Has your question been resolved?
obtuse pebbleBOT
@fiery condor Has your question been resolved?
quick verge
obtuse pebbleBOT
quick verge
im not quite sure how to integrate it
i think i have to use u subsituation but not sure how
i got 4/3x^3 + 3/2x^2 + 2√x as the anti-derivative but i dont think that correct
edgy matrix
Maybe try that again.
edgy matrix
Which did you try?
I haven't done it to see which is easiest, sorry.
Was it something like this?
obtuse pebbleBOT
@quick verge Has your question been resolved?
obtuse pebbleBOT
@quick verge Has your question been resolved?
tame narwhal
you can just divide by sqrt(x), right?
rigid fog
kinda need help with the bounds
remote skiff
This is just a square, what part of the bounds are you having trouble with
rigid fog
so one of the bounds will be from 0 to 1
remote skiff
yes
rigid fog
okay whats the other
remote skiff
If you know one I'm not sure what is making you uncertain about the other
remote skiff
Yes
rigid fog
might jus thave a math error then
obtuse pebbleBOT
@rigid fog Has your question been resolved?
fallen inlet
How do o find the exponential growth factor if there are no numbers ?
obtuse pebbleBOT
How do o find the exponential growth factor if there are no numbers ?
azure anchor
write out a basic exponential growth function, sub x for each point's x, then sub y for each y. you could even do this in your head if you know the function well.
obtuse pebbleBOT
obtuse pebbleBOT
✅
azure anchor
really? what was (0, y) for y?
fallen inlet
I’m just beginning to get into this stuff so the k and pt)) stuff doesn’t make sense
quick verge
you can just divide by sqrt(x), right?
wdym
azure anchor
if you click the points it doesnt show?
azure anchor
well uhh im glad its right. strange to me though
fallen inlet
Yea we are beginning this topic so it’s super simple rn
No complicated
But thx!
I have one more question
A problem tells me there 1000 dollars and increases 3% each year. What amount will be in 3 years?
I’m not so sure but I multiplied 1000 by 1.03 three times
It’s wrong
How should I do this?
azure anchor
what level math is this
azure anchor
not judging, do you have the formula they give you?
fallen inlet
I missed a day in school when we were doing percents 😞😞😞😞
No
They just tell the story problem
One is linear problem and the other is exponential
azure anchor
can you post the actual problem from the book?
azure anchor
Simple Interest Formula: $$I = Prt$$
Where
$P = $Principal (Initial Value)
$r = $Interest rate
$t = $time (years, months, etc.)
warm shaleBOT
b0ngl0rd
