$$5x^3 = 535 - 4y^2$$
$$5x^3 - 5*27 = 400 - 4y^2$$
$$5(x^3 - 27) = 4(100 - y^2)$$
$$5(x-3)(x^2+3x+9) = 4(10-y)(10+y)$$
#help-27
haughty cloak
I see where that came from
It wont work for all equations though, would it?
woven radishBOT
musava_ribica
finite shore
You may be able to apply this technique to similar problems
obtuse slate
im having trouble with the first part. did i mess up somewhere?
devout snowBOT
im having trouble with the first part. did i mess up somewhere?
@obtuse slate Has your question been resolved?
obtuse slate
<@&286206848099549185>
timber pebble
im having trouble with the first part. did i mess up somewhere?
this period looks wrong
try plotting it
timber pebble
its not 3?
i dont think it gives you the right period
just look at it
,w plot cos(3x)
woven radishBOT
obtuse slate
it's stated on the instructions
but it didnt give the frequency so i cant find the period
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strange basin
Hey
devout snowBOT
devout snowBOT
Available help channel!
marsh bane
devout snowBOT
marsh bane
what did u guys get?
marsh bane
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stray lark
Best way to derive y-2x/2y-x
devout snowBOT
Best way to derive y-2x/2y-x
stray lark
I was thinking of using quotient rule, but could it be easier with the product rule?
Idk if this is useful but it's the second derivative ^^
narrow plank
With respect to what variable?
copper mango
Best way to derive y-2x/2y-x
you cant differentiate that as it's not an equation
stray lark
With respect to what variable?
I guess x
narrow plank
If you assume y is a function of x, which is usually the case, you can take that derivative
d/dx (y - 2x) / (2y - x)
stray lark
y' = y-2x/2y-x
stray lark
If you assume y is a function of x, which is usually the case, you can take that...
with the quotient rule I guess?
copper mango
is it that or is it what you're trying to type?
narrow plank
y' = y-2x/2y-x
This isn't the same as what you originally posted
What is your question?
copper mango
(y-2x)/(2y-x) or y-2x/2y-x?
stray lark
This isn't the same as what you originally posted
I'm trying to find the derivative of y' = y-2x/2y-x
I already derived the original equation once
narrow plank
oh ok
narrow plank
Just quotient rule
stray lark
I see
narrow plank
Yes
stray lark
since everything is with respect to x
narrow plank
d/dx y = dy/dx = y'
stray lark
Would this be implicit differentiation
wait no
this is just normal differentiation
I swore you used power rule before, when you saw y it would become 1?
Wait am I losing it
stray lark
d/dx y = dy/dx = y'
was it always like this?
stray lark
I see
I might be losing it lol
how does the power rule apply then
does it have to be with respect to the variable that uses the rule
e.g. d/dx x^2 will be 2x
can it work for something like d/dx y^2?
stray lark
d/dx y^2: *Chain Rule!*
I see
I am losing it indeed
I mean technically you charin rule that too
chain*
@narrow plank How many chain rules would I need for e^x * cosx
narrow plank
None
stray lark
fr?
narrow plank
d/dx e^x cos x doesn't use chain rule
narrow plank
$\frac{d}{dx} e^x \cos x$
woven radishBOT
Shen
stray lark
would it be product?
narrow plank
It'll give you steps n stuff
narrow plank
stray lark
Oh I never learned the exponent rule
cloud oasis
devout snowBOT
bold prism
do you how to distribute the negative sign?
cloud oasis
No tbh im not the sharpest tool in the shed
bold prism
Alright so when you have a negative sign to be distributed, you flip the signs inside the bracket
so forexample if you had
a - (b + c)
it'd become a - b - c
or if you had a - (b - c)
cloud oasis
oh ok I see
cloud oasis
so itd be come - x-6 ?
cloud oasis
oh ok I get then last thing is if you add a number with a variable to a number without what happens?
bold prism
can you give an example
cloud oasis
7a + 9
cloud oasis
oh ok I get thankyou very much
bold prism
cloud oasis
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devout snowBOT
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Available help channel!
marble hare
devout snowBOT
marble hare
jolly mango
I question the legibility of your scratch paper
ivory kayak
Yeah this is pretty rough lol
marble hare
silk plank
Hi everyone
marble hare
I just did break numerator to x²+1+2
silk plank
Could somebody please help me
silk plank
A car dealership hires Anne to wash cars. She is paid
$28 per day plus $6 for every car she washes. Anne shares the money equally
with a friend who assists her. After five days, Anne’s share of the pay is $130.
How many cars did Anne and her friend wash?
marble hare
Bruh
jolly mango
I'l help him in dms
marble hare
I'l help him in dms
Who will help me then
jolly mango
@ivory kayak
ivory kayak
Who will help me then<:pandaHmm:858834883760750602>
What're you stuck on
jolly mango
sorry
marble hare
Ohk
marble hare
Here
ivory kayak
Don't know ow what to do next?
ivory kayak
Do you know partial fraction decomposition
marble hare
Ik but this question is given in the chapter starting when it's not introduced yet so maybe some other method would be there too to solve this..
ivory kayak
What section is it in
marble hare
I can't even do long division, can't complete the square, no identity is applying which i can think of..
ivory kayak
I don't really see any useful substitutions
marble hare
What section is it in
First exersise
2 question of the first exercise
2 question of the chapter you can say.
ivory kayak
You cannot have learned nothing
marble hare
Like i know, but not according to book
ivory kayak
What methods has the book given so far
marble hare
Just solving by basic factorising the numerator, long division, identities of cubes and squares...
ivory kayak
Yeah, not sure what it's looking for of not PFD, sorry
marble hare
Yeah, not sure what it's looking for of not PFD, sorry
Oh.. its just adding and subtracting 2x² until numerator just becomes 1+x² ...
Anyways... Thanks for helping 
.close
lime linden
If I roll two dice what's the probability of both being six given I know one is a six
devout snowBOT
```If I roll two dice what's the probability of both being six given I know one ...
lime linden
this would be 1/6 right?
since the P(D1 = 6) = 6/6
we 100% know the first die is a 6
but the P(D2 = 6) = 1/6
since there is 1 six in it, and the other die goes up to six
since there is one six in a die, and the die goes from one thrugh six
copper mango
Yes
The sample space is reduced to 1 die rolling a 6
Since P(1st is 6 and 2nd is 6)=1/36 and P(1st is 6) is 1/6
You get 6/36=1/6
lime linden
k
golden quiver
devout snowBOT
golden quiver
Havent done maths in a long time trying to re-learn stuff.
I've attempted rearranging the algebra and substituting to get a quadratic equation but have been struggling
as it wants the quadratic expressions in terms of d only
devout snowBOT
@golden quiver Has your question been resolved?
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patent harbor
If I have 2 matrices, matrix A = for example a 3x4 matrix, and matrix B is a 1x1
lets say B = [5]
If I have A * B, can I just write A * 5?
Question 2: Does x * y = y * x also count for matrices?
devout snowBOT
If I have 2 matrices, matrix A = for example a 3x4 matrix, and matrix B is a 1x1...
patent harbor
Ooh true I forgot, my bad
rustic kiln
You can multiply A by a scalar of 5 and write it as 5A though yes
patent harbor
okay
rustic kiln
Second question, also no
AB isn't guaranteed to be equal to BA
AB could be valid and BA could be invalid in the same way, too
patent harbor
Okay thanks for answering, so [5] = 5 right?
rustic kiln
[5] is a matrix, 5 is just a scalar
Matrices can't just be treated as normal numbers
So [5] =/= 5
patent harbor
Okay thanks a lot!
rustic kiln
No problem
patent harbor
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final pivot
Hello guys. Im trying to find limit of 2x^4 / (x^2 - 3) where limit goes to infinity. I understand that the answer is 0, but im trying to understand how is this possible? I devide all elements by highest power element which in this case is x^4 and i get (2x^4 /x^4 ) / (x^2/x^4 - 3/x^4) where we get after clearing stuff 2/(1/x^2 - 3/x^4) which is 2/0 and its undefined??
devout snowBOT
Hello guys. Im trying to find limit of 2x^4 / (x^2 - 3) where limit goes to infi...
final pivot
1/x^2 is 0 when x goes to infinity and 3/x^4 is also 0 so i get 2/0.... Im confused what did i do wrong?
<@&286206848099549185> I appreciate all the work and help you guys are putting into this community.
winter patrol
the answer isn't 0
tawdry trellis
Yes, it is infinity
winter patrol
also you should be dividing based on the highest power in the denominator
final pivot
dividing based on the highest power in the denominator not like numerator together?
winter patrol
you might be misrepresenting them
infinite limits of rational functions can be determine by looking at the leading terms of the numerator and denominator without having to do this sort of division
final pivot
is this correct?
tawdry trellis
Did you type your question correctly?
Your question follows the rule (2), so why do you believe the result to be 0?
final pivot
Because one online calculator showed it so i tripped out
winter patrol
which online calc?
final pivot
trying to find it right now, i checked like 20 to show me steps but each one wants registration
seems like it tripped me out
winter patrol
for case 1), you can consider the ratio of leading coefficients directly
for case 2) you may need to be careful of signs of leading coefficients as that will affect whether you have + or - inf
indigo abyss
how do i solve this
final pivot
for case 1), you can consider the ratio of leading coefficients directly
for cas...
ty
devout snowBOT
Available help channel!
visual lagoon
devout snowBOT
muted reef
just start the series, and then make a judgement
visual lagoon
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Available help channel!
devout shadow
So this is more of an applied maths question but I think it’s still relevant asking in the maths server. How do I go about formulating this differential equation( btw the mass of the sphere is 2kg, the spring constant is 50, the natural length is 0.3m and it is at equilibrium when the spring is 0.7 m long, it said all this in a previous part)
devout snowBOT
So this is more of an applied maths question but I think it’s still relevant ask...
devout shadow
So in terms of the direction of forces, the weight and the resistive force have to act in the same direction right?
And then you have the tension from hooke’s law
copper mango
can you take a better picture?
devout shadow
But how do I express the extension in terms of algebra?
Yeah sure gimme a sec
9bii) is actually fine as that’s just solving a bog standard 2nd order ODE
It’s just the formulation for me which is problematic
As it says ‘show that’
copper mango
ok so yeah, $\sum F=ma$, where we take everything scalar since it's 1D motion
woven radishBOT
Mosh
devout shadow
Yep
devout shadow
So in terms of the direction of forces, the weight and the resistive force have ...
So is this correct then in terms of the sign of the forces
copper mango
so $mg-20v-kx=ma$ no?
woven radishBOT
Mosh
devout shadow
But why is it -20v?
copper mango
gravity is downward, and if the object moves in +x (downward), then the oil and spring forces act up
devout shadow
Isn’t the object moving up?
devout shadow
It says it’s released at rest from the base of the bucket
devout shadow
So surely it would just move up initially, so initially the resistance will be acting downwards in the same direction as the weight
To oppose the motion
So I don’t really get how it’s +10dx/dt
copper mango
,calc 10^2-4(1)(25)
woven radishBOT
Result:
0
so yeah, it never oscillates, so yeah should only go up
oh right
$F_s=-kx$ but you're travelling in $-x$
woven radishBOT
Mosh
copper mango
so the negatives cancel
I believe, you might be better off asking this in the physics server lol
devout shadow
I did and they recommended me asking this is the maths server haha so I’m kinda stuck
Between a rock and a hard place
devout shadow
Alright I’ll try and figure it out; thanks for the help anyway
devout snowBOT
@devout shadow Has your question been resolved?
devout snowBOT
@devout shadow Has your question been resolved?
marsh linden
Can you please send the full question
I’ve done further maths a level
so I’ve seen these typa questions
@devout shadow
It’s just further maths a level,
not a physics question really
but you missed out the actual question
so there is a lot of info yet
that needs to be sorted
If you see this message
dm me
I’ll help you with it in my dm
if this thing closes tomorrow morning
which is today morning
god it’s 02:08AM
marsh linden
for example, weight = 2g
fading mural
devout snowBOT
fading mural
i dont understand how to do this can someone please help me?
devout snowBOT
@fading mural Has your question been resolved?
native panther
What is a correct two-points answer?
devout snowBOT
What is a correct two-points answer?
hybrid snow
What is a correct two-points answer?
main gull
What is a correct two-points answer?
Sounds like a question that Google could answer
hybrid snow
I gotta learn how to use the bot lol
main gull
And not for someone to look up for you
hybrid snow
:)
hybrid snow
And not for someone to look up for you
Too bad, I did it for them
main gull
Too bad, I did it for them
You shouldn't have because people are capable of doing things themselves
native panther
Is y - (-4) = 4x a correct two-point?
hybrid snow
Depends
mortal nimbus
devout snowBOT
mortal nimbus
Can I get some help with this?
I'm thinking about setting u = everything inside sqrt
But I can't continue after that
graceful cosmos
Do you have any guarantee such an integral is possible?
graceful cosmos
Ah, try a trig identity
mortal nimbus
I think I see ohe
That looks very much like the right side of a half angle identity
The numerator
Oh
Thanks a lot @graceful cosmos
Found it
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devout snowBOT
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Available help channel!
tiny cargo
devout snowBOT
tiny cargo
I don't know how to solve this at all, I tried the 2nd option in the following way =>
$x = (p + q)/2$
woven radishBOT
King_ftw
tiny cargo
since p + q is sum of roots which is equal to -b/a I thought it might lead me to something
$x = -b/2a$
woven radishBOT
King_ftw
tiny cargo
Substituting this value of x in ax^2 + bx + c and solving further I get this =>
$-(b^2 - 4ac) / 4a$
woven radishBOT
King_ftw
tiny cargo
Now from the question it is known that the discriminant b^2 - 4a is positive (since the roots are real and unequal) so looking at it gives an impression that this above expression as a whole is negative hence the 2nd option is correct ? But I don't think so because according to the question statement a (main coefficient of the quadratic) is negative, so the whole expression will be consequently positive therefore the 2nd option cannot be true. That's what I think.
I don't know where to ever start if i want to check other options.
Oh wait I think I got it nvm.
I was overthinking this xD
.close
tiny cargo
devout snowBOT
tiny cargo
Last 2 are correct from what I know
Second option is wrong I think
How do I find out if the first one is correct ?
steel sage
First one is correct because false can induce true
Sorry misread it
<=0 I thought <0
By the condition x=y=0
Then 4^2=2^4
tiny cargo
By the condition x=y=0
Hmm wait how do we get that
steel sage
Sum of two non-negative numbers being non-positive implies that they are both 0
tiny cargo
Also since $x^2 <= -y^2$ is only possible if both are 0
woven radishBOT
King_ftw
steel sage
Np
tiny cargo
.close
restive river
For a proof, I want to show that a matrix in the finite field of 3 is diagonalizable even if it has distinct linear eigenvalues
devout snowBOT
For a proof, I want to show that a matrix in the finite field of 3 is diagonaliz...
restive river
I choose the matrix [2,0,0; 0,2,0; 0,0,1]
so I got the charact pol: (x-2)^2*(x-1)
which I made it to the F3: (x+2)^3
so the eigenvalues are x=1, x=1,x=1 right?
am i correct?
steel sage
For a proof, I want to show that a matrix in the finite field of 3 is diagonaliz...
You mean duplicated eigenvalues?
restive river
You mean duplicated eigenvalues?
yes sorry not distinct, I mean to show it can be diagonalizable even if its not have distinct linear eigenvalues
am I clear?
but in finite field of 3
steel sage
I choose the matrix [2,0,0; 0,2,0; 0,0,1]
You chose a diagonal matrix and tried to diagonalize it?😂
restive river
hmm not exactly I want to show that this is false: a matrix in F3 is diagonalizable iff it has n distinct linear eigenvalues
so I came up with this example
steel sage
hmm not exactly I want to show that this is false: a matrix in F3 is diagonaliza...
This is false
Identity matrix is diagonalizable but it doesn’t have distinct eigenvalues
Don’t really understand what you want to do here
If you want a matrix of order 3 that isn’t diagonalizable in any field I can give you
$\begin{pmatrix}1&0&1\0&1&0\0&0&1\end{pmatrix}$
woven radishBOT
Cogwheels of the mind
restive river
okay so now (x-1)^3 is my characteristic polynomial which in F3 would be => x^3-3x^2+3x-1 => (x+2)^3. Thus x=-2 which in F3 is 1. Thus Identity matrix in F3 has 3 eigenvalues which all are 1. right?
restive river
yes there are not distinct eigenvalues but the matrix is diagonalisable so the statement is false
I just not sure if I do it correctly
bcs we never solved polynomials in finite fields like this
steel sage
It doesn’t make any real difference
restive river
thank @steel sage
steel sage
Np
restive river
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devout snowBOT
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clear vine
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clear vine
From what I understand I need to find dy/dx then input those points to get the slope
I get -5
Then I use point slope form to get the equation
\frac{-4y-8y^2}{-4x+3y^2} is what I get dy/dx equal to
glass mauve
you have the right idea
clear vine
Am I just making a simple math error somewhere?
<@&286206848099549185> Am still stuck
stiff ruin
I would simplify the equation first. You may need implicit but dont quote me on it
clear vine
Maybe, I got -14 for the slope this time, which doesn't seem right but its new
didn't work
No clue what I'm doing apparently
This question is making me feel thoroughly stupid
stiff ruin
no no not at all
whenever you have a y you need to take y'. After you should simplify/factor to get the value of y'
clear vine
the value of y' should be my slope right?
stiff ruin
yes
clear vine
So I have the concept down, which means I'm just making some math error I'm not spotting
stiff ruin
prob
patent tartan
What's the original problem?
First inequality can be rewritten to
$$x + 19 \leq 0$$
woven radishBOT
Navix
patent tartan
What steps did you do to simplify the first inequality?
$$\frac{x+3}{2} \leq \frac{x-5}{3}$$
Multiply both sides by 2 and 3
$$3(x+3) \leq 2(x-5)$$
woven radishBOT
Navix
patent tartan
not really
fathom oracle
devout snowBOT
fathom oracle
ye I did all that but I dont understand how I reduce the explicit equation
fathom oracle
when I put it all together I got ((sqrt(x)^4)-3)+7
wooden zodiac
no
wooden zodiac
(sqrt(x)-3))^4 +7
it's this
devout snowBOT
fathom oracle
okay... makes sense
thanks
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Available help channel!
gaunt solstice
Hello helpers I'm stuck in this question, I really don't understand what this question is trying to say
devout snowBOT
Hello helpers I'm stuck in this question, I really don't understand what this qu...
@gaunt solstice Has your question been resolved?
gaunt solstice
<@&286206848099549185>
devout snowBOT
@gaunt solstice Has your question been resolved?
devout snowBOT
@gaunt solstice Has your question been resolved?
cobalt cloak
devout snowBOT
cobalt cloak
,rotate
Crap
Well could someone check if I'm plugging these numbers in right
I'm getting a very wrong answer for the right math I think
And idk if thr calculation is error or the answer key
devout snowBOT
@cobalt cloak Has your question been resolved?
astral turtle
devout snowBOT
copper mango
ln(1+x) ~ x
astral turtle
ye but for small here we are going to infinity
copper mango
(-1)^n/n=x
however x is still going to 0 regardless of the alternating sign 
alternatively you argue that ln(1+(-1)^n/n) is asymptotic to (-1)^n/n
both get you to the same thing
runic rock
devout snowBOT
runic rock
so i was looking at the solution of this linear exam and i was wondering if anyone could explain to me the geometry of it
i dont understand why u-kv is perpendicular to vectors u and v
anyone??
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celest tide
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celest tide
@steel sage is there any other way to solve this? other than jensen's ineqaulity (I dont understand it)
leaden aurora
jensen. if u dont know jensen maybe u can make some argument about the concavity of sin(x) idk
celest tide
hmm havent really studied functions to that depth
devout snowBOT
@celest tide Has your question been resolved?
devout snowBOT
@celest tide Has your question been resolved?
supple knot
No there aren't easier ways to prove it than Jensen's inequality.
https://www.tutorialspoint.com/convex_optimization/convex_optimization_jensens_inequality.htm
celest tide
hm ok
hoary kernel
I’ve been stuck on this question for a while now
devout snowBOT
I’ve been stuck on this question for a while now
hoary kernel
I somehow don’t get the result and keep getting some other messy term
supple knot
do yo know $2^{-n}z^n = \left(\frac{z}{?}\right)^n$
woven radishBOT
riemann
hoary kernel
where did that +1 come from?
My bad it’s minus 1
supple knot
looks good otherwise
hoary kernel
But either way the subsequent part I tried to take the imaginary part of it so the accidental +1 shouldn’t matter I think
supple knot
show that part then
hoary kernel
Uhhhhh it’s probably riddled with mistakes tho
I mean I’m not proud of it but here it is anyway
Last step especially
Dk what in gods name im doing
supple knot
This part at least is correct so far yes?
Get the imaginary part of this expression (z) instead of plugging in $z = e^{i\pi/14}$ right away
woven radishBOT
riemann
supple knot
This part at least is correct so far yes?
put terms over a common denominator
hoary kernel
put terms over a common denominator
Including the one?
supple knot
I’ve been stuck on this question for a while now
You want to get it into the form given, and that has only one fraction
hoary kernel
I’ve been stuck on this form, I checked the calculator and it seems correct but I’m not sure how to convert it to cos from here
We need to somehow show
2sin(pi/14) -2^(-13)sin(15pi/14) = 16835cos(3pi/7)/8192
supple knot
Use sin(x+ pi) = -sin(x)
devout snowBOT
@hoary kernel Has your question been resolved?
pulsar dock
I don't want to invest too much time into a computational problem like this, but you are making it harder for yourself by not noticing that at z = cos(pi/14) + isin(pi/14), you have (z/2)(1-(z/2)^14) = (z/2) - (z/2^15)
by taking the 15th power instead of the 14th you are making the computation a lot harder
ornate kindle
If this certain oatmeal is 1.7x more expernsive then the other type what percentage
devout snowBOT
If this certain oatmeal is 1.7x more expernsive then the other type what percent...
ornate kindle
Is it just 170% more expensive
torn vessel
When you talk about "Percentage more" you generally only talk about the change.
ornate kindle
When you talk about "Percentage more" you generally only talk about the change.
Ah
So 70%?
Or how do I find the increase change
@torn vessel
Ohhh
Alr
Thx
@torn vessel but what’s the reasoning behind this
torn vessel
If you say something is x% more you're already saying the whole original amount is there
and that this new amount is x% over the original amount
trail wing
hello
rare acorn
hi
rare acorn
trail wing
hey, this my question:
im stuck on inner/outer bounds for the integral part
im not sure why its wrong since outer is y (x^2) - (-4)
and inner should de smallest distance, so y^2 (x) - (-4)
thats the only part wrong
i checked desmos too, so i cant see why it would be wrong
rare acorn
The bounds of integration are the zeros of the first equation minus the second.
rare acorn
trail wing
i did washer method
should be like this
<@&286206848099549185>
the only way its wrong which it is is if my R(y) and r(y) are wrong
rare acorn
then try to recalculate them
trail wing
i did. greates one then add 4 for outer
since x= -4
so radius is added 4 to both
as for the functions
Y^2 is the shortes length (checked desmos) so its outer function
<@&286206848099549185>
devout snowBOT
@trail wing Has your question been resolved?
timber flame
devout snowBOT
timber flame
How do I get the z and point it towards the s with the political of c in formal of the y?
<@&286206848099549185>
woven radishBOT
oak harness
i somehow immediately thought of group theory
hybrid snow
I think it was a joke
oak harness
How do I get the z and point it towards the s with the political of c in formal ...
In any case, the answer is that you obviously consider the Party isomorphism of the political of C, then embed that into the Kneut-transformed isometricized informality metric of the formal of y. Then solving this simple electorial we get z. Pointing it to s is left as an exercise to the reader. Hint: It will involve the College-Vote System of Metrics.
</s>
hybrid snow
The fuck
supple knot
In any case, the answer is that you obviously consider the Party isomorphism of ...
sounded legit jesus christ
anyway that was fun.
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cerulean halo
i would like help with problems 88 and 90
devout snowBOT
i would like help with problems 88 and 90
supple knot
use f(-x) = -f(x) for odd functions f(x)
cerulean halo
but how do you do that for integrals?
supple knot
any bigger a hint i'd basically be giving it away
just plug it in
ok another hint. split your integral up by domain
quick meadow
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quick meadow
I know how to find asymptotes and intercepts through f(x), how would I apple it to this problem?
Apply
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@quick meadow Has your question been resolved?
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@quick meadow Has your question been resolved?
mental anchor
ok
so there are 2 vertical asymptotes so you know the denominator is (x+2)(x-2)
then the graph also tends to 1 at both ends so you know that the top must have a quadratic on the top as well and since it tends to 1 the coefficient of x^2 on the top will be 1
It also crosses the origin so you know there is no constant term on the numerator
then you are given 1 point (-1,1) so you can plug that in and you should be able to find an answer
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Question 17
graceful cosmos
A function has a max/min at some x = a, when f'(a) = 0
quick sapphire
A function has a max/min at some x = a, when f'(a) = 0
Tbh. Idek how to apply that
graceful cosmos
x = 0 is a minimum. Therefore f'(0) = 0
graceful cosmos
No it isn't. You instead used the fact that f(0) = -6
The fact that f'(0) = 0 is unrelated
graceful cosmos
You applied f(0) = 6 perfectly, this is just the same thing except with f' as the function
quick sapphire
If f’(0)=0
Then what term does that represent
Oh
Its the c value
Wait wat
C value is left in the equation
But how do I know that c = 0
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@quick sapphire Has your question been resolved?
restive river
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oak panther
1/a = 4b
Nope
The reciprocal of 1 number = 4 x the reciprocal of the other number
1/a = 4 (1/b)
restive river
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restive river
how do I find this out?
bronze peak
The way to get the biggest product from addition variables is by dividing the sum by the parts
restive river
restive river
The way to get the biggest product from addition variables is by dividing the su...
wdym dividing the sum by the parts?
do u have an example
bronze peak
Like the value of 10 is split evenly between the variables
Take like x + y = 6
We can try many different combonations
2 + 4
2*4=8
bronze peak
But the biggest value we get is when x = 3 and y=3
So using this theory we can solve the problem
restive river
@bronze peak alright
but can we do a = 5, m = 3, c = 2
you would get 30
can u get bigger than that?
bronze peak
There is nothing in the problem that says A M and C dont equal eachother
So maybe try that
restive river
oh ok
then 3x3x4
is the biggest
36
36 + 12 + 12 +9
so is it 69....?
@bronze peak
frozen hollow
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frozen hollow
can someody help me with this question
im getting confused
<@&286206848099549185>
hey?
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@frozen hollow Has your question been resolved?
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@frozen hollow Has your question been resolved?
restive river
find CM first
then let the intersection point of CV and ON be C'
and find C'N
and finally use similar triangles to find the CV
and thus you can find the volume
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blissful elk
Time to return to a help channel with this Oblique Collisions question for some tasksheet that I'm doing at the moment. Colossally stuck on trying to calculate the speed of B after the initial collision.
I get that they only have horizontal velocity and no vertical velocity. I get that impulse of B will be calculated as 2m(v-2u) as 2m is the mass and 2u is the initial velocity of it. But what I don't get, it how to get from the beginning to the end.
I've done about a page of workings on paper and so far all the calculations seem...just wrong. I'm not getting anywhere with this. I've found pointless distances, an angle which I thought was going to come in handy but so far, nothing I've done has brought me closer to the answer.
Would really appreciate it if someone could help, if not, walk me through how to do this question. I've done purely vertical, purely horizontal collisions in lesson but this is basically brand new as it's so different.
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Time to return to a help channel with this Oblique Collisions question for some ...
@blissful elk Has your question been resolved?
blissful elk
<@&286206848099549185> Please?
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@blissful elk Has your question been resolved?
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@blissful elk Has your question been resolved?
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@blissful elk Has your question been resolved?
blissful elk
<@&286206848099549185>
Please? Anyone? I'm near the point of begging
polar bolt
Try a physics server?
blissful elk
Is there a physics server out there with help channels?
Despite this being a maths question too, just mechanics based
blissful elk
I've been in the physics server and it's not laid out the same as here
limpid lion
@blissful elk ig along tangent joining the circles velocities remain the same and along normal vel(separation)/vel(approach) = coeff of restitution
blissful elk
What do you mean by that?
Like, in terms of the question. Would you be saying Sep/app = 1/6
But we know that the speed of approach is 3u so...Sep/3u = 1/6?
limpid lion
nope take components
yeah sep/app = 1/6
so u get an angle of 37 if i'm not wrong as per the q
blissful elk
Now this is where my main question comes in....
Both of the objects in the question only have horizontal components...so how would I deal with that?
limpid lion
see on collision they rebound not head-on so they'll not travel in the same line
i'm sorry can't give a diagram..
blissful elk
I can kind of see that they will bounce off and move in different directions, like for A they will move "upwards" at an angle while B will move "down" at an angle
limpid lion
yupp
so there'll be an initial component along the 'bounce-off' line n one perpendicular to it (along their geometrical tangent)
blissful elk
So the end thing is I need to take the line if centres as basically the diagonal as they are colliding?
blissful elk
Riiigghhhtt...Lemme see what I can make of this
limpid lion
the components along their lines give sep/app =1/6
limpid lion
Riiigghhhtt...Lemme see what I can make of this
yupp give it a shot
blissful elk
So I'm getting somewhere I think. I've got the perpendicular and parallel components of A and B I think.
blissful elk
Sounds like a plan, but I'm not the most confident with my answers so
limpid lion
lol u got company dw
blissful elk
I think and hope that I have a final answer for the impulse
limpid lion
i got 63/25 mu 🤞
blissful elk
That's not what I got....hmmmm
limpid lion
wait what did u get
blissful elk
My final impulse was 6.6mNs
limpid lion
but shouldn't it be in terms of m n u?
blissful elk
Or 6.6mu
limpid lion
oh ok
blissful elk
Hmmmm
limpid lion
waitt
blissful elk
What did you get as the speed of approach for the spheres?
blissful elk
My perpendicular velocities were
A - 4u/5
B - 8u/5
blissful elk
Ahhhh...
I think I got my perpendicular and parallel the wrong way around
Because that's what I got for the parallel velocities
limpid lion
wait i'll come back..
blissful elk
This is a really bad drawing of what my line of centres was with A and B
limpid lion
yupp correct ig
blissful elk
Using this as the line of centres, what will do we get for the perpendicular and parallel components?
blissful elk
This is my a m a z i n g paint skills on show for a diagram
limpid lion
lol
blissful elk
Question, for the speed of separation. Did you add the unknowns or take them away?
First try I did addition
limpid lion
see u get 2 eq if i'm not wrong
one using coeff of rest
n one using linear momentum conservation
so i solved simultaneously
so approach will be usin(phi)+2ucos(theta) as per ur diagram
blissful elk
So approach would be 3u/5 + 6u/5. Then apply them to the conservation of momentum?
blissful elk
So the approach speed would be... 21u/5?
limpid lion
as approach is relative velocity
limpid lion
*uses
blissful elk
So what do you get as the speed of approach?
limpid lion
9u/5
but conservation of momentum they'll be in opp directions
like 1 -ve 1 +ve as per ur conventions
blissful elk
My calcs are:
A - (3u/5 * 3m)
B - (-6u/5 * 2m)
This is probably wrong
Set that equal to 3v + 2w
blissful elk
Yeah
limpid lion
then wrong
cuz again they in opp directions in conservation
so rigorously u cd do using vectors
but in the restitution part we just directly adding magnitudes as we can predict that they'll be in opp directions
so relative to each other their magnitudes add up
blissful elk
So..should the calculation be something like
A - B = 3v - 2w or something?
blissful elk
If I go with that then I end up with -3u/5 = 3v - 2w
limpid lion
or do it at full length using a coordinate system n vectors to avoid errors
yeah i got something like that i guess my signs just opp
so see if u can get someone with a confident answer
mine was 63mu/25
hopefully this is correct
limpid lion
ok so i took u3 as the v for 3m (perp)
n analogously u2
so (u3+u2)/(3u/5+3*2u/5) = 1/6
blissful elk
How come your speed of approach is 9u/5 and yet mine is -3u/5
limpid lion
n for momentum conservation 3m(3u/5)-2m(6u/5) = -3mu_3+2mu_2
they are coming towards each other
so their approach speed is high
magnitude
blissful elk
Yeah but with that first equation you end up with 9mu/5 - 12mu/5
limpid lion
see i'm doing with the convention of A->B direction +ve
blissful elk
That's the same as what I'm doing
limpid lion
Yeah but with that first equation you end up with 9mu/5 - 12mu/5
yeah this is correct
limpid lion
yeah correct ryt
blissful elk
So that's one of the simultaneous equations, right?
limpid lion
then solve simult eq with the restitution
yeah
just wolfram it for now see if it works
blissful elk
So the speed of approach is -3mu/5 (Unless you cancel the masses)
We know that e is 1/6. And the speed of separation is v+w?
limpid lion
no approach speed is 9u/5
blissful elk
How?
limpid lion
cuz they coming towards each other
so their mags add up
basically 3u/5 - (-6u/5) if u go by the relative vel definition
blissful elk
So are you only taking the speeds of them, not involving the momentum?
I think that's what I'm missing
limpid lion
yeah cuz that's the use of the coeff
limpid lion
So are you only taking the speeds of them, not involving the momentum?
yes this
ok uh bro i'll prolly have to go
gl
pulsar sonnet
I don't know how to solve this
devout snowBOT
I don't know how to solve this
pulsar sonnet
Like does expression mean equation or do I have to give the solution?
rare mantle
Like does expression mean equation or do I have to give the solution?
equation, an example is V = x^3
they’re asking for the expression that V=
rare mantle
Lol cuz for some reason V = X times X times X didn't work
Yeah that’s not the answer
I was giving an example
pulsar sonnet
just found out what that v thing meant
rare mantle
What you want to do is subtract the volume of the cube by the volume of a cone as the cone appears to be hollow
And you’ve already solved the expression for the cube’s volume
So all is left is find the expression for the volume of the cone
hallow dune
I am once again asking for your help... I honestly don't understand very well what they are asking for, I don't know where to start
Let Ui ~ iid uniform(0,1), i=1,...,n, define the random variables (see image) with 𝛼 >0 and 𝛽>0.
a) find the function of density of W1 and
b) determine (see second image)
devout snowBOT
I am once again asking for your help... I honestly don't understand very well wh...
@hallow dune Has your question been resolved?
pulsar dock
I don't really do this, but I assume the idea is that you can generate a random variable from sampling a uniform random variable by doing an integral transform
So W_i is generated by a F^(-1)(U) and invert the function to get back to an F then differentiate to get back to the underlying pdf, but that's a pretty high level sketch so you'd need to check the details carefully
See: http://www.columbia.edu/~ks20/4404-Sigman/4404-Notes-ITM.pdf for example
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@hallow dune Has your question been resolved?
hallow dune
oh god, I heard about integral transformations, I just didn't think I would have to use them here
thanks!
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surreal pulsar
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surreal pulsar
c is a constant
grim swallow
Try distributing the terms?
raw hamlet
and then use linearity of expectation or something
graceful cosmos
How do you subtract a constant from a set?
surreal pulsar
X_i and X_j are random variables
graceful cosmos
Ah mb. I see now.
surreal pulsar
my argumentation would have been, since for a function g applies, if X__i and X_j are independet
surreal pulsar
is this true
that would have to be right, wouldn't it?
the statement even applies also to
grim swallow
I do not know why generic functions need to come in
When the original question involved only basic addition and multiplication
surreal pulsar
When the original question involved only basic addition and multiplication
i'll try this, give me a second 🙂
surreal pulsar
When the original question involved only basic addition and multiplication
okay, so if I just use linearity of the expected value and properties of the expected value I obviously get the same result
But I could also argue about the statement with functions or?
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@surreal pulsar Has your question been resolved?
pulsar dock
It is true, but the crux of it is the property that if X_i and X_j are independent, then their joint distribution f(x,y) = f(x)f(y), so that the double integral splits. You are sort of trying to invoke the law of the unconscious statistician, on g(x) = x-c which gets you part of the way there, but that isn't the most critical property here.
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surreal pulsar
.reopen
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✅
surreal pulsar
It is true, but the crux of it is the property that if X_i and X_j are independe...
Okay, I think I know what you're trying to tell me.
Thanks for the help 🙂
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Available help channel!
novel compass
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@novel compass Has your question been resolved?
slow hill
did i solve it right?
devout snowBOT
did i solve it right?
slow hill
For safety, try C
Yea i went for d until I saw they asked to write in form a + b i
Btw this is a mock quizzes I’m just trying to practice
hybrid snow
Ah
slow hill
What about this one, some of my colleagues thinks its b because the answer is not in the a + bi form
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Available help channel!
warm hearth
what happens if the position is 15 (less than 18)
