that will make ur work a bit lengthier
#help-28
orchid lake
2?
pure basin
yes
orchid lake
2(x+4)?
orchid lake
Ohhh I see
orchid lake
I’m confused sorry
orchid lake
I got 2x^2 + 16x + 32
orchid lake
Yes I got c value is 32 but it says the answer is 16
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orchid lake
.close
radiant wave
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radiant wave
im confused
any clues
i got no idea what to do
tell me if this is right, multiply by B^2 then A^2
lunar veldt
i would say just use AM GM for 4*a/b and b/a
lunar veldt
$\frac{x+y}{2} \geq \sqrt{x y}$
glossy valveBOT
tm
lunar veldt
uses this inequality with well-chosen x and y values
hearty holly
AM = arithmetic mean.
GM = geometric mean
lunar veldt
it simplify it very much
hearty holly
have you tried jut simplifying without am gm
radiant wave
nvm i give up
urban nebula
have you tried jut simplifying without am gm
We can have ||(2a-b)²|| ???
radiant wave
.close
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hoary ember
??
lunar veldt
nvm i give up
lmaooo
void magnet
Bruh
hearty holly
We can have ||(2a-b)²|| ???
yes
lunar veldt
ragequit
hearty holly
since we get that, it's always true for all real numbers @urban nebula
hoary ember
ts pmo 🥀
hearty holly
where did main guy go
urban nebula
He left
hoary ember
anyway can someone answer my doubt its rotting in there
your doubt?
hoary ember
dunno just be patient or sum
glossy valveBOT
tm
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willow geode
Initially, only one elf is in a good mood (day 0). Every day, a cheerful elf has a chance to make a grumpy friend smile (and thus become cheerful) with probability p (not equal to 0). The elves form a complete graph, meaning every elf is friends with every other elf.
A grumpy elf becomes cheerful if at least one cheerful friend smiles at them. Importantly, an elf in a good mood can smile at multiple grumpy elves in the same day.
We define τ as the total number of days required until all n elves are cheerful. Compute E(τ).
willow geode
I found some weird sum at the end by considering the variable giving the nb of days to go from k-1 cheerful elves to k cheerful elves, but Python simulations give me another result.
For p=1/2 and n=10, simulation gives 2.07 and formula gives 9 and decimals...
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willow geode
<@&286206848099549185>
cerulean cargo
Initially, only one elf is in a good mood (day 0). Every day, a cheerful elf has...
if i udnerstand it correctly, for each happy elf, a particular grumpy elf has a probability p to become happy on a given day?
also it wants a formula for E in terms of p and n?
willow geode
if i udnerstand it correctly, for each happy elf, a particular grumpy elf has a ...
no a happy elf can make another grumpy elf
happy
willow geode
also it wants a formula for E in terms of p and n?
yes
knotty grail
then the probability for a grumpy elf to not be happy at the end of a day is $(1-p)^{n_h}$, where $n_h$ is the number of happy elves at that day?
glossy valveBOT
willow geode
then the probability for a grumpy elf to not be happy at the end of a day is $(1...
yes
fiery hemlock
can a grumpy elf who became happy today, make others elves happy?
willow geode
can a grumpy elf who became happy today, make others elves happy?
yes
But the next day
Btw the thing starts on day 0
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torn jolt
.
hollow fjord
how do u even do this bro
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how do u even do this bro
hollow fjord
i would show work if i even had a clue on the 1st step to solving this
austere cove
well, do you know how to shift a graph up and down?
Try playing around with this.
knotty grail
how do u even do this bro
i might sound like a jerk
but just substitute zero
and then try something else if it doesn't work
they've even been nice enough to give you the value of g(0) = -2
normally it's just subtracting 2 to shift it down
hollow fjord
https://www.desmos.com/calculator/minhdlqvlk
uh i made this after playing around but how do i like get the equation
austere cove
uh i made this after playing around but how do i like get the equation
Cool, look at a, b, c, and d and then plug them into the equation for g(x) and see what you get.
austere cove
so the final function is with a -2
!nosols please
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so the final function is with a -2
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
frosty gyro
i would show work if i even had a clue on the 1st step to solving this
first things first do u know how transformations look on a function
frosty gyro
like if f(x) ws translated up by 2 would u know what would happen to f(x)
austere cove
I mean, that's why I didn't tell quack the steps, instead I gave her the desmos graph to try to get her used to what each parameter does.
knotty grail
oh
hollow fjord
i am confuzzled
austere cove
So @hollow fjord in your desmos tab, what are the values of a, b, c, and d?
after you have moved the graph to the correct location?
hollow fjord
0, -2, 1, 1
austere cove
ok cool.
Can you describe what each variable does to the resulting graph?
Qualitatively that is
hollow fjord
a moves it left and right, b changes the size, c elongates it, d changes the width (squeezes it together ig)
hollow fjord
oh yea
austere cove
ok so
I can tell you that 0, -2, 1, 1 is correct. If you look at the definition of g, what do you get when you replace a with 0, b with -2, and so on?
austere cove
🎉
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frank gulch
Can anyone help w part A? I wrote out the converse but I'm just not sure how to start the proof.
charred raft
show what u did @frank gulch
frank gulch
so for part A)
converse: if $g \circ f: A \rightarrow C$ is surjective, then f and g are both surjective
i started out by saying if $g \circ f$ is surjective then g o f covers every $c \in C$ so for some $a$, $(g \circ f)(a)=g(f(a))=c$. then every c is in the image of g, so g is surjective
but then idk how to show if f is surjective or not
charred raft
take a counterexample
glossy valveBOT
nilo
frank gulch
so i jsut try to find A,B,C where f is not surjective?
charred raft
yes
glossy valveBOT
nilo
frank gulch
how do u write set curly brackets in latex
f is surjective?
but its missing 2 from B
charred raft
how do u write set curly brackets in latex
so i can just say like
$A={1},B={1,2},C={x}$
and
$f(1)=1,g(1)=x,g(2)=x$
glossy valveBOT
Goëtia
charred raft
f is surjective?
wanted to write g, im on phone
frank gulch
ah nws
frank gulch
wanted to write g, im on phone
but thats fine though right since we have shown g is surjective earlier
so the converse is not true
charred raft
yes any counterexample where $f(A) \subset B$ is valid
glossy valveBOT
Goëtia
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short gull
Can someone explain where I am going wrong? Calc 2
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Can someone explain where I am going wrong? Calc 2
short gull
gritty rose
where's this formula from
short gull
Previous question
I thought that was correct cause we used it in lab as well
(I am a bio major, Calc 2 is the last time I will touch math. It has been a struggle... lol)
But I just gotta pass my final and I am good lol
Also its area so it cant be negative right? I have no idea what I am doing wrong
wet stream
sin^2 is not 1-cos
short gull
I thought double angle was only if it was cos(2theta)
gritty rose
2 * 1/2 = 1
short gull
OHHHH
wet stream
I thought double angle was only if it was cos(2theta)
yes, cos(2x)=1-2sin^2(x)
wet stream
yes
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tranquil belfry
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tranquil belfry
idk how to get e ii)
i did e i) and got 105
but idk e ii) cz i can't assume isoceles triangle
rest of q
tranquil belfry
but how do we know
robust slate
It’s the field and the same fences?
robust slate
,w find x/2 if 392/x^2 (x+sin x)=460, 0<x<pi
glossy valveBOT
robust slate
tranquil belfry
kk
robust slate
Alright I assume that you can do the rest yourself
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boreal folio
I need help with this question
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I need help with this question
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
ok so i tried a few things, basicly im wondering if i can use fermat's little therom to show x^p+a = x+a
then it is always irreducable as the only zero would be -a, which gives x+a as a factor or itsself
but idk if this holds
<@&286206848099549185>
I asked this question, channel timed out, and then asked again which is why i tagged lmao
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peak moon
write x^2-8x+10 in the form of (x-p)^2 - q.
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write x^2-8x+10 in the form of (x-p)^2 - q.
hoary ember
try to expand (x-p)^2-q and try to match the terms with x^2-8x+10
green merlin
Compare the coefficients
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mortal sigil
@peak moon would you like help?
compact sorrel
thats why i posted it here.
have you tried doing what skissue told?
mortal sigil
can you try expanding (x-p)^2 - q ?
peak moon
have you tried doing what skissue told?
thats not how its done. we have to write the term i wrote in that form. we dont have to play with that term itself
peak moon
no
compact sorrel
thats not how its done. we have to write the term i wrote in that form. we dont ...
I mean you could also just try converting the quadratic given to you in perfect square
both approach are fine
mortal sigil
I actually think skissue's is very clever and very intuitive
peak moon
I mean you could also just try converting the quadratic given to you in perfect ...
i dont think so. i'll lose marks
compact sorrel
when it comes to math all solutions are equally valid, it doesn't matter which way you take
unless it is explicitly mentioned in the problem you have to use x method, you can basically use any
mortal sigil
look, imagine I ask you to write x^2 + 8x + 16 in the form of (x+a)^2,
if you expand (x+a)^2 you can match the terms and write it like how I asked
so lets try doing it too, here
how would you expand (x-p)^2 - q?
peak moon
x^2 - 2(x)(p) + p^2 - q
peak moon
x^2
mortal sigil
and the last term too
peak moon
thats +........o ya that doesnt matter right?
mortal sigil
ofc, you could subtitute q for -10 and it would give you +10
so lets see
we need to write -8x in terms of -2xp + p^2
lets drop the negative signs so we dont get confused
8x must equal 2xp+p^2
maybe we could make an equation?
peak moon
2xp+p^2 = 8x
peak moon
write x^2-8x+10 in the form of (x-p)^2 - q.
i rmbred just now. the process we have to use is completing the square.
mortal sigil
oh yes I'm noting that too
since we could write 4x = xp
then p^2 would be turned into 10 by the -q term
try doing it, if you need help you can ask
I think the result would end up being ||(x-4)^2 - 6||
peak moon
o yaa sameee. it must be right then
i used the other wayy tho
i didnt understand ur way but im interested
mortal sigil
well
8x = 2xp
4x = xp
p = 4
then we have p^2 - q = 10
4^2 - q = 10
16 - q = 10
q = 6
peak moon
ohh damn, this one seems to be more logical. i understand this better now 😩 thnxx 🫶
mortal sigil
anything else you need help with?
peak moon
no thnxx, i'll let uk 👍
robust slate
.close
unkempt venture
im having trouble with this problem
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im having trouble with this problem
gritty rose
,w int 0 to inf 1/(1+x^4)
glossy valveBOT
gritty rose
Do you know the beta and gamma functions
unkempt venture
no
gritty rose
Do you know residue theorem
unkempt venture
no
languid junco
you could try x^2 = tan(t) as a substitution
this is a tough integral with limited integral technique knowledge
gritty rose
Try splitting the integral from 0 to 1 and 1 to infinity then use u = 1/x
latent lava
unkempt venture
but then the bounds for 0 to 1 becomes 1/0 and 1
unkempt venture
Try splitting the integral from 0 to 1 and 1 to infinity then use u = 1/x
how does that work
does it become infinity?
gritty rose
x is positive so the limit as x goes to 0 from the right, u goes to ?
unkempt venture
infinity?
storm lintel
hi
narrow ermine
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willow geode
Initially, only one elf is in a good mood (day 0). Every day, a cheerful elf has a chance to make a grumpy friend smile (and thus become cheerful) with probability p (not equal to 0). The elves form a complete graph, meaning every elf is friends with every other elf.
A grumpy elf becomes cheerful if at least one cheerful friend smiles at them. Importantly, an elf in a good mood can smile at multiple grumpy elves in the same day.
We define τ as the total number of days required until all n elves are cheerful. Compute E(τ).
I found some weird sum at the end by considering the variable giving the nb of days to go from k-1 cheerful elves to k cheerful elves, but Python simulations give me another result.
For p=1/2 and n=10, simulation gives 2.07 and formula gives 9 and decimals...
willow geode
$
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willow geode
<@1294931104217956414> Has your question been resolved?
stop closing
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stop closing
willow geode
Initially, only one elf is in a good mood (day 0). Every day, a cheerful elf has a chance to make a grumpy friend smile (and thus become cheerful) with probability p (not equal to 0). The elves form a complete graph, meaning every elf is friends with every other elf.
A grumpy elf becomes cheerful if at least one cheerful friend smiles at them. Importantly, an elf in a good mood can smile at multiple grumpy elves in the same day.
We define τ as the total number of days required until all n elves are cheerful. Compute E(τ).
I found some weird sum at the end by considering the variable giving the nb of days to go from k-1 cheerful elves to k cheerful elves, but Python simulations give me another result.
For p=1/2 and n=10, simulation gives 2.07 and formula gives 9 and decimals...
DONT CLOSE THIS
onyx glen
stop closing
you're the one letting it time out without pressing ❌ on the prompt lmao
willow geode
you're the one letting it time out without pressing ❌ on the prompt lmao
bud i cant check this thread every hour
i have to sleep also
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hoary ember
find the largest natural number $a$ such that there exists a positive integer $b$ where
$$ab+a+b\mid 5a^2+4ab+6a+4b+1$$
glossy valveBOT
skissue.in.a.teacup
hoary ember
ok so first thing its equiv to $ab+a+b\mid 5a^2+2a+1$ but im not sure how to continue it
glossy valveBOT
skissue.in.a.teacup
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grand hatch
So you have that $$5a^2+2a+1=k(b(a+1)+a)$$ for some integer $k$. Solving for $b$ we have that $$b =\frac{5a^2+(2-k)a+1}{k(a+1)}$$
Now use the condition that $b$ is a positive integer
glossy valveBOT
Asteroid
grand hatch
The use the fact that b must be positive
hoary ember
6-2+k=0
k=-4
glossy valveBOT
Asteroid
hoary ember
-(5a+1)/4 has to be a positive integer?
hoary ember
im p sure its correct?
well, (2,1) is a solution?
well a+1 doesent always have to divide the numerator, there can exist k such that a+1 doesent divide the numerator for all a
all it matters is for some a it can divide the numerator
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grand hatch
Ahh wait this is easily fixed. So we need $a+1$ to divide $5a^2+(2-k)a+1$ which is equiv to $$a + 1 | k+4$$
Maybe you can get something out of these
bright bronze
You just returned back to the problem, didnt you?
grand hatch
You just returned back to the problem, didnt you?
Wdym
bright bronze
You just returned back to the problem, didnt you?
well, k is the quotient when this happens
so saying k divides this doesnt give you anything
grand hatch
Oh the second condition💀
glossy valveBOT
Asteroid
rare drift
hoary ember
scroll above
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@hoary ember Has your question been resolved?
hoary ember
.close im sleeping
covert heath
same
lucid flower
.close
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spiral vigil
.close
covert heath
problem solved
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placid ember
The sum of twice the length of a side and the base of a right-angled triangle is 36 cm. Using a mathematical model in the form of a quadratic function, determine the maximum possible area of the triangle.
placid ember
is this correct?
hot herald
y' wasn't needed, but yes
wanton basin
How can I solve b
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How can I solve b
leaden ermine
How can I solve b
try some examples
starting with reflexive, clearly if you were born then you and yourself share the same bday
so you in that sense a ~ a
wanton basin
okay I think I get reflexivity for this one
leaden ermine
now symmetry if you and and your friend share the same bday, does your friend and your share the same bday
?
leaden ermine
transitivity?
wanton basin
if both have the same bday they both have the same bday so a,b and b,a work
well if I share the same bday as someone else, and they share the same bday as another person, then I share the same bday with the other person
so yes
leaden ermine
yes
leaden ermine
now antisymmetric?
wanton basin
if I share the same bday as another person
they can't share the same birthday as me
but that can't be the case
so no antisymmetry?
leaden ermine
antisymmetry would mean here if you share the same bday with your friend then you and your friend must be the same person
wanton basin
because antisymmetry is defined as if a,b then b,a cannot be in R (unless a = b)
I see
leaden ermine
leaden ermine
well it's not true because just because ppl share the same bday doesnt mean they are the same person
wanton basin
is that what the question is asking though?
leaden ermine
R is a relation on the set of people
We would assume each element in people is unique
leaden ermine
and two people can have the same bday without having it to be the same person
wanton basin
so when we say a = b we are saying two different people with the same bday
not necessarily strictly looking at bdays
because if the question said strictly looking at bdays we wouldn't care about the uniqueness of the person?
umbral dome
by "a = b" we mean a and b are the same person
by "aRb" we mean a and b share the same birthday
leaden ermine
antisymmetry is just claiming that if two people share the same bday then these two people are the very same person
wanton basin
okay so a and b are born on the same day is represented as aRb not a = b
leaden ermine
yes
wanton basin
okay
leaden ermine
or a ~ b too for aRb
wanton basin
and aRb simply defines a = b as sharing the same birthday of the two people
but a = b means same person
leaden ermine
yes
wanton basin
ok
I think I can wrap my mind around it now
I was struggling to convert the sentence into notation
umbral dome
and aRb simply defines a = b as sharing the same birthday of the two people
R is the relation, don't use = when talking about R, just aRb (imagine R is a new symbol which is somehow similar to =)
minor crater
=)
wanton basin
okay so aRb means the ordered pair (a, b) is part of the relation R iff a and b are the same date
not necessarily the same person?
is that a more precise way for me to think about it
leaden ermine
yes
umbral dome
yes, just like how a = b means (a,b) is part of the equality relation (where we are defining that to mean they are the same person)
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heady heron
hey guys, what’s the answer to this if x = 20.38? I keep getting different answers
gritty rose
hey guys, what’s the answer to this if x = 20.38? I keep getting different answe...
!show
unique wagon
lets have a look
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hey guys, what’s the answer to this if x = 20.38? I keep getting different answe...
Show your work, and if possible, explain where you are stuck.
heady heron
!show
i put it on the calculator multiple times and it keeps giving me different results, i thought i put it in wrong and i put it in chatgpt and it gave me a diff answer
unique wagon
,w calculate y=-0.09(20.38)^3+1.46(20.38)^2+5.43(20.38)+44.96
glossy valveBOT
gritty rose
i put it on the calculator multiple times and it keeps giving me different resul...
just show what you put
heady heron
,w calculate y=-0.09(20.38)^3+1.46(20.38)^2+5.43(20.38)+44.96
thank you!
heady heron
just show what you put
it’s the second one highlighted
gritty rose
that's only one. where's the second
heady heron
that's only one. where's the second
i put this onto the calculator
void nova
And what result did you get?
gritty rose
none of those show the full calculator entry
heady heron
none of those show the full calculator entry
I can’t show the full calculations for the other ai ones bc they’re too big but here’s for the calculator and chat
void nova
!nogpt
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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
void nova
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they ...
Especially with calculations you can do with a normal calculator
heady heron
Especially with calculations you can do with a normal calculator
idk if I put it in wrong tho that’s why i used ai
void nova
If you don't fully show how you input the calculations we can't help you understand why you get a wrong result 🤷♂️
heady heron
If you don't fully show how you input the calculations we can't help you underst...
i showed the photo
for the one on the calc
idk if i inputted it right tho
void nova
This isn't the full (or whole) input...
heady heron
This isn't the **full** (or **whole**) input...
last part is just + 44.92
void nova
And before -0.09?
glossy valveBOT
void nova
What result should you get instead?
heady heron
Well, then it's correct
okay thanks
heady heron
What result should you get instead?
idk?? that’s why im asking you guys? 😭😭
unique wagon
this is wrong
because at the end it is 44.96 but in the question it is supposed to be 44.92
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chrome elbow
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chrome elbow
how do i do taht
ik how to do the one where the quaficient of x^2 is one but not if its greater then 1
chrome elbow
you can compare coefficients
wdym by compare
unique wagon
for example
lets say
3x^4 + 5x = ax^4+kx
it must hold that 3=a because x^4 coefficient is unique
this is what we call comparing coefficients
chrome elbow
ohhh
unique wagon
this works for identities where for any x, both sides of the equations are the same like
cos^2(x)+sin^2(x) = 1 is an identity
chrome elbow
yea
unique wagon
try doing it for 2x^2+16x+26
unique wagon
factor out the 2
2(x^2+8)+26
in general, you factor out the coefficient of the square term
if it is not 1
unique wagon
we only need to focus on the linear and quadratic term first
unique wagon
okay lets perhaps try an alternative method
expand the a(x+b)^2+c
fully
and simplify
slender bane
chrome elbow
expand (x+b)^2
x^2+2bx+b^2
unique wagon
correct!
so u have
2x^2+16x+26 = ax^2+2abx+b^2+c
we can now look at term by term comparison
unique wagon
lets say
3x^4 + 5x = ax^4+kx
looking at this, what do u think a is in our equation?
chrome elbow
the 2
unique wagon
yups!
now lets look at the linear term
what do you think b is?
(hint: 2abx = 16x by comparing)
chrome elbow
b is the term that u devide by 2
unique wagon
correct
now i want u to find c yourself
remember that the constant term on both sides should be equal as we did with other terms
chrome elbow
is it 30 or 17
unique wagon
so u have
2x^2+16x+26 = ax^2+2abx+b^2+c
we can now look at term by term compari...
look at the expansion again
i made a mistake before writing c^2
it should be c
chrome elbow
so its 30 then
unique wagon
what is the constant term in the right hand side?
chrome elbow
a i think
unique wagon
ax^2+2abx+b^2+c
in that equation, which terms are independent of x?
https://www.youtube.com/watch?v=Ah6Xtlk7K3c
perhaps take a look at this
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real wasp
i dont really know where to start here is my issue.. and the reasoning statement depends on what you pick for statement. could someone walk me through it?
modest obsidian
i dont really know where to start here is my issue.. and the reasoning statement...
$\angle BAC = \angle CAD$ as they are alternating angles...
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parabolicinsanity
modest obsidian
so its kinda redundant to display congruency
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@real wasp Has your question been resolved?
real wasp
$\angle BAC = \angle CAD$ as they are alternating angles...
let me see what i get from that
wait
so which option would i pick for that?
so i looked at thge deltamath example
could i not just use the statement and reason from 3 in the video for my answer?
they look to be the exact same question
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real wasp
.reopen
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✅
real wasp
soo...
narrow path
alright
real wasp
im terrible with proofs so im really just unsure on EVERYTHING here..
i feel like
the first 2 are the
parallel lines cut by a transversal form confgruent alternate interior angles?
and the third one.. i want to say given but its just reversed the order.. so would it still be considered given?
narrow path
real wasp
parallel lines cut by a transversal form confgruent alternate interior angles?
so i was right on this for the first 2?
and then my question on the third proof
i cant tell
its not reflexive
the midpoint has nothing to do with this
and nither does a segment bisector
thats why im thinking given but idk
does this look right
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twin willow
is there an easy way to calc A^6? i got that A isn't diagonalizable, with CP = (x-1)(x+1)^2
onyx glen
well you can like
go the repeated-squaring/rawdog route
do A^2, then A^4 as (A^2)^2, then A^6 as A^2 * A^4
twin willow
thats the best i can do?
onyx glen
can't think of anything less laborious
did you actually get that A isnt diagonalizable tho
or did you only get that its charpoly has repeated roots
twin willow
yes, since it doesnt have 3 eigenvalues
onyx glen
which by itself just means it might not be diagonalizable
did you check the geometric multiplicity of -1
twin willow
which by itself just means it _might not_ be diagonalizable
how do i prove it is then?
onyx glen
find dim ker(A + I)
twin willow
did you check the geometric multiplicity of -1
wdym? i did also calc A^{-1}
twin willow
find dim ker(A + I)
why?
twin willow
oh
onyx glen
A is diagonalizable iff dim ker(A+I) = 2
if you find a basis then those will be your (-1)-eigenvectors
youll need a 1-eigenvector to complete it obviously but thats always gonna be there
twin willow
u are saying it could that my diagonal matrix will have -1 twice and once 1 maybe?
onyx glen
your diagonal matrix will be that if it exists
based on the charpoly
we're now figuring out the P in A = PDP^-1
sturdy valve
is there an easy way to calc A^6? i got that A isn't diagonalizable, with CP = (...
not sure what eigen values are or what u guys are talking about but i can give u a way to find A^6 easily
onyx glen
not sure what eigen values are or what u guys are talking about but i can give u...
well, out with it then
we're trying to determine if OP's claim that A isnt diagonalizable is correct
or im trying to give him the tools to do it
are you about to suggest repeated squaring or what
sturdy valve
well, out with it then
write it as A = (X+I)
X^2 = 0
A^6=(I+X)^6, just use binomial expansion ull only have to write for the first 2 terms
sturdy valve
you're saying (A-I)^2 = 0 ?
yes
onyx glen
i call bullshit cause no the fuck it dont
sturdy valve
ok let me retry
onyx glen
well if you're not versed in eigenshit then you are literally stumbling around in the dark
recommend against trying to help here and now specifically, because, to put it bluntly, you dont know your shit
sturdy valve
well if you're not versed in eigenshit then you are literally stumbling around i...
my bad, the first row came out to be 0 so i thought the whole matrix would be 0
twin willow
your diagonal matrix _will_ be that if it exists
i found the statement that proves it, but is there a way to get the third eigenvalue in that case for the diagonal matrix?
onyx glen
wdym
your eigenvalues are 1, -1 and -1
-1 is a repeated (double) root of the charpoly
twin willow
-1 is a repeated (double) root of the charpoly
oh, i think i get it
becuase the ker(-1*I-A) will have dim =2
ty mate i get it now
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thorny shuttle
how to approach this?
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how to approach this?
frozen fiber
i would help but I don't remember the formula for pressure
thorny shuttle
P=F/A however the thing is F=Intensity times mass inside which is however variable
its just way too complicated not sure how to start
frozen fiber
is that how you're given force?
thorny shuttle
unique wagon
you can start by finding a function of mass with respect to r
thorny shuttle
you can use shell theorem for this or use gauss law in electrostats and swap out G for K
thorny shuttle
if someone has a background in physics feel free to answer
frozen fiber
I reckon you could generalise pressure for a sphere radius R
^
I'm currently doing physics
(I'm just useless at remembering formulae)
thorny shuttle
actually i have an idea
i think i was right
i would have to integrate thin shell elements i think i saw an hint
fathom saddle
Can you use multiple integration?
I was thinking in terms of a triple integral, but you are thinking in terms of a single integral
frozen fiber
I was thinking in terms of a triple integral, but you are thinking in terms of a...
the triple integral collapses into a single integral after evaluating the two angle components' integrals
unique wagon
$ \item $\displaystyle \rho=\frac{3M}{4\pi R^{3}}$
\item $\displaystyle m(r)=\frac{4\pi\rho r^{3}}{3}$
\item $\displaystyle g(r)=\frac{G,m(r)}{r^{2}}=\frac{4\pi G\rho}{3},r$
\item $\displaystyle \frac{dp}{dr}=-\rho,g(r)=-\frac{4\pi G\rho^{2}}{3},r$
\item $\displaystyle p(r)=\int_{r}^{R}\frac{4\pi G\rho^{2}}{3},s,ds
=\frac{2\pi G\rho^{2}}{3}\left(R^{2}-r^{2}\right)$
\item $\displaystyle p(r)=\frac{3GM^{2}}{8\pi R^{4}}
\left(1-\frac{r^{2}}{R^{2}}\right)$
\item $\displaystyle p(0)=\frac{3GM^{2}}{8\pi R^{4}}$
$
glossy valveBOT
mia
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
unique wagon
the mass function is needed since only the mass inside radius r creates a field at r
your idea of integrating shells is used when finding p(r) from the DE of dp/dr
thorn marten
Irodov?
unique wagon
**mia**
Compile Error! Click the <:errors:504266556054962196> reaction for more ...
R is the surface
r is the position of interest from the center
rho is density
p is pressure
btw
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stable jackal
My teacher didn't explain anything correctly
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stable jackal
I meant to send this nooo
Is it working?
Hello
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Sorry if I am freaking out too much stress and then this stupid stuff gets in my way
Omg
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ruby nova
Do you need help@stable jackal
stable jackal
Do you need help<@1290083885337677845>
https://discord.com/channels/268882317391429632/908078029778083872 I moved there now
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iron imp
|2x+1| > x
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|2x+1| > x
iron imp
how do i solve this
i tried 2x+1 > x or 2x+1 < -x
but it didn't give me the right answer
void nova
i tried 2x+1 > x or 2x+1 < -x
Good, but you need some conditions about x
gritty flax
You know that x has to be what ?
iron imp
no
void nova
Then why did you split that way?
iron imp
Then why did you split that way?
why is it wrong?
void nova
Because x can't take on any value
iron imp
whats the correct way of solving it?
void nova
Using the definition of modulus (absolute value)
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barren warren
jmc question, im sure there's a really easy trick to it but the problem is i dont know where to start 😭
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jmc question, im sure there's a really easy trick to it but the problem is i don...
@barren warren Has your question been resolved?
wind orchid
jmc question, im sure there's a really easy trick to it but the problem is i don...
is the ans 110
barren warren
is the ans 110
yes
my friend told me most of how to get there
using
simultaneous equations
BUT
the thing is
we havent been taught that yet
wind orchid
wait i am sending my solution and its very easy give me a min
only two eqs are formed but they are not hard
This is my solution sorry for my writing tho
barren warren
it is ok sir
wind orchid
tell me if you dont understand something in it
barren warren
ok sir
thank you sir
what does this mean
equation 1 and equation 2?
OH
I get it
.close
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surreal hamlet
I require assistance
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I require assistance
gritty flax
10-9 Roger that what do you need assistance with
surreal hamlet
You know how to go by this?
gritty flax
,rccw
glossy valveBOT
surreal hamlet
Hello?
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desert bane
is the path traced in this Qs an ellipse?
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is the path traced in this Qs an ellipse?
torn jolt
how do you have so many questions lol
desert bane
is the path traced in this Qs an ellipse?
tbh im not really sure on how to solve it either, my guess is that if its an ellipse the semi major axis must be the greatest distance, which must be the resultant of the two unit vectors
it would help guide on where i should begin
robust slate
is the path traced in this Qs an ellipse?
Probably. You don’t need that tho.
robust slate
it would help guide on where i should begin
Did you start by finding $\left |\overrightarrow{OP} \right|$ explicitly?
glossy valveBOT
Civil Service Pigeon
desert bane
**Civil Service Pigeon**
sqrt(1+2costsintcosθ)=sqrt(1+sin2tcosθ)
ohhhh sin2t will have max value 1
so sqrt(1+cosθ)=sqrt(1+a.b)
robust slate
k I assume ur good now then
desert bane
k I assume ur good now then
wait how do i check the direcn?
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urban nebula
How to find the maximum value of cos(theta) + cos(90-theta)
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How to find the maximum value of cos(theta) + cos(90-theta)
odd scarab
You can differentiate
Nice name
urban nebula
You can differentiate
This one worked for me
Thanks for the help
My answer was 45
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storm charm
what did i do wrong
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what did i do wrong
storm charm
pure basin
,rccw
glossy valveBOT
languid junco
doesn't look like you subtracted off your "evaluated at 1" part at all
midnight sun
is my answer correct?
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is my answer correct?
languid junco
why wouldn't it be counted?
midnight sun
too high
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@midnight sun Has your question been resolved?
midnight sun
No
midnight sun
is my answer correct?
Can anyone check and see if I’m correct with this
pure basin
Type .reopen
pure basin
Too late rip
rain merlin
too high
the criteria to consider a value as an outlier in terms of the median is it lying more than 1.5 times the interquartile range away from that quartile (in this case the upper)
rather than having to make a full cumulative frequency graph just make the table and observe where the median lies. you'll see better from there
another method for skewness is Q3 - Median relation with Median - Q1
e.g. if Q3 - Median > Median - Q1, then the upper half of the data is more spread out than the lower half, signifying a right or positive skewness
rain merlin
im afraid the 60 is not counted tho
after working out values, i feel like your reasoning was incorrect but you got the answer correct 😭
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rain merlin
@midnight sun recall that skewness means where the data tails off, i.e. in a left skewed data the majority of your data lies on the right and there's fewer values on the left that are skewing the average to that side.
that should help understand why your answer is correct
dawn gazelle
In this sort of exercise i basically need to get a solution in the form of u(x,t)=sin(kπx) (for example) , with k=1,2,...inf
I must have done something wrong along the way, can you please help? The 2 pages are my attempt to solve the exercise
dawn gazelle
Its basically a PDE with separation of variables that i need help with specifically
languid junco
gonna be real with you, this is very hard to read lol
dawn gazelle
want me to re-write it and send it again? i'll brb no worries
Dont mind the previous 2 pages
<@&286206848099549185> please help
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dawn gazelle
<@226468924848472065> Has your question been resolved?
we haven't even started man 😂, wait a bit
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@dawn gazelle Has your question been resolved?
dawn gazelle
Basically i have almost no issue until T(t)
maybe if the exercise included derivatives of xthen maybe i would have a bit more questions lol
dawn gazelle
<@&286206848099549185>
dawn gazelle
you mean these?
sand escarp
Oh nevermind
dawn gazelle
can you help please?
sand escarp
Don't think so... maybe you can get help in the advanced channels
dawn gazelle
advanced pdes?
sand escarp
I'd just ask the question there and close this
dawn gazelle
ok then
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sand escarp
Not sure where the bar of "advanced" really is
dawn gazelle
fair
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minor drift
Consider the function $f : \mathbb{R}^2 \to \mathbb{R}$ given by
$$f(x) = 2x_1^3 - 3x_1^2 - 6x_1x_2(x_1-x_2-1).$$
Show that $\nabla^2f(\cdot)$ is $L$-Lipschitz continuous and give the constant $L$ explicitly.
I've calculated
$$\nabla^2 f(x) = \begin{bmatrix}
6(2x_1-2x_2-1) & 6(-2x_1+2x_2+1)\
6(-2x_1+2x_2+1) & 6(2x_1) \end{bmatrix}$$
But I'm not sure how to proceed from here. Usually we are asked to show Lipschitz-continuity for a function or its gradient, this is the first time I'm dealing with the hessian, so i'm confused 😦
glossy valveBOT
ego
rapid rain
Consider the function $f : \mathbb{R}^2 \to \mathbb{R}$ given by
$$f(x) = 2x_1^3...
$|A| = \sqrt{\operatorname{Tr}(A^\top A)}$
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rafilou is not not born in 2003
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minor drift
ohhh got it thanks 🙂
minor crater
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minor crater
i don't quite get this part
he says that not containing any open set is much stronger than non-density
does this mean that density is stronger than containing an open set?
Q is dense in R but has no open sets
minor crater
aha i see
keen vector
isn't an example just [0,1]
or do u mean to say A is uncountable and non-dense in the interval (infA, supA)?
minor crater
or do u mean to say A is uncountable and non-dense in the interval (infA, supA)?
yeah that
minor crater
Nowhere dense is the **closure** has no open subset
and the closure of cantor set is itself right
hushed oar
How. He switched the -5 and -2 other way around didnt he. IT WAS SUPPOSED TO BE: (2x-2) (X-5)
hushed oar
because originally they were 2 and 5
odd scarab
multiply it out and see
There's another easier way to prove it
stiff musk
plug in a value for x?
hushed oar
no, (2x-2)(x-5) doesn't equal 2x^2 - 9x + 10
yeah but without proving how did he know he had to switch those
normally we wouldve done -2 and -5
not -5 and -2
stiff musk
well you can say that it will be of the form (2x-a)(x-b), where ab = 10 and a + 2b = 9
stiff musk
from that you can solve for a and b
atomic hare
bro is clearly double checking if he chose the roots correctly in subtitles
hushed oar
bro is clearly double checking if he chose the roots correctly in subtitles
He's doing it after making those brackets
i can do that too
atomic hare
uh yeah
hushed oar
but normally he puts it in order
hushed oar
but normally he puts it in order
WITHOUT double checking
atomic hare
well he already rehearsed this problem to show you guys so he knows the answer...
he chooses the right order first out of brevity
that or its just luck
odd scarab
WITHOUT double checking
U need to double check
hushed oar
U need to double check
Any quick way to double check then?
expanding would take some time
atomic hare
use ur brain i heard its cool
odd scarab
This was easier with multiple the whole two brackets
odd scarab
Any quick way to double check then?
Look at the pic above
atomic hare
Any quick way to double check then?
check the coefficient of the x term
it should he -9
odd scarab
it should he -9
Exactly
odd scarab
Ok this image helped me
Np buddy
narrow ermine
Any quick way to double check then?
As an aside, double checking is obviously good, although in the full method you can just split the middle term and double factor
$$2x^2 -9x + 10 = 2x^2 - 4x - 5x + 10 = 2x(x-2) -5(x-2) = (2x-5)(x-2)$$
odd scarab
Ok this image helped me
Don't forget the signs while u r checking
glossy valveBOT
Azyrashacorki
odd scarab
As an aside, double checking is obviously good, although in the full method you ...
This way takes forever and it makes no sense to use this type of question
It may be helpful with other questions
narrow ermine
I wouldn’t say it takes forever, granted you then don’t need to check you made the right guess. I also fail to see why it makes no sense for this type of question as it’s exactly what the question asks.
hushed oar
how did u get +10 from that method
narrow ermine
Regardless either way is fine ig
odd scarab
how did u get +10 from that method
U have the long equation which is
2x²-9x+10
U need to simplify it and u don't know the correct orders in the brackets
So u put
(2x-2) (X-5)
Check using my way
The answer will be -10x
Dose it equals the coefficient of x in the main equation (No)
So switch the numbers in the brackets
odd scarab
I wouldn’t say it takes forever, granted you then don’t need to check you made t...
Yeah, I totally agree with u but schools unfortunately don't focus on this concept so if u try to teach a student how to use he'll maybe get a little bit confused
narrow ermine
I think the product-sum method is pretty common. I wouldn’t even be surprised that’s what this person is being taught to factor those types of quadratics.
Moreover, the right pair is -4,-5, not 2,5. The point is it’s just a coincidence that the constants in the factors are -2 and -5, in general your factor pairs won’t necessarily appear in the final factored form…
odd scarab
@hushed oar, if u need any help tag me
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sleek shore
When dealing with determinants is it only the first row you are allowed to move the k outside?
Example det([ka,kb],[c,d])=k*det([a,b],[c,d])
umbral dome
you can move it out of any row
or any column
generally any property of the determinant that applies to the first row should apply to every other row and every other column
sleek shore
another diffrent question when you swap 2 row you have to multiply it by -
what happens when you swap columns?
umbral dome
same thing
every property that applies to rows also applies to columns, because of the fact that the determinant of the transpose is the same
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oblique swallow
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oblique swallow
anyone, help pls?
austere cove
I would probably approach this by finding the determinant as depending on a. Then using the determinant formula we know that det(M^2) = det(M)^2. Then we have a quintic to solve in a.
oblique swallow
I would probably approach this by finding the determinant as depending on a. Th...
there must be some trick.... how do u solve a quintic?
austere cove
oh, good news, the determinant isn't even dependent on a.
So there is no quintic. Just a linear equation in a
austere cove
there must be some trick.... how do u solve a quintic?
Well, I was thinking that they specified the "integer value of a," which implied to me that the rational root theorem would have been of use.
But thankfully it won't come to that.
oblique swallow
Well, I was thinking that they specified the "integer value of a," which implied...
ok.. so how do we move forward?
austere cove
ok, so do you remember what it means for a matrix to be non-invertable.
oblique swallow
ok, so do you remember what it means for a matrix to be non-invertable.
det = 0?
after that?
austere cove
I feel like I've been reasonably explicit with the steps, so let's step back
we want the determinant to be 0, so we want to select a such that the equation at the bottom has determinant zero.
We know that det(AB) = det(A) det(B), therefore det(A^n) = det(A)^n
what do you think we should do from here?
oblique swallow
We know that det(AB) = det(A) det(B), therefore det(A^n) = det(A)^n
WAIT WHATT
1s
lemme google smthng
austere cove
So one trick you can do to simplify the calculation is notice that everything is divisible by M^3, so we can factor that out.
oblique swallow
So one trick you can do to simplify the calculation is notice that everything is...
orrrrrrrrr we can take out factor as M^2?
That will fit in with the char formula?
austere cove
what?