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#help-17
vocal sleetBOT
vocal sleetBOT
Available help channel!
oblique tree
help
oblique tree
i still dont understand derivatives..
solar cape
i still dont understand derivatives..
Express each root in indice form
oblique tree
our prof was too lazy to teach us bruh
solar cape
$\sqrt[3]{x^2}=x^{\frac{2}{3}}$
oblique tree
where did the 3 came from
twin meteorBOT
denzio321
solar cape
**denzio321**
From here you can use power rule
oblique tree
i dont get the 3/2 square root of x
solar cape
Well can you express the square root of x in indice form
Alright do you like
Remember your indice laws
oblique tree
he didnt tell us about indice laws..
solar cape
No I mean like
oblique tree
we're doing self learning
oblique tree
idk what that is
solar cape
Well fuck
oblique tree
im cooked fr
solar cape
So $\sqrt[n]{x}=x^{\frac{1}{n}}$
twin meteorBOT
denzio321
solar cape
So for sqrt(x) its the square root
So n=2
So sqrt(x)= x^(1/2)🙏
Now you can use power rule
agile imp
Basically you'll just turn the radical into its "reverse form"
solar cape
Basically you'll just turn the radical into its "reverse form"
Bro why am I getting skull emojied
agile imp
Cuz why not 🤷🏿
oblique tree
do yall know the answer? cs im kinda slow learning step by step😭
solar cape
@oblique tree do you know how to use power rule
Just ask your teacher to stop fucking slacking
oblique tree
i prefer studying it after getting the answer
agile imp
do yall know the answer? cs im kinda slow learning step by step😭
We can't just give the answer instantly, we're here to teach you step by step
oblique tree
Just ask your teacher to stop fucking slacking
fr we've been backstabbing him
oblique tree
<@851882680852938754> do you know how to use power rule
can u tell me
oblique tree
its confusing
agile imp
Asking ppl online
How about do a vm
agile imp
oblique tree
ty ty, ill do it now
solar cape
Go cheat faster🔥
agile imp
Bro tolerated
vocal sleetBOT
vocal sleetBOT
Available help channel!
heavy palm
Is there a way to check that you're comparing to the right thing? For Direct and Limit Comparison test?
vocal sleetBOT
Is there a way to check that you're comparing to the right thing? For Direct and...
heavy palm
series and sequences
winter hawk
Is there a way to check that you're comparing to the right thing? For Direct and...
yes when the main condition of limit comparison is satisfied
heavy palm
what is that main condition?
winter hawk
$\lim\frac{a_n}{b_n}=c\in(0,\infty)$
twin meteorBOT
ロケットジャンプ
winter hawk
np
heavy palm
.close
pseudo forge
for an induction proof, i want my algebra in the induction step to reach 1 - 1/(m + 1), but i'm unsure what to do from what i have so far
vocal sleetBOT
for an induction proof, i want my algebra in the induction step to reach 1 - 1/(...
pseudo forge
In order to prove the induction step what do you need to show
the end of the induction step should end up as 1 - 1/(m + 1)
half imp
Well, it could end up as less than that as well
pseudo forge
true. i was thinking of saying that m/(m+1) < 1
half imp
I don't see how that helps
half imp
the end of the induction step should end up as 1 - 1/(m + 1)
What do you get if you simplify 1-1/(m+1)?
half imp
Yeah looks good
strong gyro
Hi! Taking calc and I’m stumped with part j) here. Pls ignore the state of my page lol
How would you go about solving that?
My answers to the other parts are these (fact checked):
g) y= (80/1849)x^2
h) (-√(1849/2)) or abt -30.4056 for the x value, y value is 40
i) y= -2.631095x - 40
Thank you sm!
vocal sleetBOT
Hi! Taking calc and I’m stumped with part j) here. Pls ignore the state of my pa...
@strong gyro Has your question been resolved?
cunning plaza
Okay. Had to do a double take. We can assume that when the water skier lets go of the boat, they fly in a perfectly straight line (like that line you drew then erased)
The slope of this line is simply the derivative at the point in which you let go. That’s the definition of the derivative
So you need to find a point on the parabola such that a line with slope equal to the derivative at that point (and obviously originating from/intersecting that point) will hit the dock
strong gyro
So you need to find a point on the parabola such that a line with slope equal to...
ohh okay. that makes sense, thank you sm!
is there a specific way to go abt this or is it just guessing from here
cunning plaza
You can set up an equation. You can get a function (of x) for the derivative. Plug in that as your slope. Plug in the variable x and f(x) as your point (into the slope intercept formula of a line, or wtv u call it). And set the resulting x,y pair equal to the coordinates of the dock. Then you should be able to solve for x
vocal sleetBOT
vocal sleetBOT
Available help channel!
mossy belfry
How do I show that If A and B are independent and A and C intersect B are independent then A and C is independent
vocal sleetBOT
How do I show that If A and B are independent and A and C intersect B are indepe...
green crow
Independent what?
green crow
Oh, events
spiral turtle
By the definition of independence, we have P(A and B) = P(A) P(B)
Similarly we have P(A and B and C) = P(A) P(B) P(C)
We want to prove that P(A and C) = P(A) P(C)
Consider P(A and not B and C)
If we can prove this value is equal to what, then we can prove our goal
green crow
If B intersection C is dependent on A, then either B or C or both B and C should be dependent on it. But since it's not, both B and C are independent of A
That's what I think, I'm not sure whether it's the correct approach though
grim crow
Looking for some help with this question. When calculating the upper flux (Circle with z=6), I get -144pi. However, answer says 144pi. Wondering where I went wrong.
vocal sleetBOT
Looking for some help with this question. When calculating the upper flux (Circl...
grim crow
I get the integral of -36r dr dtheta where 0<=r<=2 and 0<=theta<=2pi
flat whale
can you show your full work
flat whale
,rotate
twin meteorBOT
grim crow
I changed the surface from the cylinder to two circles at z=6 and z=1
From there I get the normal vector of <0,0,r>
One thing I'm confused about is how I should orient this vector
I realise that if I flip the orietation of this vector to be <0,0,-r> for the top and <0,0,r> for the bottom, I would get the correct answer, but not really sure why
flat whale
use right hand rule?
grim crow
I used right hand rule initially to determine the orietation of the boundary
But once I switch surfaces, I'm not sure how to use right hand rule/if I can use it
I'm not sure if you can since my working is slightly messy, but the orientation of the top circle is counterclockwise given that outward normal is used for the cylinder
flat whale
turn your hand upside down and use right hand rule again
grim crow
Does that mean after I swap the surface, that is my orientation?
Ok, so I use right hand rule again to determine that after surface swap, I now have downward normal for top circle and upward normal for bottom circle?
flat whale
you're supposed to have an outward pointing normal
grim crow
Yea
Im a little confused, if I use <0,0,-r> for the top circle after applying right hand rule again, isn't that not outward anymore?
🥴 kinda confused sorry
vocal sleetBOT
@grim crow Has your question been resolved?
grim crow
<@&286206848099549185> sorry for the ping
I now also have a question about this. Is there a reason why I'm not given the direction of the normal vector?
spiral turtle
@grim crow normal vectors generally, by convention, point outward, but if you're intended to prove that the flux is zero, then the orientation of the normal vector does not matter
(because -0 = 0)
grim crow
<@700972707826761809> normal vectors generally, by convention, point outward, bu...
I see, but how about for part c?
I can show part b is true, but then not sure how to approach part c
spiral turtle
Well, you can use linearity
grim crow
I can see that I = flux of F + flux of G
spiral turtle
F = G + <0, 0, z^2>
spiral turtle
Yes exactly
grim crow
However, can I use stoke's theorem here?
Probably not right?
Since <0,0,z^2> isn't a curl of some function?
spiral turtle
You can just integrate over the surface
grim crow
Ahhh so what I need here is a standard surface integral using G(theta, phi)
Rather than trying to use line integral = curl(F)
spiral turtle
Exactly
grim crow
Looking for some help with this question. When calculating the upper flux (Circl...
sorry coming back to this question
Would it be possible to help clarify some of my confusions?
spiral turtle
And z is simply cos θ assuming you're using θ as the polar angle
grim crow
And z is simply cos θ assuming you're using θ as the polar angle
Yep, gotcha.
spiral turtle
Well r cos theta
grim crow
Here's my working for this question
grim crow
Well r cos theta
but r=1 so it's just cos theta
spiral turtle
Here's my working for this question
I'll be honest, it's been a hot minute for me and the particulars of orientations with vector surfaces. I was able to help with the sphere because I had a strong enough memory of that scenario. But edge orientation of a non-closed manifold with a hole is something I'm not super confident on.
grim crow
I'll be honest, it's been a hot minute for me and the particulars of orientation...
Gotcha. Ty! If you wanna through you're opinion in, that'd be great too
spiral turtle
I can try to Google it
Oh
Both are rotating clockwise when viewed looking at the circle
So if you're looking at it from the side, the top is rotating to the left, and the bottom to the right
Essentially, imagine your normal vector as having a very small counterclockwise oriented circle around it, and move this vector around.
When it's near the bottom, the bottom is going right at the bottom, near the top it's going left at the top
@grim crow
grim crow
Ok this is gonna take me some time to take in 😓
grim crow
Just curious, so the orientation should only affect the direction of the normal right?
The parametrization of the surface itself is independent of the direction of the normal?
spiral turtle
If the surface normal is different so is the orientation of the edge
But other than that, yeah
grim crow
But other than that, yeah
but the edge doesn't affect the parametrization of the surface though no?
spiral turtle
The edge shouldn't?
I guess if you're talking about the parametrization of the surface for the purpose of performing a surface integral it absolutely doesn't
@grim crow
I'm not entirely sure that a parameterization for other purposes would be independent of the edge, but for the integral, yeah absolutely, the edge doesn't matter.
vocal sleetBOT
@grim crow Has your question been resolved?
lilac sluice
could someone guide me through the explanation of why the curve has exactly one x-int?
vocal sleetBOT
could someone guide me through the explanation of why the curve has exactly one ...
paper depot
do you know what the definition of an increasing function is?
(hint: it does not involve derivatives)
paper depot
bad on both counts sorry
paper depot
we say that a function is increasing if, for any a and b in its domain with a < b, we have f(a) < f(b).
which can be phrased informally as "higher inputs give higher outputs".
an x-intercept is a value of x such that f(x) = 0.
but if f(x) were 0 for two different x's, the definition of increasing-ness would be violated.
paper depot
...
f(1) should be higher than f(0)
at no point did i imply that f(0) = f(1).,
what i said is,
if it were the case that f had at least two x-intercepts,
i.e. if f(SOMETHING) were equal to f(SOMETHING ELSE),
then the definition of f being an increasing function would be violated
lilac sluice
mmmmm
oh
so since the function f(x) = x^3 + x - 1 is increasing
therefore there cannot be more than 1 x-int
hence there is only one x-int?
paper depot
therefore there cannot be more than 1 x-int
hence there is only one x-int?
this needs extra justification
why does an x-int need to exist at all?
lilac sluice
would it be because it’s a polynomial so it must intercept the x-axis at least once?
paper depot
ok, so why does this polynomial of yours have to have at least one x-intercept?
clearly the reason cannot be merely that it is a polynomial, for x^2 + 1 is also a polynomial yet lacks any x-intercept.
lilac sluice
could i have a hint
@paper depot would it be that since this polynomial is of odd-degree, then it must go from -inf to +inf and so it must cross the x-axis once
which gives it its one x-int
winter hawk
f(0)=?
lilac sluice
f(0) is -1
winter hawk
f(1)=?
lilac sluice
1
winter hawk
so is it possible to have a root between 0 and 1?
winter hawk
if u believe it rigorously prove it
lilac sluice
erm idk
winter hawk
does f have any nice relevant properties?
lilac sluice
what does that mean
winter hawk
does f have any property relevant to proving existence of roots
did u learn any theorems about this
lilac sluice
nope
winter hawk
do u know any theorems about continuous functions
lilac sluice
no
only proving continuous functions with limits i have
other than that idk abything else
winter hawk
that sucks bc u need one here
winter hawk
intermediate value thm
paper depot
^
lilac sluice
yea i haven’t learnt that
winter hawk
heres the down n dirty
if $f$ is continuous on $[a,b]$ and $y$ is between $f(a)$ and $f(b)$ then there exists $x\in(a,b)$ such that $y=f(x)$
twin meteorBOT
ロケットジャンプ
winter hawk
in plain speak f will hit every value between f(a) and f(b)
thats why its called intermediate value
lilac sluice
but surely there’s another way we can explain the answer to this question without using this
winter hawk
in general theres no other way 🙂
lilac sluice
that’s strange
winter hawk
this is one of the most famous theorems in calc and is the strat for proving roots exist
lilac sluice
the tutors wouldn’t ask me smth on smth i havent learnt
lilac sluice
this is one of the most famous theorems in calc and is the strat for proving roo...
i’ll probably be learning it this week then, or over the next few weeks
winter hawk
idk smth went wrong in the curriculum
lilac sluice
<@183668144404037632> would it be that since this polynomial is of odd-degree, t...
so this is invalid?
winter hawk
the proof of the odd degree fact depends on my theorem
lilac sluice
is there any other name for the theorem u stated
lilac sluice
alrlr
winter hawk
then yell at them to teach u the theorem 🙂
lilac sluice
gotcha
lilac sluice
nah it’s fine
i’ll ask on thursday
cus if i learn it this week then ill learn the proof for it too
winter hawk
sounds good
lilac sluice
alrlr thanks
winter hawk
np 🙂
winter hawk
<@150414892225134592>
yes
lilac sluice
lesh go
for question 1, what am i missing
im not sure if i should be drawing the curve up or down when y<0
atomic jetty
im not sure if i should be drawing the curve up or down when y<0
Down
lilac sluice
why
winter hawk
this looks ok
atomic jetty
Because if you see the question, the value of tangent for negative x is negative
winter hawk
u should do it for x<0 tho
lilac sluice
u should do it for x<0 tho
yea that’s what im asking for rn
winter hawk
u said y<0
lilac sluice
u said y<0
oh whoops
winter hawk
slope<0 if x<0
lilac sluice
slope<0 if x<0
but if i draw the curve down then the gradient becomes positive
atomic jetty
You dont care about that rn
You just trace the gradient of the original eqn
I mean function
lilac sluice
so it’s basically - 0 + 0 - 0 +
those are the gradients of the original function
if the gradient is negative, then the function is decreasing at that point right?
f’(x) = y’
so y’ < 0
which is why the curve goes down?
is what i said true
atomic jetty
Yes
lilac sluice
ohhhh
atomic jetty
Just see what is the direction of the original function at that point
lilac sluice
yes
hearty chasm
for part b. iv i dont get what its asking me for
vocal sleetBOT
for part b. iv i dont get what its asking me for
hearty chasm
ive done everything up to that question
dusty marlin
@hearty chasm If I am to assume that part a was to find the terms that agree with the individual logics, then part B should be the probability of each logic happening
dusty marlin
Use this for part biv ^
cyan forge
Im working with statics and find myself making mistakes when projecting forces in some situations like this. What is an easy way to project this mg-force in the x and y components or like what is an easy way of thinking about it?
vocal sleetBOT
Im working with statics and find myself making mistakes when projecting forces i...
cyan forge
edgy kayak
as you did, you need to change your axis
view the normal force as the y axis and friction as x axis
cyan forge
But im asking with the axis as shown
edgy kayak
they are doing exactly what i said
cyan forge
Yes, but what about getting it right in terms of sin or cos
That is what im trying to ask sorry
cyan forge
Yes
edgy kayak
now this angle will be equal to 30 degrees
the top one
then you can simply find the components
stark flicker
Can someone explain how you would approach a problem like this?
vocal sleetBOT
Can someone explain how you would approach a problem like this?
sweet birch
Can someone explain how you would approach a problem like this?
well you've got xy on one part and abc on the other, so I'd start by unifying those somehow
and I'd also use the fact that sqrt(ab) = sqrt(a)sqrt(b) plus everything involved is nonnegative so you can happily multiply and divide across the inequality without issue
vocal sleetBOT
@stark flicker Has your question been resolved?
finite hatch
how did it go from 2 to 4 terms
vocal sleetBOT
how did it go from 2 to 4 terms
river kettle
bum chicken
river kettle
nice
finite hatch
and i got a pH of 19
river kettle
gg
finite hatch
am i cooked
river kettle
yws
river kettle
which step confuse u
river kettle
where did ur cos term go
river kettle
it just evaporated
river kettle
its not u just have to becareful with ur algebra
river kettle
what did it say the answer was
finite hatch
river kettle
try the second derivative again
river kettle
is not
finite hatch
i knew i shouldnt have done selective school past test
vocal sleetBOT
finite hatch
.reopen
vocal sleetBOT
✅
river kettle
if it makes it easeier
river kettle
no
finite hatch
oh
finite hatch
ok how do i draw it then ugly
dull bear
Well 
river kettle
Well <:catThink:519997422194393108>
dull bear
it just has to satisfy the requirements
river kettle
u should label x=1 and x=3
dull bear
is it like this
You need a vertical asymptote at x = 1 as well
river kettle
chartbit technicall what if u jst draw a massive hole at x=1 and x=3 
dull bear
chartbit technicall what if u jst draw a massive hole at x=1 and x=3 <:opencry:5...
At least for the x < 1 parts, that isn't too bad, you want it to be positive, increasing, and having an asymptote at x = 1
river kettle
also is this not implied in the first dot point where f'>0 for all x except xneq 1 and 3
because if f' >0 then f>0
finite hatch
ITS TOO HARD RIGHT
dull bear
because if f' >0 then f>0
Not necessarily, e.g. f(x) = ln(x)
dull bear
but like thasts a weird function
You're a weird function 
river kettle
ITS TOO HARD RIGHT
draw the first 2 dot points
dull bear
Differentiate it and rearrange 
dull bear
u cant js skip every hard q
Agreed!
finite hatch
dull bear
dull bear
Careful, what's the derivative of -x^2 + 1?
dull bear
Yep, that (-1) should rather be -2x instead
But once you've done that, you can factor out a common factor between everything 
river kettle
chartbit is great a vectors too u should ask chartbit vector questions 
anything with geometry
dull bear
anything with geometry
river kettle
finite hatch
OMG I DID IT
YESS
i am, so smart..
i jussst wanna thank.
my parents..
and ...
Jesus..
river kettle
thank me
finite hatch
for giving me this opportunjity
to solve this problem
by myself
thank u so much 😭
river kettle
blud thanked everyone but the person helping you
vocal sleetBOT
vocal sleetBOT
Available help channel!
shell flax
hey guys im student in grade 7 i have a exam tomorrow can you help me with these math converting
vocal sleetBOT
hey guys im student in grade 7 i have a exam tomorrow can you help me with these...
green crow
hey guys im student in grade 7 i have a exam tomorrow can you help me with these...
Tell what you need the help with
shell flax
so i have convert like 2.7 mm to m
with full solution
mm cm dm m dam hm km
mass length and capacity
green crow
with full solution
I'm not sure what steps they taught you as the full solution, but this should be it
You can add any extra details according to your notebook's solutions
vocal sleetBOT
@shell flax Has your question been resolved?
vocal sleetBOT
<#903463353417072641>
sweet birch
,rcw
twin meteorBOT
fallow isle
twin meteorBOT
fallow isle
quiet echo
,rccw
twin meteorBOT
quiet echo
Okay, which one do you want to start with?
fallow isle
i am new discord i don't even now how to use it
fallow isle
this one
quiet echo
Use a right isosceles triangle.
^
fallow isle
ahhh how
fallow isle
cosine = hyp/Perpendicular
fallow isle
.
quiet echo
cosine = hyp/Perpendicular
So, if we use a right isosceles triangle, what angles does it have?
vocal sleetBOT
@fallow isle Has your question been resolved?
vocal sleetBOT
@fallow isle Has your question been resolved?
shell flax
You can add any extra details according to your notebook's solutions
thank you so much man
vocal sleetBOT
@fallow isle Has your question been resolved?
tranquil charm
@fallow isle
fallow isle
<@779222796651069470>
yes
tranquil charm
ok?
tranquil charm
,rcacw
twin meteorBOT
tranquil charm
Nothing just rotating ur image
fallow isle
thanks
tranquil charm
so you do not understand question no 5?
fallow isle
so you do not understand question no 5?
i have get answer of the other question from another group
fallow isle
yes
tranquil charm
ok
so basically if we change it by 2pi (360) it basically doesn't change
since it just moves back to it's starting point
You understood that
fallow isle
nop
first when they convert rad into degreedegree
i solve this question by another way
i got correct answer
tranquil charm
Ok tel
tranquil charm
I just see them removing pairs of 2pi
That is what they did?
They did the exact same thing @fallow isle
fallow isle
how
tranquil charm
You added it
fallow isle
how they know to solve these into 60degree -3(360)
tranquil charm
so basically
- 17 pie/3
-17pi/3 we can take 2pi=360 and remove it hence 2pi=-6/3
we take 2pi out 3 times so we get -17/3 -(-18/3)
That is pi/3=60
fallow isle
i think get better understanding by written
can u please solve this by writing for me
tranquil charm
i think get better understanding by written
Ok so what they did is you get -1020 degrees and since you can add/subtract 360 and it doesn't change so you find multiples of 360 so 360 x 3=1080 and then -(360*3)=-1080 so we do -1020 - (-1080) and we get 60
fallow isle
ah nice
fallow isle
Ok so what they did is you get -1020 degrees and since you can add/subtract 360 ...
i convert it into degreen from rad
thanks @tranquil charm
flat whale
how to close
!done
vocal sleetBOT
how to close
If you are done with this channel, please mark your problem as solved by typing .close
fallow isle
.close
vocal sleetBOT
fallow isle
!done
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
vocal sleetBOT
Available help channel!
dense trout
does {0} under multiplication forms a group?
vocal sleetBOT
does {0} under multiplication forms a group?
dense trout
chatgpt says it does not cuz in multiplication, the identity is 1, which is not present in the set....
But I think it should form a group because though 1 is the identity in multiplication in general, but in this specific case, the set only has one element which when multiplied by itself gives itself, 0.
paper depot
!nogpt
vocal sleetBOT
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).
paper depot
but also this is a set with 1 element
dense trout
so......... it forms a group?
dense trout
but it does not satisfies inverse property anyways.....
fleet ember
a way to see it is to notice that since 0 is the only element, 0*0 = 0 and 0 is an identity
but then... 0*0 = e also says that 0 is the inverse of 0, everything holds
what gpt didn't like is that it's not called 1, so it can't think correctly about the inverse
but you can : )
dense trout
ok thnx
.close
no but 0 cant be inverse of itself cuz 0/0 is not 0
so I think its not a group
fleet ember
there is no division in a group
an inverse is defined by the property of element * inverse = indentity
fleet ember
yes, for the 3rd time
vocal sleetBOT
vocal sleetBOT
Available help channel!
white mesa
Here's the translation of the problem into English:
"A diagnostic test for a rare disease has a 1% false positive rate and a 0.5% false negative rate. The incidence of this disease is 50 people per million. Calculate the probability that:
a) A person who is sick will test positive. b) A person who tests negative will be healthy. c) A person who tests positive will be sick."
white mesa
I'm not sure how to answer point B i'll explain my logic
If you test 10^6 people you expect 10^6 -50 to be sane
of those one hundredth are diagnozed positive
so 99%(10^6 -50) : 10^6 = x :100
pallid flax
Here's the translation of the problem into English:
"A diagnostic test for a ra...
this is a mathematical "paradox" I'm pretty sure I've seen something really similar on YouTube, would you like me to see if I can find the video
white mesa
yeah if you could
pallid flax
vocal sleetBOT
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white mesa
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atomic hill
can someone help me with this
vocal sleetBOT
can someone help me with this
atomic hill
im a bit stuck
manic dawn
can someone help me with this
for the inductive step, start by multiplying both sides by (2(n+1)+1)/(2(n+1))
vocal sleetBOT
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untold meteor
HI everyone I am trying to derive the Sackur-Treode equation for the translational entropy of an ideal gas. Unfortunately however, I am having a lot of trouble getting the final constant of -1.15, can anyone help explain what Im missing/doing wrong
vocal sleetBOT
HI everyone I am trying to derive the Sackur-Treode equation for the translation...
untold meteor
well essentially, my main problem is the constant, and I think it has something to do with the "dimensionless" aspect of it
like im not sure if my use of units in SI is correct
flat whale
your error could be anywhere so it's hard to determine where unless you explain the non-obvious steps
untold meteor
what steps are unclear? I feel like for the most part its a straight forward derivation. there isnt any strange operations or anything
each step is essentially a substitution or cancelling
or rearrangment of ln
I appreciate any help
flat whale
¯_(ツ)_/¯
vocal sleetBOT
@untold meteor Has your question been resolved?
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@untold meteor Has your question been resolved?
vocal sleetBOT
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grim crow
Would like to double check my working here
vocal sleetBOT
Would like to double check my working here
grim crow
So once I apply Stokes theorem, I get the double integral of 4 dS where S is surface vector
so then I should have 4 dot unit normal dS
Which should give me 4sqrt3 dS?
Then I simply multiply 4sqrt3 by 16?
vocal sleetBOT
@grim crow Has your question been resolved?
winter hawk
,w curl[-z^2,2zx,4y-x^2]
twin meteorBOT
grim crow
Yea and the unit normal of the surface is 1/sqrt3<1,1,1>
Which results in 4/sqrt3
However I'm unsure if I'm doing it correctly
winter hawk
,w [4-2x,2(x-z),2z] dot [1,1,1]
twin meteorBOT
winter hawk
its right so far
grim crow
My question is what do I do from here
Like I feel like the answer should be sqrt3/3 * 64
or sorry 64*sqrt3/3
winter hawk
curlF.n=4/sqrt3 yes?
grim crow
yes
winter hawk
np 🙂
delicate cairn
Could someone please help me out, on how they got from the first form to the second?
vocal sleetBOT
Could someone please help me out, on how they got from the first form to the sec...
last harbor
Could someone please help me out, on how they got from the first form to the sec...
heya let me take a look
delicate cairn
Thanks I appreciate it!
cobalt crypt
probably lhopital
last harbor
i think it is lhopital
delicate cairn
It is
thin vale
okay that is how
last harbor
uhh quick question to you guys
delicate cairn
OH it's the derivative!
delicate cairn
no no i get it , sorry I see now!
last harbor
👍
thin vale
do we have to use the formatting thing
You don't have to but you should figure out how to use it, its fairly easy and very useful
you'll pick it up quick if you try
delicate cairn
dumb brain moment, cheers folks
last harbor
You don't have to but you should figure out how to use it, its fairly easy and v...
perhaps i will then thanks 
delicate cairn
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vagrant gorge
hi anybody here to help
vocal sleetBOT
hi anybody here to help
vagrant gorge
😭
alpine kestrel
whats ur question
vagrant gorge
white whale
!status
vocal sleetBOT
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
@vagrant gorge
white whale
Have you been taught vector?
white whale
Okay, let's get more elementary, then.
vagrant gorge
aight
white whale
Can you sketch the movement of the boat?
vagrant gorge
yeah
white whale
Ping me if you have finished.
vocal sleetBOT
@vagrant gorge Has your question been resolved?
white whale
No, just the sketch first.
vagrant gorge
i have the sketch
white whale
Post it here.
white whale
Now, from the 3km line, draw a line perpendicular to Y axis. It will form a triangle. Calculate the height and base of the triangle.
Then the bearing can be calculated by using atan.
vagrant gorge
Now, from the 3km line, draw a line perpendicular to Y axis. It will form a tria...
ok ive done this
now what do i do
@white whale
white whale
Send me the sketch, but with the vertices labelled
white whale
I'd go with this, tbh
You know OA, AB. Angle BAC can be calculated from the bearing given. Now you have to find the angle BOA, which then you can use to calculate the bearing.
vagrant gorge
sorry had to go afk
back now
if angle bac is 110 degrees, how do i calculate BOA
@white whale
white whale
if angle bac is 110 degrees, how do i calculate BOA
Uh, what?
BAC is not 110 degress.
white whale
Then you find out two of the BC, BO, and AC.
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bleak prawn
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bleak prawn
The slope of the tangent on path P is y'(pi/4)/x'(pi/4)
x'(t) = cos(t) - 4sin(t)cos(t)
y'(t) = -sin(t)
-sin(pi/4)/(cos(pi/4) - 4sin(pi/4)cos(pi/4))
-(sqrt(2)/2)/(sqrt(2/2) - 4(sqrt(2/2)sqrt(2/2))
-(1)/(1 - 4sqrt(2/2)
-1/(1 - 2sqrt(2))
The slope of y = x + 1 is just 1
arctan(-1/(1 - 2sqrt(2))) - arctan(1)
Is that my answer?
<@&286206848099549185>
.close
hybrid sinew
Hi, I can't find the answers to this question. I need to match the diagrams with the functions, can anyone help?
vocal sleetBOT
Hi, I can't find the answers to this question. I need to match the diagrams with...
hybrid sinew
I've done it but not sure if I got them correct or not :/
green crow
Send your answers here, I'll verify it
hybrid sinew
B D A F H E
green crow
B D A F C E
hybrid sinew
B D A F C E
why is H incorrect?
green crow
On simplification, the equation would be 3(x+1)(x+2)
From this, we can say that it's C
hybrid sinew
But H, the derivative before x = -1.5 is negative, and after is positive
Also the arrows, so is H not correct?
green crow
$f'(x) = 6x+9$
twin meteorBOT
Suika
hybrid sinew
Right, so it is negative
twin meteorBOT
Suika
green crow
It should be - for x < -1 and + for x > -1
K, nevermind
That's f directly
Isn't it possible for a question to have 2 answers?
green crow
No, it's B
green crow
Isn't it possible for a question to have 2 answers?
Is it?
I think your answers are correct
Just a misunderstanding on my part
vocal sleetBOT
@hybrid sinew Has your question been resolved?
lapis jacinth
find x
lapis jacinth
Try openning brackets and abbreviation.
I cant bracket:(
lean iris
@lapis jacinth
lapis jacinth
yes
lean iris
U cant open brackets?
lapis jacinth
U cant open brackets?
yes
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
lean iris
Dude, how do u want to solve it without general rules, and without simplification
@lapis jacinth
Try to solve delta and find x1 and x2
lapis jacinth
Try to solve delta and find x1 and x2
;v
river arch
I'm trying to check the differentiablity of $f(z) = \bar z^2/z$ at $z = 0$
twin meteorBOT
dyxn
river arch
So I just used the limit definition of a derivative and ended up with
$$\lim_{z \to 0} \left ( \frac{\bar z}{z} \right)^2$$
twin meteorBOT
dyxn
vocal sleetBOT
@river arch Has your question been resolved?
cyan talon
well seeing conj(z)/z I'm not super hopeful the limit exists
have you tried finding two paths for which the limit of f(z)/z is different ?
@river arch
river arch
well seeing conj(z)/z I'm not super hopeful the limit exists
Yeah I know that limit doesn't exist
I checked along x = ky and all the limits are -1
Am I allowed to do other paths like was done in multivariable calculus?
y = x^2 and stuff
cyan talon
I checked along x = ky and all the limits are -1
hmmmmm
so like z = x + ikx stuff like that ?
I don't get -1 at all
how do you end up with that ?
@river arch
river arch
Oh
Wait
😭
I made a stupid mistake
((1 - ik)/(1 + ik))^2 = ((1 - k^2 - 2ik)/(1 + k^2))^2
yeah okay so different values of k give different values of the limit
therefore it's not differentiable
cyan talon
yeah it works nice here
vocal sleetBOT
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heavy palm
What am I suppose to do after this step? I don’t know how to simplify this further
vocal sleetBOT
What am I suppose to do after this step? I don’t know how to simplify this furth...
heavy palm
6
Answer key shows me this
I have no idea how that left expression
Turns into that right
How do they simplify that factorial?
Can someone explain it to me please
alpine kestrel
wait i legit did this worksheet in my calc class lmao
alpine kestrel
the left part is from ((-3)^n+1)/((-3)^n)=-3
heavy palm
What am I suppose to do after this step? I don’t know how to simplify this furth...
This is what I did so far
alpine kestrel
sorry didnt see that lol
heavy palm
All good
alpine kestrel
ya then u just see that 2(n+1)+1=2n+3
and (2n+1)!/(2n+3)! = 1/(2n+2)(2n+3)
thats where it comes from (:
do u know the definition of factorial?
heavy palm
and (2n+1)!/(2n+3)! = 1/(2n+2)(2n+3)
I understand the line above this but how do they simplify into that? Removing the factorial
alpine kestrel
bc x!=x*(x-1)!
like (2n+3)!=(2n+3)(2n+2)(2n+1)!
so (2n+1)!/(2n+3)!=1/(2n+2)(2n+3)
vocal sleetBOT
@heavy palm Has your question been resolved?
silk cipher
i really dont get this
vocal sleetBOT
i really dont get this
silk cipher
i got 1570
paper depot
do you know in general how to read a cumulative freq graph
paper depot
i got 1570
show work?
silk cipher
do you know in general how to read a cumulative freq graph
no
paper depot
ok right so... do you know what "cumulative frequency" means in general
silk cipher
show work?
top line approx 10
second line approx 60
thrid line 10
silk cipher
ok right so... do you know what "cumulative frequency" means in general
the frequency with the previous added
paper depot
top line approx 10
second line approx 60
thrid line 10
wdym by "top line"?
silk cipher
in the chart
the entry prices chart
with the 0 < x< 15
ik it isnt just < i cant find the corrent char on the keyboard
paper depot
ok so you found that there are:
- 10 kids under 5
- 60 kids aged between 5 and 15
- 10 people aged 15 and up
you said you don't know how to read cumulative frequency graphs, yet you just did exactly that...
paper depot
idk how to figure out the price tho
the price for each age category is literally given to you
an under-5y/o ticket costs £12 and there were 10 such tickets sold, how much does that give?
silk cipher
120
paper depot
can you do the same for the other two age categories
silk cipher
60*20 is 1200 i think
so 1320 so far
plus 25*10 is 250
so 1570
i put that in but it said it was wrong
vocal sleetBOT
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rigid needle
gray slate
What's the set theory?
vocal sleetBOT
What's the set theory?
paper depot
hushed tree
vocal sleetBOT
@gray slate Has your question been resolved?
strange charm
Hi, id like someone to critize my proof
vocal sleetBOT
Hi, id like someone to critize my proof
strange charm
or if im doing something wrong
i feel like second line doesnt do anything so i just got rid of it
gray slate
<@1172659259436187710> Has your question been resolved?
yes isr
vocal sleetBOT
@strange charm Has your question been resolved?
craggy crypt
i really dont get this
mfw they draw the discrete random variable like a continuous one
OH WAIT SHIT this is not the active question uhhhh
sorry for the ping
vocal sleetBOT
@strange charm Has your question been resolved?
restive tundra
You've got the right idea but there are a few typos in it. For instance, you did the chain rule wrong and wrote f(x_0) instead of f'(x_0)
You also said that g'(x_0) is differentiable instead of g(x_0)
Some of the typesetting isn't my favorite either, if you care about that
The second line is needed because it justifies that f is injective
You can cut out a whole line at the end by just writing "= 0. This is a contradiction." if you wanted to make it more concise
vocal sleetBOT
@strange charm Has your question been resolved?
strange charm
You've got the right idea but there are a few typos in it. For instance, you did...
Thank you!
vocal sleetBOT
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tawny nacelle
If $M \subseteq \R^n$ is an orientable $(n - 1)$-dimensional manifold, show that there is an open set $A \subseteq \R^n$ and a differentiable $g: A \to \R$ so that $M = g^{-1}(0)$ and $g'(x)$ has rank 1 for $x \in M$.
vocal sleetBOT
If $M \subseteq \R^n$ is an orientable $(n - 1)$-dimensional manifold, show that...
twin meteorBOT
higher!
tawny nacelle
I need a hint to start this
I literally have no idea what to do to construct this A and g
anything will help 
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pulsar star
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uncut anvil
$1 - \tan(x) = \frac{\cos(x) - \sin(x)}{\cos(x)}. \text{then use} \frac{a}{\frac{b}{c}} = \frac{ac}{b}$
twin meteorBOT
8n2
pulsar star
$1 - \tan(x) = \frac{\cos(x) - \sin(x)}{\cos(x)}. \text{then use} \frac{a}{\frac...
i already did that i think
oh
oh
nvm
ok
proper lava
pulsar star
yup i did it like that thanks for confirming
vocal sleetBOT
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past sail
twin meteorBOT
salagata
