didn’t you just give the expansion for 5!
#help-36
cobalt lodge
spice field
Yes but I don't how to work with (n-1)!
tired walrus
do we not just cancel out the (n-1)!'s
it is the other factorial that gets expanded
cobalt lodge
yes but i want to force this first otherwise they don’t understand why it reduces to the form below
otherwise they won’t be asking in here
tired walrus
do you know what a factorial is generally, yes or no
tired walrus
can you tell me in your own words what the factorial of a natural number is?
(also don't use "real numbers" to mean "raw numbers")
spice field
it's to multiply from 1 to n where n is n!
tired walrus
where n is n!
dont like this
but ok
n! means the product of all natural numbers from 1 to n
so then
(n-1)! = 1 * 2 * ... * (n-2) * (n-1)
spice field
Oh I was replacing n by (n-1)
then n by (n)
then n (n+1)
Didn't know you want me to write it this way
(n+2)! = 1 * 2 * ... * (n+1) * (n+2)
tired walrus
$\frac{(n-1)!}{(n+2)!} = \frac{1 \cdot 2 \cdots (n-2) \cdot (n-1)}{1 \cdot 2 \cdots (n-2) \cdot (n-1) \cdot n \cdot (n+1) \cdot (n+2)}$
soft zealotBOT
Ann
spice field
so all terms cancel out I get 1/n.(n+1).(n+2)?
spice field
Yes now I understand thank you so much
And when doing LCT to find something that behaves similar to the series we take highest degree in numerator / highest degree in denominator?
tired walrus
if that is something that makes sense to do then yes sure
(not an ironclad rule by any means tho)
tired walrus
there is no silver bullet no
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
heavy plaza
finishing off a proof, is this okay to write? here R3' is a translated/rotated coordinate system of R3 with unit vectors i', j', k'
final saddleBOT
finishing off a proof, is this okay to write? here R3' is a translated/rotated c...
heavy plaza
and A,B are fixed
final saddleBOT
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latent wren
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torpid sage
pls help
tranquil pine
Nope
tranquil pine
Check again between where derivative is zero *
frail pebble
it s b no ?
tranquil pine
Is the derivative negative or positive between would you say?
frail pebble
yes xdd i m troll i don t see xd
tranquil pine
NP xd
torpid sage
Check again between where derivative is zero *
of which graph?
frail pebble
Q
tranquil pine
0?
If you look at Q. What is the derivative between -1 and 1? Is it positive or negative? Look at the slope
torpid sage
If you look at Q. What is the derivative between -1 and 1? Is it positive or neg...
it's 0
since it's flat
sorry for taking too much to answer
tranquil pine
Nah don’t worry 😅
tranquil pine
Cuz C is positive between -1 and 1
But we know it should be negative values there
Since the slope was negative
torpid sage
Since the slope was negative
wait what
why is it positive
it's going down innit
decreasing*
tranquil pine
Yeah so negative
You need to look at the Y-values at the graphs
They represent the slopes value
So if slope is negative between -1, 1, then the Y-values also have to be negative
tranquil pine
Yeah I know it’s confusing
The graphs show the f’(x)
Which is the derivative of f(x)
Devil is in the details. Are you comfortable with what derivative means?
torpid sage
So if slope is negative between -1, 1, then the Y-values also have to be negativ...
;-;, r u talking about graph A or c?
torpid sage
Devil is in the details. Are you comfortable with what derivative means?
yeah
i understand the concept and im trying to get on with the problems
tranquil pine
Graph Q shows f(x) , all others supposedly show f’(x)
torpid sage
especially graphing haha
torpid sage
Graph Q shows f(x) , all others supposedly show f’(x)
💀
tranquil pine
Yeah I know it confusing in the start
torpid sage
this is why i love linear equations
tranquil pine
Hahah
torpid sage
it's... simple
tranquil pine
Wait til you do vector calculus
But my tip now is
Why don’t you sketch f’(x)
Based on the information you can visually see from graph Q
And then you will understand why graph A shows f’(x)
tranquil pine
Just by hand
Draw the x y plane
And pick some points where so easily can see what f’(x) is
For example at -1 and 1 you know f’(x) = 0
torpid sage
And pick some points where so easily can see what f’(x) is
ohok cool
ima try that on the board at school tmr
torpid sage
So if slope is negative between -1, 1, then the Y-values also have to be negativ...
hold on
if it is negative
that it is similar to -1 to 1 of Q
wait, can u explain it pls bro :)) @tranquil pine feel like ima about to finally get this one
sorry for bothering
final saddleBOT
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torpid sage
<@1029664568584175716> Has your question been resolved?
no
final saddleBOT
tranquil pine
wait, can u explain it pls bro :)) <@456226577798135808> feel like ima about to ...
Sorry, what did you need further explanation about?
final saddleBOT
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torpid sage
Sorry, what did you need further explanation about?
oh srry bro
tranquil pine
Great! No problem
final saddleBOT
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final saddleBOT
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snow burrow
How do i find x, ive already found y
final saddleBOT
How do i find x, ive already found y
forest mantle
How do i find x, ive already found y
what is y?
forest mantle
wait a second
1/2?
Do this: 2(2y+64) + 50 = 180. Now solve for y.
oh wait you're right
Now this is what you do:
Think of the bottom line as a straight line
Now: 2y+64 plus the supplementary angle = 180
So, the supplementary angle = 180 - 65 = 115
Now, since the left angle is isosceles triangle, 115 + 2(45 - x/4) = 180
I do not see any trig in here.
@snow burrow does this make sense?
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@snow burrow Has your question been resolved?
vivid walrus
final saddleBOT
vivid walrus
for this question do I need to apply 0.6 into the equation given?
tranquil pine
you don't have to. the equation already shows that at t = 0, h(0) = 0.6
which is consistent
so you are looking for when h(t) = 0
final saddleBOT
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final saddleBOT
full halo
limit as what tends to what
N -> +inf
final saddleBOT
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full halo
<@&286206848099549185>
vital crag
,rotate
soft zealotBOT
vital crag
yea i can't read that
earnest magnet
Yup
vital crag
maybe type it out or take a better picture
vital crag
,rotate
soft zealotBOT
vital crag
you need to factor out 4 and then do a change of variables to get the term in (something)^n to converge to exp(something else)
full halo
you need to factor out 4 and then do a change of variables to get the term in (s...
?
Isnt this limit = +inf?
vital crag
,w lim n to inf 3^(-n)
soft zealotBOT
vital crag
maybe! but you saying that isn't enough of a proof
vital crag
you need to factor out 4 and then do a change of variables to get the term in (s...
do this instead
full halo
How bro
soft zealotBOT
riemann
manic flame
is this 9/3 or 4/3
vital crag
How do I splve that parentesis
you use the limit definition of e
full halo
is this 9/3 or 4/3
4/3
full halo
you use the limit definition of e
e^4?
manic flame
$\left(\frac{4}{3}-\frac{1}{3x}\right)^{x}=\left(\frac{4}{3}\right)^{x}\left(1-\frac{1}{4x}\right)^{x}$
soft zealotBOT
Combustion
full halo
what are you saying equals e^4
The parentesis
manic flame
whoops instead of x put n
vital crag
The parentesis
how did you get e^4?
full halo
Oh damn its not?
manic flame
$lim_{\left(n\to\infty\right)}\left(1+\frac{a}{n}\right)^{n}=e^{a}$
soft zealotBOT
Combustion
full halo
But thats not the case
manic flame
**Combustion**
look at this
full halo
We have 1-(1/4n)
manic flame
that's it
full halo
1/e?
full halo
1/e
manic flame
but don't forget the (4/3)^n lol
full halo
Is it right
full halo
E^-1
manic flame
manic flame
$\left(1-\frac{1}{4n}\right)^{n}=\left(1+\frac{\left(\frac{-1}{4}\right)}{n}\right)^{n}=e^{-\frac{1}{4}}$
soft zealotBOT
Combustion
full halo
Wtf
manic flame
of course the limit as n->infinity
but (4/3)^n also goes to infinity as n goes to infinity
so this whole limit just goes to infinity
full halo
No wait what
manic flame
?
full halo
$(a+b)^c = a^c (1 + b/a)^c$
If I do this i dont get inf
vital crag
If I do this i dont get inf
what?
full halo
Yea
vital crag
where's your work
full halo
vital crag
,rotate
soft zealotBOT
manic flame
(4/3)^n
manic flame
manic flame
yeah you're right
full halo
yeah you're right
So everyime i got e stuff
If a>1
Its inf
This time since I had 3^-n i had to see if a>3 thats it
Right
manic flame
This time since I had 3^-n i had to see if a>3 thats it
what
full halo
Like everytimr theres a parentesi of something almost 0 with a addition to something and ^inf then if a>1 its inf thats it
And if a<1 0
Thats it
Always
Right
manic flame
if it looks something like $\left(a+\frac{b}{n}\right)^{n}$ then sure
soft zealotBOT
Combustion
full halo
Ight thx
manic flame
ah gotcha yeah
final saddleBOT
@full halo Has your question been resolved?
torn elm
yo can i get some help
final saddleBOT
yo can i get some help
final saddleBOT
@torn elm Has your question been resolved?
torn elm
<@&286206848099549185>
final saddleBOT
@torn elm Has your question been resolved?
torn elm
<@&286206848099549185> any help?
final saddleBOT
@torn elm Has your question been resolved?
green ibex
$V(t)=\frac{4 \pi}{3}(r(t)^{3})$
soft zealotBOT
Moosey
green ibex
you agree this is the volume as a function of time yes? because radius is also a function of time?
@torn elm
oh wait
yea your answer looks fine, if its something weird going on try getting rid of negative
because it's already saying how fast it's decreasing
final saddleBOT
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shut path
hi everyone i had a problem about identifying patterns, the problem goes as such:
figure 1 has 1 square, figure 2 has 3 squares, figure 3 has 6 squares, and figure 4 has 10 squares. find the pattern
im not sure how to go about solving it
thanks!
final saddleBOT
hi everyone i had a problem about identifying patterns, the problem goes as such...
shut path
.close
normal hill
final saddleBOT
normal hill
for part C
for my 3 edges
Its says make parametric equations in the anti clockwise direction
these are my boundaries on a 2d plane
the vertical line x=0
woud anticlockwise mean start form 1
or start from 0
if it starts at 1
and ends at 0
i could have
(0, -t, -t^2)
where t exists -1<= t <= 0
final saddleBOT
@normal hill Has your question been resolved?
unborn pilot
mb accidental
final saddleBOT
@normal hill Has your question been resolved?
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@normal hill Has your question been resolved?
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@normal hill Has your question been resolved?
final saddleBOT
@normal hill Has your question been resolved?
jaunty portal
jaunty portal
https://gyazo.com/568232dad70c6bb16b7d49328d164729
Hello, they mean this by anticlockwise ^
final saddleBOT
@normal hill Has your question been resolved?
normal hill
Hello, they mean this by anticlockwise ^
Ok thank you
Can i ask you figured that out
hardy ledge
so there is a integration rule that says if 1/ax+b the integral = 1/a ln(ax+b) right?
final saddleBOT
so there is a integration rule that says if 1/ax+b the integral = 1/a ln(ax+b) r...
hardy ledge
but what if you have 1/2x for example and say you move it out of the integration so you are left with 1/2 (integration sign) 1/x dx. where the integration would then be 1/2 ln(x)?
+c
amber moss
yes
warm ether
are you asking for the scenario of something like 1/(1/2 x)?
youd pull out 2, not 1/2 2( [1/2]/[1/2 x])
youd get 2ln(1/2 x)+C
hardy ledge
no i mean 1/2*x
1/(2*x)
as 2 = a and b=0 so therfor 1/aln(ax+b) is 1/2ln(2x)
but if you would move the 1/2 which is a constant you would get 1/2ln(x)
+c
and both is correct after my understanding?
amber moss
yes i think
hardy ledge
but i mean how. how can you have 2 answers
amber moss
1/2ln(2) counts as a constant ig
amber moss
1/2ln(2x) =1/2ln(2) + 1/2ln(x)
hardy ledge
oh and it wouldnt matter if its a constant because we could just argue that "c" takes care of the difference of the soulutions?
and you would technacly end up with the same answer
amber moss
yes
cursive marlin
Guys, the solution should be $\frac{x}{9y^7}$ and for some reason everything is right for me expect that coefficient, can you spot the mistake?
final saddleBOT
Guys, the solution should be $\frac{x}{9y^7}$ and for some reason everything is ...
soft zealotBOT
Gabe
cursive marlin
little python
what have u done in second line
cursive marlin
so is $3x^{\frac{3}{2}}$ is not equal to $\sqrt{(3x)^3}$ ?
soft zealotBOT
Gabe
cursive marlin
or not sure what you mean
soft zealotBOT
!Yajat!
cursive marlin
ooh yeah its the second
my mistake was that I've taken the whole thing including 3 to the power of 3 over 2
little python
yea
cursive marlin
ohh yeah, now I got the solution, thanks very much.
final saddleBOT
If you are done with this channel, please mark your problem as solved by typing .close
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stoic bay
this question's solution doesnt make sense to me. basically it says dr/dt is constant 0 when the water level changes but thats just completely wrong because r changes when the water level changes for a semi hemisphere. please someone tell me this question is flawed
final saddleBOT
this question's solution doesnt make sense to me. basically it says dr/dt is con...
ornate knot
this question's solution doesnt make sense to me. basically it says dr/dt is con...
uh r is radius
and radius would be constant
stoic bay
does r mean the radius of the whole pool or the radius of the volume of the water if you know what im saying
because i thought it was like calculating for the volume of the water
ornate knot
pretty sure radius of the pool
stoic bay
i got this when i drew it
r is 10
so i made 10 like the r of the whole pool
but like the r for the hemisphere of the water changes
this is so confusing
because if its dh/dt for the height of the water than it should also be dr/dt for the radius of the water right
idk maybe im doing something dumb
final saddleBOT
atomic moss
I'm just asking for clarification whether or not my definitions are correct
final saddleBOT
@atomic moss Has your question been resolved?
atomic moss
.co
gleaming elm
Absolute and relative error, 1/3≈0,33
final saddleBOT
Absolute and relative error, 1/3≈0,33
gleaming elm
Here's what I've done, I'm unsure if relative error part is correct, if 0,00(3)/0,(3) is equal to 1/100
vital crag
,rotate
soft zealotBOT
final saddleBOT
@gleaming elm Has your question been resolved?
gleaming elm
<@&286206848099549185> ?
final saddleBOT
@gleaming elm Has your question been resolved?
gleaming elm
No bruh
<@&286206848099549185> I just need this checked if its correct, I've done the task
.close
grand anchor
We have a few euro coins spread out in three piles. We move twelve coins from the third pile to the second, and then we move ten from the second pile to the first. Once this is done, all three stacks have the same amount of coins.
a) With this data, we can determine the amount of coins there were
initially in each stack? Justify the answer.
b) Find the number of coins there were initially
Bot
final saddleBOT
We have a few euro coins spread out in three piles. We move twelve coins from th...
grand anchor
i want to confirm something
gleaming elm
Bruh this is easy
final saddleBOT
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shadow aspen
i want to confirm something
What do you want to confirm?
final saddleBOT
final saddleBOT
Available help channel!
heavy nexus
not sure how to do b)
final saddleBOT
not sure how to do b)
@heavy nexus Has your question been resolved?
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rapid folio
final saddleBOT
rapid folio
how do i turn the top equation into the bottom one
tranquil flume
First, they are not equations
rapid folio
yeah sorry i forgot the word for it
tranquil flume
Expressions
rapid folio
how would i turn it to the 2nd expression?
tranquil flume
I don't understand the handwriting 💀
rapid folio
x-5/x+2 - x+5/x-2
rapid folio
yeah a 5
vivid walrus
this is rational expression
you need to make your denominator same
so divide them by x+2 and x-2
hint: ||Dividing Rational Expressions||
are you familiar with this?
rapid folio
no
vivid walrus
;-;
rapid folio
👍
vivid walrus
vivid walrus
gimme sec
vivid walrus
yeah no im lost
okay here's another hint
your LCD is ((x+2)(x+2))
LCD means lowest common denominator
gilded pulsar
I'm doing a proof book to try to strengthen my knowledge of it, but this one stumped me so far.
final saddleBOT
I'm doing a proof book to try to strengthen my knowledge of it, but this one stu...
gilded pulsar
It's about graph theory
Let r(n, m) be the smallest value N for which every red/blue coloring of $K_N$ contains either a red $K_n$ or a blue $K_m$. Prove that r(n, 2) = n.
soft zealotBOT
VexedRumble
gilded pulsar
I think I'm understanding the concept
I know $K_1, K_2, K_3$ are just shapes, like a dot, a line, and a triangle, but does including a red $K_4$ mean the diagonals as well?
soft zealotBOT
VexedRumble
gilded pulsar
This is a (poorly drawn) $K_5$ graph, if those diagonals weren't red would that not be a red $K_4$ anymore?
soft zealotBOT
VexedRumble
tranquil flume
It looks like K5 to me..
gilded pulsar
But looking at the red part, is that K4 enclosed in the first one?
But the red is not K4 in the second one?
I feel so strange asking questions like that, I’m not sure if I’m asking them correctly
tranquil flume
Shouldn't blue be K_2?
gilded pulsar
It’s red K_5 or blue K_2
For every red/blue coloring of K_5*
But for K_1 - K_3, there are no diagonals to draw
For K_4 and greater, it includes diagonals. I was just wondering if to have a red K_4 within a K_5 graph, if I had to include those diagonals or not.
My thought is yes but I want to double check
tranquil flume
Yes it is diagonal included
K_n is complete graph
Each node is connected to all the other nodes
gilded pulsar
Awesome, I don’t think that’s important for the question but it was eating me up lol
Ty!
.close
Oops hold up
.close
limpid torrent
I have been getting really confused in discrete math, so for example what exactly is a) asking me to find (I'm completely confused)
final saddleBOT
I have been getting really confused in discrete math, so for example what exactl...
cobalt lodge
do you understand the notation
limpid torrent
the union?
cobalt lodge
ok good,
then find the union of the two sets defined above
limpid torrent
how?
cobalt lodge
when you see something of the form ${\text{element}|\text{condition}}$ it means “the set of all elements satisfying the condition”
soft zealotBOT
IV
cobalt lodge
figuring out what are some examples of elements in each set is usually a good start
limpid torrent
a and b?
cobalt lodge
what
limpid torrent
I'm so lost
cobalt lodge
give me an example of an element in $R_1$, that is 2 integers a and b where a divides b
soft zealotBOT
IV
limpid torrent
is it just like asking for {(a,b) ∣a divides b or a is a multiple of b}
cobalt lodge
ye that’s fine
limpid torrent
that would be an answer?
cobalt lodge
but im slightly worried that you can’t give an element in the set
cobalt lodge
ye that’ll do
limpid torrent
but like what is the question asking for? does it want a = 2, b =4 or does it want me to like write {(a,b) ∣a divides b or a is a multiple of b
cobalt lodge
well, the union of 2 sets is another set, so it’s asking for another set
and the same goes for all of the questions
limpid torrent
so if I wrote (2,4) that would be a satisfiable answer to the question?
cobalt lodge
no, because 1. it’s not a set and 2. it’s only 1 of the infinitely many elements in the desired set
it’s like me asking you “give me a set of all integers “ and you said 5
limpid torrent
so does it want something like { (a,b) | a,b,c ∈ Z+ and b/a or a*c=b}
cobalt lodge
yes
limpid torrent
would that answer satisfy what the question is asking?
cobalt lodge
eh, close but not quite
limpid torrent
positive integers?
cobalt lodge
yes and one of your conditions need to be tweaked
limpid torrent
{ (a,b,c) | a,b,c ∈ Z+ and b/a or a*c=b} ?
cobalt lodge
is it just like asking for {(a,b) ∣a divides b or a is a multiple of b}
that being said this is already an acceptable answer
ok i assume you mean b|a, and then yes that would do
limpid torrent
ok i assume you mean b|a, and then yes that would do
what
limpid torrent
{ (a,b,) | a,b,c ∈ Z+ and b/a or a*c=b} so I can't have (a,b,c) and there is still 1 more problem with this?
cobalt lodge
ye, you can only have (a,b) then impose restrictions on a,b
limpid torrent
can I not have the c in general?
cobalt lodge
you can, just not as part of the set
limpid torrent
oh ok
cobalt lodge
you can introduce whatever you want in the conditions
limpid torrent
so there is still a problem with { (a,b,) | a,b,c ∈ Z+ and b/a or a*c=b} ?
cobalt lodge
eh, i would say good enough
cobalt lodge
no because you introduced redundancy now
ok so your answer wasn’t fine then because it wasn’t what i thought you were trying to express
a*c=b is the condition for $R_1$, where are you accounting for $R_2$?
soft zealotBOT
IV
cobalt lodge
but b/a=c is the same thing as ac=b
limpid torrent
so I need to find a way to express a as a multiple of b
is that what you meant by the notation a|b
cobalt lodge
yes
limpid torrent
is a | b the equivalent of saying b = 0 (mod a)
cobalt lodge
yes b = 0 mod a
limpid torrent
thats what I meant to write
cobalt lodge
nvm yes
limpid torrent
so b = 0(mod a)?
cobalt lodge
y
cobalt lodge
that’s still the same thing
cobalt lodge
no but you’re tantalizingly close
cobalt lodge
your problem is that you keep expressing b is a multiple of a but you also need a condition to let a to be a multiple of b
limpid torrent
so I need another conditioN?
cobalt lodge
well yeah, because you want to construct a union
so you must allow elements from either set
limpid torrent
so what like a,b ∈ R1, R2
{ (a,b,) | a,b ∈ R1, R2 ∧ a,b,c ∈ Z+ ∧ b = 0(mod a) ∨ a*c=b}
cobalt lodge
what
i mean if you write they’re in $R_1$ or $R_2$ you can already throw out everything else
soft zealotBOT
IV
limpid torrent
so back to { (a,b,) | a,b,c ∈ Z+ and b = 0(mod a) or a*c=b}
I just don't see what I'm missing
cobalt lodge
b=0 mod a means b is a multiple of a
which means ac=b for some c
so it’s just a redundant condition
meanwhile you still haven’t allowed the case where a is a multiple of b
limpid torrent
so i need a = 0(mod b) instead of b=0(mod a)?
cobalt lodge
ye that’s it
limpid torrent
so { (a,b) | a,b,c ∈ Z+ and a = 0(mod b) or a*c=b}
cobalt lodge
or for the sake of consistency, either ac=b or bc=a, or a=0mod b or b = 0 mod a
but yes it’s fine now
limpid torrent
so { (a,b) | a,b,c ∈ Z+ and a = 0(mod b) or a*c=b}
so this would be acceptable to write as an answer
cobalt lodge
yes
cobalt lodge
it means the set of elements in $R_1$ not in $R_2$
soft zealotBOT
IV
cobalt lodge
also i recommend reviewing set notation
limpid torrent
my professor's notes are very hard to read
and he teaches fast
so my notes have become sloppy in turn
cobalt lodge
yes
limpid torrent
{ (a,b) | a,c ∈ Z+ and b∈ Z- and a = 0(mod b) and a*c=b} would this satisfy R2 - R1?
limpid torrent
so no matter what all elements have to be positive integers?
cobalt lodge
your sets are defined on positive integers in the first sentence
limpid torrent
oops
final saddleBOT
@limpid torrent Has your question been resolved?
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final saddleBOT
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lofty perch
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lofty perch
I think I'm missing something
Because I have the 2 lengths of the sides but don't I need atleast one angle
lucid wind
If I remember correctly there is this SSS similarity criteria as well.
However in your question, you are already given the 3 angles which are same.( thr dotted one, the heavy shaded one and the light shaded one)
So by similarity condition, you can simple write
GH/QR = HF/ RP = GF/ PQ
lofty perch
How do you know they are the same?
lucid wind
The angles gave away the criteria
Usually they do so in these questions
If you notice carefully
Both angle FGH and angle RQP are dark shaded. Thus indicating they are same.
Similar comparison goes for the dotted one and the light shaded one.
shut gazelle
It also says the shapes are similar
lofty perch
So they would all be 60 then
shut gazelle
Wdym 60?
lucid wind
If I remember correctly there is this SSS similarity criteria as well.
However i...
You are to calculate the sides using these ratios
It's not 60
lofty perch
60 degrees
lucid wind
What?
shut gazelle
60 degrees
No
It doesn't mean the angles are 60
It just means that angles in the larger triangle are the same as the one in the smaller one but you don't know the measure
lucid wind
You can't comment about the angle that way
Also in no way are they gonna be 60 cuz that'll mean that all sides must be equal
You can see in both these triangles, you are given different lengths
shut gazelle
But you don't need the angles
shut gazelle
It's similar shapes, where you use the ratio of the sides
lofty perch
I thought that you were saying that the angles in ONE triangle were the same, which is how I got 60
shut gazelle
Given above
So by similarity condition, you can simple write
GH/QR = HF/ RP = GF/ PQ
lofty perch
.close
final saddleBOT
final saddleBOT
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raven plover
So, this is related to my last question
final saddleBOT
So, this is related to my last question
raven plover
If y' = (x-3)/(3-y) and I need to find the point P(x,y) where the slope is vertical, why do I need to find y such that the denominator becomes 0
I don't understand the logic, if I divide by 0, wouldnt that mean the slope would be undefined?
mild forge
a vertical line has a slope like that
raven plover
undefined?
raven plover
ohhhh
mild forge
(for positive a)
low prairie
Hi,
Let R= C(Q) /~.
C(Q) is the set of Cauchy sequences in Q.
~ is an equivalence relation defined by:
(x_n)n ~ (y_n)n <=> |x_n - y_n| -> 0 if n-> +inf
There is one question I'm stuck on:
It asks me to define the product and the sum on R.
But I feel it a little bit weird to multiply /adding equivalence classes together. Any hints?
low prairie
An equivalence class is a set.
desert mantle
a set consisting of things that can be added/multiplied
the most straightforward thing would be to try to set [a]+[b] = [a+b]
low prairie
Yes that was my first idea for the sum
desert mantle
however, you would need to check that if for example [a]=[c] and [b]=[d], then [a+b]=[c+d]
in other words, the choice of the representative for the class doesnt matter
low prairie
I never heard the "choice of representative"
desert mantle
S=[a]=[c]. S is an equivalence class. we can either represent it using a or we can represent it using c
a or c is called a representative
our definition of + uses such a representative
but it shouldnt matter which representative we choose, the result should always be the same
low prairie
Alright understood
desert mantle
for + to be well-defined
low prairie
As for the product, I thought something like that:
[a_n] x [b_n] = [a_n x b_n]
But not sure if my idea works well.
tranquil pine
I laballed the one at the origin with A, the other one on the x axis as B and the the one on the y axis C.
final saddleBOT
I laballed the one at the origin with A, the other one on the x axis as B and th...
tranquil pine
Would [
\vb{F}{\t{net}} = \p{- \f1{\s2}F{BC}}\vc\I + \p{ F_{AC} + \f1{\s 2} F_{BC} }\vc \J
]
be fine as answer
F_(xy) to be read as "the force from x on y"
hybrid heath
You did not label your points. What are A, B,C?
tranquil pine
I did. Read my original post
hybrid heath
Oh Oops 
The problem here is that you designated F as a vector, which makes no sense if it is a component of i or j unit vectors
Unless you meant their magnitudes
tranquil pine
Ah, yes indeed.
soft zealotBOT
tranquil pine
Yeah no worries
the solution intends to find the electric force first
but my expression above should be equivalent irrespective of that, right?
okay thanks regardless!
i will close this
.close
hybrid heath
okay thanks regardless!
.Was still reading
tranquil pine
oh sorry i thought you left
final saddleBOT
oh sorry i thought you left
hybrid heath
the solution intends to find the electric force first
In your first field, why did you do 2Q and not -2Q?
Oh did you move the minus to the j unit vector?
tranquil pine
Oh did you move the minus to the j unit vector?
thats not my working, thats just the answer key they wrote
tranquil pine
my answer is this though
hybrid heath
my answer is this though
Then that answer is incomplete as you need to calculate F for AB and BC still
hybrid heath
but my expression above should be equivalent irrespective of that, right?
To answer this question, no it is not equivalent (not until you calculate F)
tranquil pine
Then that answer is incomplete as you need to calculate F for AB and BC still
yeah i just wanted to know if the non-simplified form is equivalent
the rest is pretty much algebra if my expression for the vector is correct
tranquil pine
So for this, i know that we have to form three cases for this for all three intervals
final saddleBOT
So for this, i know that we have to form three cases for this for all three inte...
tranquil pine
say we are considering a point $p$ that is in the interval $x < a$, and labelling the first charge $A$ and the second $B$:
\env{align*}{
\vb{E}_{\t{net}} &= \p{-E_A + E_B}\vc \I \ &= \p{-\f Q{(a-p)^2} + \f{2Q}{(2a-p)^2}}\vc\I
}
soft zealotBOT
tranquil pine
is my formulation correct?
hybrid heath
I would say $E_A+E_B$. Do not implicitly add a minus sign just because the charge at A is negative. Resolve that once you actually calculate the field.
soft zealotBOT
SWR
tranquil pine
no you are mistaken
i added because of the direction of the electric field, not because of the charge
if i had done that for the charge, id have wrote - for E_B instead, no?
steep sequoia
Even then, you shouldn't have to. Sign of your charge will implicitly take care of that.
hybrid heath
Then do that. Or better, $(E_A+E_b)(-\hat{i})$
soft zealotBOT
SWR
tranquil pine
but thats not correct is it, because E_A goes to the left and E_B to the right 
hybrid heath
but thats not correct is it, because E_A goes to the left and E_B to the right <...
Like Magento said, the sign of your charge will take care of that
tranquil pine
i mean okay no worries
also
unrelated question
well it is related to my calculation
but, [
x^2 = y^2 \implies x = y
]
this implication doesnt always hold, what would be a better way to represent it?
soft zealotBOT
tranquil pine
im guessing |x| = |y|?
hybrid heath
I am not sure what you are trying to represent
hybrid heath
im guessing |x| = |y|?
This is true, but I'm still not sure what you are trying to show
tranquil pine
well in my calculations i arrive at [
\p{\f1{a-p}}^2 = \p{\f{\s2}{2a-p}}^2
]
soft zealotBOT
hybrid heath
Ah. Then yeah
hybrid heath
Also, this will hold if you know $x,y\ge0$
soft zealotBOT
SWR
tranquil pine
yeah
hybrid heath
Or even when $x,y\le0$
soft zealotBOT
SWR
tranquil pine
for this the cancellation is safe because a > p always
so a-p and 2a-p is always positive
okay thank you
let me carry one
okay so i arrive at [
p = \f{2-\s2}{1-\s2} a
]
soft zealotBOT
tranquil pine
this can be rationalised i suppose, but there is no need
hybrid heath
I'll trust your algebra.
Wait
This leads to p>a doesn't it?
Oh nvm. Demon is negative
tranquil pine
yeah so for the other two intervals
the inbetween obviously wont be 0 because the vectors point in the same direction
for the interval x > 2a i arrive at like
[
p = -\f{\s2 -1}{2-\s2}a
]
soft zealotBOT
tranquil pine
which is a contradiction i an guessing?
hybrid heath
Looks like, yeah
final saddleBOT
tranquil pine
.reopen
final saddleBOT
✅
tranquil pine
Well sorry for the second ping @hybrid heath but just want clarification
to recover the radius of the semicircle
we can go like
perimeter of the thing = pi*r (this is a semicircle minus its base)
as we know its perimeter is L
can we conclude r = L/pi?
okay amazing thanks!
i will keep this open abit longer just to see if i will get it right
okay so E_y dies from symmetry
So, $\vb E_x$: [
\vb E_x = \p{\f1{4\pi\eps_0}\f Q{\pi r^2} \int_{-\ff \pi 2}^{\ff \pi 2}\m\cos\theta \dd \theta}\vc\I
]
soft zealotBOT
tranquil pine
right?
that integral should simplify to 2
i think
,w \int cosx from -pi/2 to pi/2
soft zealotBOT
soft zealotBOT
tranquil pine
thank you
tranquil pine
no i think its correct
i checked just now so i tihnk its fine
Are u still ther ebtw
if not i will close this
.close
final saddleBOT
hybrid heath
if not i will close this
I am
final saddleBOT
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tranquil pine
are u still verifying?
worldly vale
noclopen 
hybrid heath
are u still verifying?
yes
tranquil pine
okay no worries
ust ping me
meanwhile i found this variation of the problem which is a bit harder
we cannot say that E_y cancels by symmetry here because the charge isnt uniform right
hybrid heath
This is correct.
tranquil pine
Okay great thanks
hybrid heath
I think it's better to use L instead of r though, since L was your given
tranquil pine
yeah I guess so
tranquil pine
meanwhile i found this variation of the problem which is a bit harder
okay so for this
hybrid heath
meanwhile i found this variation of the problem which is a bit harder
Yeah that's a bit more work, but the setup should be near identical.
tranquil pine
[
\dv[Q]s = \lambda \implies \dd Q = \lambda \dd s
]
soft zealotBOT
tranquil pine
[
\dd Q = \lambda \cdot R \dd \theta \implies \dd Q = -\lambda_0 \m \cos \theta R \dd \theta
]
soft zealotBOT
tranquil pine
but the answer shouldn't contain lambda_0
do we Integrate here and then solve for lambda?
hybrid heath
but the answer shouldn't contain lambda_0
correct
hybrid heath
Review what your given charge was
tranquil pine
oh -Q
soft zealotBOT
hybrid heath
and the rest is the same
the same?
tranquil pine
as before
hybrid heath
Are you sure?
tranquil pine
i mean we can work it out
hybrid heath
yes
tranquil pine
so [
\lambda_0 = \f Q{2R}
]first of all
soft zealotBOT
hybrid heath
tranquil pine
ah
hybrid heath
Need assistance or want to think on it?
tranquil pine
<cancel>\def\CancelColor{\tc r}
[
\dd Q = -\lambda_0 \m \cos \theta R \dd \theta \implies \dd Q = -\f Q{2\cancel R} \m\cos\theta\cancel R\dd \theta \implies \dd Q = -\f Q2\m\cos\theta \dd \theta
]
@hybrid heath
soft zealotBOT
mellow cedar
yo , what's up
tranquil pine
The ceiling
okay but yeah hi long time no see
also
i use your \env now
thank you for your gift to humanity
mellow cedar
final saddleBOT
grim nebula
mellow cedar
<:hmmge:1071456549207277642>
grim nebula
hi mehdi
tranquil pine
hi m
mellow cedar
hello
grim nebula
.reopen
final saddleBOT
✅
tranquil pine
what?
grim nebula
tranquil pine
do you have some input here snow
grim nebula
no
tranquil pine
dont open channels unnecessarily.
tranquil pine
next time it wont end as pretty.
robust mulch
_>
tranquil pine
.close
grim nebula
.close
final saddleBOT
grim nebula
bye
tranquil pine
bye
robust mulch
.reopen
mellow cedar
next time it wont end as pretty.
mellow cedar
next time it wont end as pretty.
i'm wondering how it will end
hybrid heath
i'm wondering how it will end
not prettily
mellow cedar
Yes, but at what level
robust mulch
Level 2
final saddleBOT
Available help channel!
hoary bison
need help
hoary bison
Problem 3.1 (1)
I have done the synthetic division and got x^2 - 2x + 3 = 0
However im unable to factorise this polynomial further
to find the x values
or rather z*
what should i do?
sorry i should also add that z = 1 is a root
hallow lantern
x^2 -2x + 3 =0
(x+sqrt(8)i) * (x -sqrt(8)i)
or:
(x-1)^2 + 2
(x-1 +isqrt(2)) * (x - 1 -isqrt(2))
final saddleBOT
@hoary bison Has your question been resolved?
karmic glen
if i know that CB * CA=CD * CE(power of point), A,B,D,E are concyclic and C lies on AB does that imply that C lies on DE?
final saddleBOT
if i know that CB * CA=CD * CE(power of point), A,B,D,E are concyclic and C lies...
final saddleBOT
@karmic glen Has your question been resolved?
karmic glen
<@&286206848099549185>
tranquil pine
Hello, I will help you, let me read your problem.
karmic glen
hello
karmic glen
okay i got it power of point implies similarity of triangles and theres only one point which lies on AB such that the similarity holds and it has to be the intersection
.close
tranquil pine
Hi so i had this question
final saddleBOT
Hi so i had this question
tranquil pine
A tube of length L is filled with ideal gas of Mass M and temperature T. If the tube is rotated with angular velocity ω in horizontal plane. Find pressure at the other end of the tube.
I know I did not use the parameters I’ve been given in the question
But I’m curious if the relation I have got here is correct or did I mess up
I’d be glad to explain my working if there is a lack of context in some parts
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
.close
fading berry
where on earth do they get the underlined bit from? im guessing its a way of just rewriting it but did they use the boundary conditions somewhere there? i cant tell, help
