16-4 isn't -20
#help-0
fervent timber
spiral haven
oh, i think i used the + * - = - thingy wrong, right?
yeah youre right. tysm yall
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zenith tinsel
so when it's asking for the explict/recursive rule do i make up one of my own or write the formula down?
lone heartBOT
so when it's asking for the explict/recursive rule do i make up one of my own or...
@zenith tinsel Has your question been resolved?
zenith tinsel
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zenith tinsel
I would assume you make your own that is specific to this question
ohh okay thank you!
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empty trail
How do I do part d?
lone heartBOT
How do I do part d?
empty trail
This is what the solutions say
This is what I did for the whole question
I got all of the other parts right but don't know how to find the solution to part d and I tried using simultaneous equations to get sin(pi/2)x=mx-1 from the two equations
I also tried changing the domain to match the equation but I don't know what I should try making mx-1 equal to to find what m should be
<@&286206848099549185>
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@empty trail Has your question been resolved?
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@empty trail Has your question been resolved?
empty trail
Does anyone know how to answer this question?
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ivory igloo
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formal ginkgo
how ?????
formal ginkgo
whats un and l
it'a sequence un and it convergers to l
mortal magnet
real numbers?
formal ginkgo
real numbers?
yes
mortal magnet
also https://www.desmos.com/calculator/j50ppkkarm
from this,
the purely red areas are where $||x|-|y||<|x-y|$ is true but $|x|<|y|+1$ isnt
ocean sealBOT
matt07734
formal ginkgo
l is constant
mortal magnet
and?
you know x and y still stand in for numbers
just have y be a number
it still doesnt work unless you say more about this un and l
mortal magnet
just have y be a number
when you take y to be a number, you take a horizontal slice of the image (y = #)
and that slice still has purely red bits and purely blue bits where one side is true but the other side isnt
formal ginkgo
it still doesnt work unless you say more about this un and l
this is the complete correction
and the translation is on the right
mortal magnet
the calculator's broken, here's how they got it\
$|u_n - l|<1$\
reverse triangle inequality: $||a|-|b||\le|a-b|$\
$||u_n|-|l|\le|u_n - l|<1\
||u_n|-|l||<1\
-1<|u_n|-|l|<1\
|u_n|<|l|+1$
ocean sealBOT
matt07734
mortal magnet
if you couldnt find it, ||a| - |b|| ≤ |a - b| (at least in english) has a more specific name
you can think of it as "if I force a and b to be positive, their distance is either the same or gets smaller"
formal ginkgo
you can think of it as "if I force a and b to be positive, their distance is eit...
okay yeah thanks for help
mortal magnet
np
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crisp tendon
How would i do this?
languid hinge
How would i do this?
what have you tried so far?
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@crisp tendon Has your question been resolved?
upbeat hornet
Is the space of all bounded functions from [0,1] to R a complete metric space?
upbeat hornet
(not necessarily continuous)
dense stratus
with what metric?
upbeat hornet
with what metric?
The supremum metric
upbeat hornet
it's a Banach space with respect to the sup norm
I thought that was just the space of continuous functions
dense stratus
they both are but on a compact space, continuity is not required for completeness
upbeat hornet
The compact condition is required? How about bounded functions on a noncompact domain?
dense stratus
no because if you have (0,1), you can have the function $1/x$ as a limit of the sequence $\frac{1}{x}\chi_{[1/n,1)}$
ocean sealBOT
emphatic_wax
upbeat hornet
Ahh
and the same example would work for infinite domains using x^2
I see
Thanks!
dense stratus
yes!
upbeat hornet
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shell narwhal
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shell narwhal
answer is J4=0
placid zinc
For example, imagine integrating around (1/√2, 1/√2), and around (1/√2, -1/√2)
Those points give opposite "values" for the integrand
It ends up being something like a regular 1D integral of an odd function
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mellow frigate
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slender gull
Not quite.
mellow frigate
and at pi/2 which is one of the limits, its undefined
mellow frigate
Not quite.
oh i just used integral calculator for it, i ddint solve it by hand
slender gull
I mean, you have integral for -1/t^3 dt
That's not -1/t^2
,w integral of -sec^2(x)/tan^3(x)
ocean sealBOT
slender gull
There.
slender gull
Yes, same thing.
Now I want you to notice how this isn't the same as what you wrote originally.
slender gull
-1/tan^2(x)
this was you
stable grotto
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stable grotto
so i did this:
so my question is shy author said it is hard to prove
this probably means that my proof is either incorrect or not general?
worn fox
Those xi* are not going to be the same
snow lodge
yo does Casio fx-95ES PLUS supports CMPLX if so how
lone heartBOT
yo does Casio fx-95ES PLUS supports CMPLX if so how
gray isle
google/read the manual
lone heartBOT
@snow lodge Has your question been resolved?
viscid knoll
given ||u||=2 and k=3 I need to find the set of points M that verify the following equation:
vec(u) * vec(AM) = k
viscid knoll
note: * means dot product and vec(AM) means the vector starting from point A to point M
my attempt was to replace u and k with their corresponding values and solve for vec(AM) so that vec(AM) = 3/2 then the answer would be that the set of points M is the circle of center A and radius 3/2
but checking the correction that seems incorrect
would someone explain why?
lone heartBOT
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viscid knoll
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analog sierra
given \||u||=2 and k=3 I need to find the set of points M that verify the follow...
Isnt there more information ?
Like the angle between vec u and AM
viscid knoll
Isnt there more information ?
forgot about this. turns out the guy who wrote the question wrote it as a seperate question but in fact it's related to the previous.
the only extra information you get from the previous is that AB=2
and as I read this I think I've figured it out
I need to replace vec u with vec ab since norm(u)=norm(ab)=2
can I do that tho? if norm(vector 1)=norm(vector 2) does that necesserly mean that vector 1 = vector 2 @analog sierra
analog sierra
forgot about this. turns out the guy who wrote the question wrote it as a sepera...
You sure this is all there is?
viscid knoll
yes, I'd screenshot the question and send it to you if you could read french but probably you can't @analog sierra
viscid knoll
You sure this is all there is?
here you go I translated. supposedly question 4 and 5 are connected
viscid knoll
You sure this is all there is?
and here is the official correction. is it correct?
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oak gulch
I have 2 problems similar problems I'm unsure how to solve:
- A person has 150000 on an account at the start of 2022. interest rate is 5% per year calculated monthly; b) What year and month does the amount break 200000 for the first time
and
- d) If the population growth in a given country is 5% per year, after how many years has the population doubled?
I don't know where to begin so I don't really have anything yet
limpid turret
Do you know how interest over time is calculated?
oak gulch
yeah
limpid turret
Can you share what you know about it?
oak gulch
yea sec
limpid turret
This problem seems to only be an application of that calculation
(with a little algebra mixed in)
oak gulch
this is a) of the same question of 2)
and i know the formula of Hn=H(1+v/t) etc
can't reallt write it
or this
and this
not entirely sure how to use the one above though
limpid turret
one sec
Need to take a look
You have a good start on a), but what you did so far was simply see how much money they have after a year
oak gulch
yeah that was what a) was supposed to answer
limpid turret
Oh oops I did not know that
okay
b) you basically want to solve for $t$ in $200.000=150.000\left(1+\frac{0,05}{12}\right)^t$
ocean sealBOT
SWR
limpid turret
t would represent the number of months.
limpid turret
that would give you the number of years instead of the number of months
Either approach is fine, as long as you are aware of your units
oak gulch
okok I'll remove it then
hmm ok im not sure what to do next though
put it in some kind of a log/ln function i guess?
oak gulch
its just that I only have 2 hours to turn this in so I'm a bit stressed
ok lemme try to find
limpid turret
Once you do log, it's just some ugly algebra and you're done
limpid turret
I don't really understand log that well
Basic log rules you should always try to know
limpid turret
Say you want to solve for $x$ in $a^x=b$, then the solution would be $x=\log_a b$
ocean sealBOT
SWR
limpid turret
(Latex bot is a little broken, open the image if you can't see the whole thing)
limpid turret
This is a good start. I would dividie out the 150000 so the exponential term is isolated
limpid turret
no worries
oak gulch
isn't it supposed to be
this is what I have
but if I divide log1.004/log1.333 I get 0.14 or something
If I put it in wolfram that is
0.014
oak gulch
oh yeah I see it
should be lik 0,75
but still what does that mean
or is it 72?
yeah hahaha
okok
I got it
can we do the other one also?
also, if it's 72 months, that's 6 years does that mean that it will reach 200000 in january 2028?
get back to my whenever you can I'm just gonna start on the other one and see if I can do it now
limpid turret
also, if it's 72 months, that's 6 years does that mean that it will reach 200000...
You can test this by plugging in 71 months and 72 months, and seeing if that's the time when your cross 200000
oak gulch
ok but if it was 72 months then it would be january 2028 right?
and if it was 71 months it would be december 2027?
I'm just really horrible with numbers honestly
wasn't too bad after using what you taught me earlier thank you
oak gulch
hmm when i plug it in it seems like it reaches 200000 between 69 and 70
that's not normal right?
limpid turret
This can happen as you remove decimals in approximation
e.g. 4/3 and 1.333 are very different
And the error between them grows rapidly in exponentiation
limpid turret
So it seems that 70 months is your answer
limpid turret
such a big discrepancy?
Yes. Such is the magic exponential growth. The errors grow exponentially as well
oak gulch
I have 2 more things I wanna get help with
since I still have time
can you or should I open a new ticket?
limpid turret
just ask here
oak gulch
ok
I got stuck on these 2 midway through as well
the second one I feel like I should factor to get the roots but I can't for the life of my figure out how
and the first one I'm kinda lost alltogether
If I could factor it then the answer would be plain to see
limpid turret
You distributed incorrectly here
oak gulch
and even after using wolfram and seeing the answer I don't get it
should be a plus?
I thought I fixed that
Is this correct?
limpid turret
Yes, but you have more to do
oak gulch
how do I proceed?
sorry for not getting it
im gonna ping helpers cuz I only have an hour left
<@&286206848099549185>
ocean sealBOT
SWR
limpid turret
quadratic will work if you cannot factor it
oak gulch
4ac is bigger than b^2 though
same for the other problem I have
couldn't do quadratic there either
limpid turret
4ac is bigger than b^2 though
It is??
limpid turret
ok but in the other one it is a negative right?
other what?
limpid turret
How did you get 7y²? You may want to check that'
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haughty haven
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haughty haven
i dont know how to do this one i have it drawn out but im not getting it ngl
alpine sable
I'm not sure
lone heartBOT
Show your work, and if possible, explain where you are stuck.
tardy stag
this language is entirely inappropriate for this server
haughty haven
yes
shy solar
shy solar
yes
tell me if u understand this
now
now for h, you can get tan(13)(5+x)=tan(27)(x)
you can get the value of x
haughty haven
I THOUGHT IT WAS SIN
shy solar
I THOUGHT IT WAS SIN
haha, hope I helped you
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haughty haven
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shy solar
i dont get it again
which part
haughty haven
ur hand writing is
something
sorry
IM GOING INSANE
I HATE WHEN I DONT GET SOMETHING
haughty haven
THE TAN part
haughty haven
which one first one or second?
I THINK I GET BUT I GOT 0.78 FT
well i rounded it 0.78
shy solar
well i rounded it 0.78
is that wrong answer?
haughty haven
i dont know
I DONT KNOW
LMAO
ima just turn it in bc i cant even see if its right
haughty haven
NOPE NOPE IM TURNING IT IN
I TRIED
THANK YOU
WAIT I MESSED UPPPPP
its law of sines and i used tan
i hate it here.
maybe the first time was right
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gritty pond
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cinder wharf
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exotic belfry
as x tends to 3 you are (at the end) in the part of x>2. so plugin x = 3.
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left mural
The problem basically sounds like this:
lone heartBOT
The problem basically sounds like this:
lone heartBOT
left mural
The problem is basically like this:
a_0, a_1, a_2, a_3... is an infinite geometric sequence whose |q|<1 and the sum of it is equal to 3.
Calculate the maximum value of a_0+a_3+a_6+...
Tried whole lotta methods but they usually end up going absolutely nowhere. Things just cancel out most of the time. Would appreciate any insights on this problem! Ask any questions you may have.
.reopen
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gusty gorge
a geometric series is defined by two parameters: a_0 and q
left mural
this problem is from an olympiad if that's of any help
gusty gorge
the sum of it being 3 gives you a relationship between a_0 and q
left mural
the sum of it being 3 gives you a relationship between a_0 and q
yeah
gusty gorge
and a_0 + a_3 + a_6 + ... is just the geometric series with a_0 and q^3
Maybe using something from calculus, even Lagrange multipliers will give it?
left mural
we haven't learned calc yet
also have no idea what lagrange is
so i doubt this requires that
but maybe
ocean sealBOT
gusty gorge
oh yes obviously it does simplify
so the sum of a_0 + a_3 + ... is given by a_0/(1-q^3), agreed?
and the sum of a_0 + a_1 + ... is a_0/(1-q) = 3
left mural
i believe so, yes
gusty gorge
now see if you can write a_0 + a_3 + ... as [some function of q] * [a_0 + a_1 + ...] = [some function of q] * 3
then, maximizing a_0 + a_3 + ... is simply a matter of maximizing some function of q, and it turns out you don't need calculus for it
left mural
now see if you can write a_0 + a_3 + ... as [some function of q] * [a_0 + a_1 +...
gimme some time to digest this information
left mural
now see if you can write a_0 + a_3 + ... as [some function of q] * [a_0 + a_1 +...
not gonna lie, I have no clue what's happening in this sentence
maybe my background in functions is too weak
gusty gorge
Let $S_1 = \sum\limits_{i=0}^\infty a_i$ and $S_3 = \sum\limits_{i=0}^\infty a_{3i}$
ocean sealBOT
Saccharine
gusty gorge
you are told that the $a_i$ are a geometric sequence, so you can write $S_1 = \frac{a_0}{1-q}$ and you can write $S_3 = \frac{a_0}{1-q^3}$
ocean sealBOT
Saccharine
gusty gorge
Further, you know $S_1 = 3$. Now write $S_3 = F(q) S_1 = 3F(q)$ for some function of q. Try to figure out this function.
left mural
Does S3 imply that there are only 3 members?
ocean sealBOT
Saccharine
gusty gorge
Does S3 imply that there are only 3 members?
what?
left mural
nevermind
this is mind blowing to me
in the most direct sense
imma take some time digesting
left mural
what?
think i understood a lil more now
is the function
supposed to be found from the S1 equation?
gusty gorge
if I ask you to find F(q) such that S_3 = F(q) S_1, a pretty natural thing to try is S_3/S_1
left mural
okay, will try that
left mural
if I ask you to find F(q) such that S_3 = F(q) S_1, a pretty natural thing to tr...
So like is the -0.5 value the qoutient?
or is it 1.(3)
gusty gorge
I think you should probably review what a function is before trying this problem
left mural
because 1.(3) wouldnt make sense
gusty gorge
this isn't something just to calculate and be done with
gusty gorge
the general approach to this problem is to figure out what value of q maximizes the value of S_3 and then use this and the fact that S_1 = 3 to figure out what the maximum value of S_3 is
it doesn't seem like you understand any part of the approach
left mural
it doesn't seem like you understand any part of the approach
true, we just started functions a week ago, so these things do be kinda new to me
perchance i'll tackle this problem after another week of functions
anyways, thank you for your help and patience
slender basin
This is a question in my book, it's in statistics, it asks to find how many students are absent for more than 6 days, so it should be very simple to do, i just add all the stundents after day 6 (so 6+5+4+2=17) but in the book, the correct answer is D) 5, they dont show any working for these questions
slender basin
so im not tripping right 😅
fallen verge
i was thinking it might be counting all students who have that many absences and more, but then 6 days has 4 which ruins that idea
also the correct answer would have been 6 as well
so like
i think the answers are just wrong
fallen verge
youre welcome
slender basin
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harsh terrace
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unreal nimbus
for a hw question like this, how would I know if i should use product rule, combinations, permutations etc?
is pub has the following selection of drinks:
• 5 different types of craft beer, B1, B2, B3, B4, B5,
• 4 different types of cider, C1, C2, C3, C4, and
• 3 different types of soda, S1, S2, S3.
Over the course of the evening you have 5 drinks. In each of the following scenarios,
count the number of possible drink combinations (the order of the drinks matters):
for example for these two questions i used product rule:
you have 5 drinks of any type and drinks may be repeated.
i did 12^5 which is product rule:
and for this: you have 5 drinks of any type, but do not have the same drink twice in a row.
12 × 11 × 11 × 11 × 11
again product rule
lone heartBOT
for a hw question like this, how would I know if i should use product rule, comb...
@unreal nimbus Has your question been resolved?
olive yarrow
@unreal nimbus yes makes sense
combinations and permutations are generally used when items cannot be repeated
tacit arch
Close one of your channels
unreal nimbus
combinations and permutations are generally used when items cannot be repeated
how about product rule
how would i know when to use which method
olive yarrow
you use the product rule when the outcome of one trial does not depend on the outcome of a previous one
unreal nimbus
also question says (the order of the drinks matters): so what does that entail
olive yarrow
also question says (the order of the drinks matters): so what does that entail
that means that ABAAA is different from AABAA
so each of these is different
unreal nimbus
so thats permuations no?
olive yarrow
yes
unreal nimbus
but i used product rule?
like here:
you have 5 drinks of any type and drinks may be repeated.
i did 12^5 which is product rule:
olive yarrow
no no wait
we would use permutations if the outcome of one trial affects the outcome of the next
so if the question said that order didnt matter...
getting AABAA would not be different than ABAAA
unreal nimbus
ok and the queastion said order matters
olive yarrow
if the order didnt matter it would be 12P5
unreal nimbus
so is that not permutation
olive yarrow
exactly
unreal nimbus
i though order matters for permuatuons
olive yarrow
it does
but in this case order mattering or not links to wheter or not you can repeat a drink
olive yarrow
if the order didnt matter it would be 12P5
im sorry my bad
i meant if the question asked if drinks are not repeatable
olive yarrow
because if order doesnt matter, you cant count AABAA and ABAAA as two seperate scenarios
unreal nimbus
if order doesnt matter wouldnt AABAA and ABAA be the same set?
ill do this question later
.close
tall pebble
What am i doing wrong?
lone heartBOT
What am i doing wrong?
placid zinc
That is not the anti-derivative of 1/e^(x)
lone heartBOT
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alpine sable
I need some help regarding studying calculus
some context, i hated maths for the last 7-8 years of my life, i still studied it anyways half hartedly until 2022
heartedly*
and i have one of the most important exams of my life coming on in less than a month, but my views on maths a completely changed, i am starting to love maths
the syllabus requires DERIVATIVES AND ITS APPLICATION and INTEGRALS
what topics do i need to study before touching these topics?
<@&286206848099549185>
alpine sable
where do i go for advices?
tacit arch
tacit arch
Or #precalculus or #calculus
river bloom
hello! can someone take a look at my proof by induction and check if it's correct?
river bloom
i'm not sure if 1) the inductive step is too circular and 2) how to format the "justifications"
pseudo ice
your handwriting is really nice 
But up to here is good enough, like just go up to here
And then convert that last bit, into something that looks like a "whole" summation and you're good 
river bloom
<:Hiii:679685133758234776> your handwriting is really nice <a:HeartEyes:67614586...
thank uu 
river bloom
And then convert that last bit, into something that looks like a "whole" summati...
sorry can you explain this a bit more? what do you mean by "whole" summation?
pseudo ice
sorry can you explain this a bit more? what do you mean by "whole" summation?
Remember what you need to prove 
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mortal magnet
,,\log_93\text{ isnt }3
ocean sealBOT
matt07734
mortal magnet
- you dont divide one number by another to get an answer
- you dont swap one number with another to get an answer
recheck what logs are then retry doing log_9(3)
yea its 1/2
np
sure
b-a = -(a-b)
(x^(a-b))^(1/2) is x^(1/2(a-b))
np
remember to .close
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ruby zinc
hello
ruby zinc
pls help
ruby zinc
i didnt do system of equations for a while
feral hemlock
Addition, subtraction, substitution
ruby zinc
how i can replace x^3 or y^3
fallen verge
use the second equation to isolate a variable then substitute
ruby zinc
-y=2-x?
fallen verge
cubics are not that easy to solve sometimes but this one is pretty nice
sly snow
multiply by -1, it's easier :)
Oh that sounds complex. Just say bring the right hand terms to the left and the left ones to the right.
mystic swallow
alr
ruby zinc
in desmos answer is 4 or -4
mystic swallow
??
ruby zinc
for x
ruby zinc
how to bring x to 4
ruby zinc
nah, just make that y = x - 2
i replaced y with that but answer is not 4
sly snow
how to bring x to 4
I reckon we shall substitute y=x-2 in the first cubic equation and arrive at x.
lone heartBOT
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oblique stirrup
I’m trying to determine if this is a linear combination or not and I don’t know how to deal with this last row… how do I turn -1 to 1?
oblique stirrup
white marsh
this is already linearly dependent as the last row has all zeros
no need to proceed any further, you got your answer
oblique stirrup
all zeros means it is a linear combination?
white marsh
in a row, yes
oblique stirrup
I see
So I have another one where it is a linear combination?
If I can’t get to row echelon form it doesn’t not just mean that it is not a linear combination right
I think I’m confused on what is a linear combination
white marsh
I think I’m confused on what is a linear combination
so basically you can form a vector with the help of other vectors (just by multiplying them by scalar factors and adding)
oblique stirrup
is it = 0?
white marsh
if there are solutions for the set of linear equations then there exists a linear combination to form the third vector (in our case)
oblique stirrup
if there are solutions for the set of linear equations then there exists a linea...
meaning as long as a row does not equal something like 0 0 | any integer?
white marsh
0 0 | any real quantity, yes it has no solution so it's not a linear combination and all the three given vectors (if three vectors) are linearly independent
white marsh
yep
oblique stirrup
i see, ty
white marsh
anytime
oblique stirrup
What about this one? I’m suppose to add all the numbers on the right side to get the solution but I could also reduce row 2 and 3 to 1 and -1 and the solution would be different
alpine sable
wait so whats the problem
white marsh
okay so it's basically your set of linear equations, if there exists a solution then v is a linear combination of the given 3 vectors a,b,c
white marsh
if theres no solution ie [ 0 0 0 | any real quantity ] then v is not a linear combination of the given three vectors, you get it?
white marsh
but couldnt it also be 6+-5+-2
just solve it like a given set of linear equations
white marsh
does the set of linear equations have a solution?
oblique stirrup
yes?
white marsh
good, so v1 is a linear combination of a,b,c
oblique stirrup
idk im lost
white marsh
idk im lost
you said that you were able to find a solution with v1 then why did you write that v1 is not a linear combination of a,b,c. well, let me solve
v1 does come out to be a linear combination of a,b,c since the set of linear equations has infinitely many solutions
oblique stirrup
yeah i just wanted to see the answer, it wanted me to input the solution but when you said " v1 is a linear combination of a,b,c" I thought that I would input a,b,c as the solution but it doesnt take commas and i dont think I can type thje entire matrix in
like v =-c
and v=2a-2c
I have no clue what its talking about
white marsh
ah the thing is, add a and b, it comes out to be
0
0
0
and -c = v1. just multiply c with -1 and see the matrix
oblique stirrup
ok that makes sense, but now for the second one how doess he reach that conclusion
like how do i translate what i wrote here into the answer
white marsh
look at the last row, -2 multiplied with the third vector is equal to v2
solve it like a linear equation, the solutions you get are basically the coefficients you multiply the vector with and add inorder to get the required linear combination. get it?
oblique stirrup
x3 is equals to two numbers, -10 and 4 tho..
white marsh
noo, x3 multiplied by 2 = -4 and x3 multiplied by 5 = -10
the elements in matrices are the coefficients of the respective variables
oblique stirrup
Ok so… row 2 and 3 are the same thing?
white marsh
yep the same thing
oblique stirrup
now i set x1 to the left and everything else to the other side
or maybe first i find x2 and then put that into ^
white marsh
you'll see that this system has infinitely many solutions
oblique stirrup
right because there are two.... free parameters is the name?
white marsh
yeah its an interesting system actually and our task is easier since a +b is a zero vector
basically a system with a and c vectors is enough since a = -b so we need not even consider b in our set of linear equations, b can be easily made by multiplying a with -1
but theres nothing wrong with how you're approaching this question, no one is going to bother much if you get the correct final solution
oblique stirrup
i still dont know how to like input the answer into this website ugh
white marsh
ah but you do know how to solve this now right?
white marsh
practice and build more confidence
lone heartBOT
@oblique stirrup Has your question been resolved?
lone heartBOT
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Available help channel!
heavy turtle
What is the flux on each surface of the cube when a charge is placed in the middle of an edge of a cube?
heavy turtle
We can assume that the charge is placed between 4 cubes
so charge through each cube is
$\frac{q}{4E_o}$
ocean sealBOT
EMINEM
ocean sealBOT
EMINEM
heavy turtle
because 6 faces to a cube
however
since flux is the dot product of Field and Area Vector
won't the flux for two sides be zero?
that would make it
4 sides to a cube
and field per cube =
$\frac{q}{16E_o}$
ocean sealBOT
EMINEM
heavy turtle
Anyways that's what I need help with
slender gull
The charge is spherical, yeah?
heavy turtle
The charge is spherical, yeah?
yes
slender gull
The flux is zero for some faces indeed.
You can't distribute the flux uniformly for each face.
It's only same for symmetrical faces.
ocean sealBOT
! What the hell am I doing here?
lone heartBOT
@heavy turtle Has your question been resolved?
heavy turtle
You can't distribute the flux uniformly for each face.
we can't?
heavy turtle
It's only same for symmetrical faces.
but they are symmetrical aren't they?
ocean sealBOT
heavy turtle
**! What the hell am I doing here?**
yes
slender gull
Imagine the top edge to be the one we're talking about.
heavy turtle
mhm
slender gull
So the flat surfaces/faces which share that edge, those are the ones where the flux is zero.
heavy turtle
yup
slender gull
Now there's two pairs of symmetrical faces.
The right and left are symmetrical but it isn't the same as the face which is at extreme behind.
You can take your time thinking about it.
heavy turtle
The right and left are symmetrical but it isn't the same as the face which is at...
right
is it because the electric field will be weaker there?
heavy turtle
I see
yes so field would be significantly less
how does one go about taking that into account though
slender gull
how does one go about taking that into account though
You have two different flux values for two different types of faces, call them x and y for a moment.
You'll have something like 2(x+y) = phi
Then similarly have 4 cubes that share that edge. And now you'll have another equation relating x, y and phi (the new flux is 4phi)
slender gull
.close
vague iris
Shouldn't this be divergent because the second term in the limit is infinity?
vague iris
how did it become zero?
tawny condor
Where?
tawny condor
The limit is, yes
alpine sable
pretty much yes
vague iris
i forgot it's negative infinity
tawny condor
And the y in front doesn't make it infinity, exponential is more dominant
lone heartBOT
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Available help channel!
karmic ravine
I need some help on F
lone heartBOT
I need some help on F
karmic ravine
All the previous question arnt written as fractions and it’s throwing me off
I’m not sure where to begin
coral flower
u can change the fractions into whole numbers
first take the LCM of the fraction and then multiply that on both sides
like for the first equation
x/2 + y/3 = 5
(3x+2y)/6 = 5
multiply both sides with 6
3x+2y = 30
@karmic ravine
coral flower
u can do it like that to i suppose
are u using matrices to solve these? if so then convert the fractions into whole numberse first before changing into matrix form
karmic ravine
so 6(x/2 + y/3 =5)?
coral flower
yes
karmic ravine
6x/12+6y/18=35?
coral flower
no
karmic ravine
oh whoops
coral flower
like for the first equation
x/2 + y/3 = 5
(3x+2y)/6 = 5
multiply both sides with...
i wrote it here for the first one
let me turn into latex so its easier
karmic ravine
thank you
coral flower
$$\frac{x}{2} + \frac{y}{3} = 5$$
taking LCM
$$\frac{(3x+2y)}{6} = 5$$
multiplying both sides with 6
$$\frac{(3x+2y)}{6} \cdot 6 = 5 \cdot 6$$
$$ 3x + 2y = 30$$
ocean sealBOT
JustToPro
coral flower
yeah
karmic ravine
so 4x+3y/12 . 12= 1 . 12?
ocean sealBOT
JustToPro
coral flower
and now u can solve them how u solved the rest
coral flower
np
karmic ravine
1 sec
coral flower
ok
the answer will be the same , dont worry
(just make sure ur calculations are correct)
coral flower
if possible can u send a screenshot/picture of 1 of the questions u solved
karmic ravine
sure 1 sec
coral flower
so i know which method u are using cuz theres many to solve these
karmic ravine
yeah haha
karmic ravine
**JustToPro**
all ive got written down is this
i was gonna use the elimination method
coral flower
ah ok
karmic ravine
to get rid of y
coral flower
then yeah , multiplying with 3 is good
karmic ravine
do i need to time the 2nd row by 2 to make the y = 6y?
what ive got so far
i was gonna subtract 9x + 6y from the 4x +3y but i cant eliminate anything
coral flower
do i need to time the 2nd row by 2 to make the y = 6y?
yes
karmic ravine
x=6?
coral flower
no
karmic ravine
karmic ravine
but i mutiplied it by 3 so i could make the y's = 6 on both lines
coral flower
$$3(3x + 2y = 30) => 9x + 6y = 90$$
ocean sealBOT
JustToPro
coral flower
yea
coral flower
both are same
karmic ravine
alr awesome
coral flower
subbing in any gives u same answer
karmic ravine
y = -84?
karmic ravine
i finally got it tysm for being patient lol
r u allowed to write it as (66, -84) ?
karmic ravine
alr ill just ask my teacher when i get back
yeah that makes more sense
tysm cya
.close
alpine sable
How do you go from the top to the bottom
lone heartBOT
How do you go from the top to the bottom
golden canyon
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
ty ty
lone heartBOT
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Available help channel!
vale oriole
im chinese so i dont understand the questions in english, would love for someone to translate to me
wheat isle
Can’t you pop it into an online translator of some sort?
vale oriole
it just translates word for word
doesnt translate the method in chinese
the methods name*
uneven rampart
You sure?
uneven rampart
What?
vale oriole
this is what i meant but thanks
uneven rampart
Oh
fallen oar
he want this
vale oriole
got it
uneven rampart
💀
vale oriole
.close
lone heartBOT
alpine sable
please dont open channels for such things lol
or someone just gonna ping mods and then youll get timed out or something
close the channel
tepid drum
do you have a question ?
cinder tundra
<@&268886789983436800>
alpine sable
lmao chill bro just close the channel instead 😋
vague turret
guh
pine gazelle
multiply both sides by 4 in the first equation for 16th
vague turret
what/
zenith bough
In 17 you can also multiply by 4 to make 4d = -8c + 12 and then put that into the bottom equation
vague turret
or you can just ditectly subtitute for y in the second equation
yeah yeah
subsitiot
opal jolt
On 16: you're already given the value of y from the first eq.
Directly substitute in the second
pine gazelle
yea
pine gazelle
do you see that the 4's cancel out
opal jolt
$a\cdot \frac{b}{c} = \frac{a}{1}\cdot \frac{b}{c}$
ocean sealBOT
LordFelix
opal jolt
$\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot c}{b\cdot d}$
vague turret
so 41/14 ?
ocean sealBOT
LordFelix
opal jolt
have you not studied operations with fractions at all before equations?
vague turret
oh so 4 x 1 and 1 x 4
vague turret
have you not studied operations with fractions at all before equations?
i forgot
opal jolt
you should take a look at them again then, they are mandatory for equations
vague turret
you should take a look at them again then, they are mandatory for equations
how?
grizzled aspen
rave you have 7x on your third last line
but you have made a mistake going from your third last, to second last line
opal jolt
also, 4/4 = 1
grizzled aspen
you have subracted 7, but you had 7x
opal jolt
no
grizzled aspen
no
you can collect your x terms together
and you can collect your constant terms together
you can't mix them
grizzled aspen
(4/4) * x = 1 * x = x
you have 7x + x
How do you simplify this ^^ by collecting like terms?
grizzled aspen
ah not quite
its not multiplying
you need to add them or "simplify by collecting like terms"
EXAMPLE:
If you have 2x, what does that mean to you?
vague turret
2x
opal jolt
you're not gonna be able to solve equations if you cant operate fractions and monomials. You really should start by looking into those again first
vague turret
and what operation is between the 2 and the x?
2 is 2 and x is a variable?
grizzled aspen
do you understand that 2x means 2 times x?
vague turret
no
grizzled aspen
ok
give me a sec
did you want to hop on a call? I can help you properly there
otherwise, I think the best chance would be for me to direct you to some online resources for now
vague turret
did you want to hop on a call? I can help you properly there
okay
alpine sable
how would i simplify this equation?
lone heartBOT
how would i simplify this equation?
alpine sable
it becomes x-5 but i don't know how and website locks it behind a paywall
thorny patio
If you have
(5 - x)
This is the same as: - ( -5 + x) = - (x - 5)
Similarly
(-x + 4) = - (x - 4)
By rewriting those two factors in the numerator like so, you will arrive at your result
alpine sable
wait i don't get it why are we just randomly rewriting the signs
sorry i am kind of very stupid
so how would we go about it step by step
with just this
thorny patio
Factor a negative out from the (-x + 4)
This is a common trick to cancel things out in fractions
alpine sable
that would be -1 * (-x+4) right?
thorny patio
No you don't want to change it
So when you pull the -1 out, everything in the parentheses has to change signs
thorny patio
We are doing this in order to make the top and bottom have a common factor
alpine sable
then x-4 cancels eachother out
thorny patio
Yep
alpine sable
and we are left with (5-x) * -1right?
alpine sable
it'd be -5+x
thorny patio
Then re write
alpine sable
x-5
thorny patio
Yep
alpine sable
.close
lone heartBOT
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Available help channel!
glossy lion
ABC is a right angle triangle with Angle A=90 degrees, and BC=8. A circle passes through A and B and cuts AC and BC at D and E respectively. If BD=CD=5, find length of AD.
glossy lion
How do I solve this?
lone heartBOT
@glossy lion Has your question been resolved?
glossy lion
<@&286206848099549185>
plush kiln
Yes?
glossy lion
could you provide me any guidence on how to solve my question?
plush kiln
It depends
alpine sable
ABC is a right angle triangle with Angle A=90 degrees, and BC=8. A circle passes...
see because it is triangles, use similarity criteria, and if it doenst work, u always have me
glossy lion
see because it is triangles, use similarity criteria, and if it doenst work, u a...
i tried sin rule to find a possible angle but then I couldn't solve it
alpine sable
u dont have to go through all those complicated rules