and (-1)^(n+1) is positive if n is even
#help-38
neon dirge
so you just multiply and divide by positive numbers if n is even
therefore the entire expression is positive in that case
if n is odd however, we multiply by a negative number, so LHS is negative and 0<LHS<1 is not true.
granite zealot
I don’t get the inequality part
What are they implying be restricting it between 0 and 1?
neon dirge
oh nvm I switched it
only if n is odd, then we multiply by a positive number
so it'd be if 0<LHS<1, then n is odd.
granite zealot
The full question is also about the n is odd with the restriction being 1<LHS<2
So even n is 0<LHS<1 and odd n is 1<LHS<2
neon dirge
hm no, because if n is even then LHS is negative
then LHS<0
try a value
n = 0 for example
then we have 30 * (-1) / (1 * 5)
= -6
is not between 0 and 1
neon dirge
you can take n=2 too
granite zealot
I see what you mean
neon dirge
it'll still be negative
granite zealot
It’s wrong isn’t it
neon dirge
yeha
granite zealot
Why
Why did they ask me to explain why as if they are right?
Is this a trick?
And instead I have to explain why it is not?
neon dirge
Is this a trick?
idk
since they used the sum notation wrongly
I'm not sure what they had in mind
granite zealot
Yeah seems to be they wrote it wrongly for the second part!
Ok thank you so much!!
Are you gonna be on this discord later?
neon dirge
if it's from a class or course, maybe ask for the correctly put task, because this isn't properly written lol
granite zealot
I wanna attempt the remaining questions before asking( pretty sure will have some questions but would like to try to solve first)
neon dirge
Are you gonna be on this discord later?
time to time, you can dm me if you want, otherwise I'm sure other wanderers will come by here to guide :)
neon dirge
I wanna attempt the remaining questions before asking( pretty sure will have som...
sure np
I might not be available, so you can just put them here and in dms once you're unsure or stuck
granite zealot
if it's from a class or course, maybe ask for the correctly put task, because th...
This is indeed from a class textbook although it’s not assigned, I’m trying to do questions as extra practices
neon dirge
kk
granite zealot
Sure! Thank you so much!!!:))
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@granite zealot Has your question been resolved?
digital musk
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wanton flare
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dawn dune
I need help with part b
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I need help with part b
amber python
i saw that coming 
trail ingot
wanton flare
math jokes
trail ingot
no jokes here
only compactness
@granite cove 😂 is banned on my messages. please purchase nitro to be able to use
granite cove
trail ingot
you've gone too far this time
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@dawn dune Has your question been resolved?
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wraith hinge
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wraith hinge
Can i get some guidance with this
im not sure how to show the first part of their hint
knotty locust
What is your doubt?
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knotty locust
ok i got the idea
Glad I could help
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Available help channel!
wraith hinge
mind
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solid kilnBOT
nyxie9151
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neon dirge
@astral ore ?
astral ore
<@596893067261509633> ?
yeah that was my question but i'll reopen
neon dirge
but what's the question
astral ore
but what's the question
it's on my other channel
trim joltBOT
Available help channel!
wraith hinge
what do i need to study to be able to answer this? i been doing online classes for 3 years and played games most of the time and now i am clueless on what to study to be able to solve these
trim joltBOT
wraith hinge
this too https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equat...
this will teach me?
wraith hinge
but it wont show you how to do it, only what youre working with
okay thank you! ill do it now
.close
proper kernel
np
wraith hinge
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granite breach
I have a quick question regarding the semantics of first-order-condition (FOC / necessary condition) and second-order-condition (SOC / sufficient condition) when evaluating stationary points of functions.
I am quite sure that I do understand the difference between necessary and sufficient.
I am a bit confused as to why the FOC (f'(x)=0) is only necessary and not sufficient? Is it not that when f'(x) = 0 there is ALWAYS a stationary point? As I understand, that would make the condition sufficient (in addition to being necessary already).
Also, is it correct to assume that SOC (f''(x) > 0, in case of maximum) is only sufficient and not necessary because there are some cases like the function x^2 where we have a minimum at x=0 despite f''(x) !> 0? Or is there another reason?
tepid hamlet
I have a quick question regarding the semantics of first-order-condition (FOC / ...
think about f(x) = x^3, is its derivative 0 anywhere?
granite breach
think about f(x) = x^3, is its derivative 0 anywhere?
Yes, at x=0. And it is a stationary point / inflection point.
But I fail to see the what you are trying to convey Im afraid
tepid hamlet
sorry, maybe i'm confused by terminology here, i'm not used to stationary point, does that mean a local extremum or something else?
vagrant prism
sorry, maybe i'm confused by terminology here, i'm not used to stationary point,...
yes
granite breach
As I was taught, a stationary point can be a global/local maximum/minimum or an inflection point.
vagrant prism
derivative = 0
tepid hamlet
gotcha
and again, i've just seen different terminology in textbooks i'm familiar with, but what does first order condition refer to, is that related to first derivative test?
granite breach
As I was taught, a stationary point can be a global/local maximum/minimum or an ...
I just looked up inflection point and what I wrote doesnt make any sense, sec
willow urchin
and again, i've just seen different terminology in textbooks i'm familiar with, ...
they explained it as necessity, 2nd order being sufficiency
granite breach
I just looked up inflection point and what I wrote doesnt make any sense, sec
What I meant with "inflection point" is a saddle point. Somehow the latter is named as the former in the class notes.
tepid hamlet
"I am a bit confused as to why the FOC (f'(x)=0) is only necessary and not sufficient?"
when you are asking this, are you asking whether it is only necessary and not sufficient for what exactly? I'm looking a bit at the definitions so it is sufficient to call it a stationary point since that's the definition of a stationary point, but it is not sufficient to call it a turning point (local extremum)
willow urchin
i think the right question is why f'=0 is necessary but not sufficient for a local extreme
turns out neither necessary nor sufficient, yall should try to find examples
granite breach
"I am a bit confused as to why the FOC (f'(x)=0) is only necessary and not suffi...
Yes you understood me right. But the way you phrased it makes me realize that you might be correct in the sense that is sufficient to determine a stationary point, but not sufficient to determine what type of stationary point is at hand. That might be the reason.
granite breach
turns out neither necessary nor sufficient, yall should try to find examples
How is it not necessary?
willow urchin
before proceeding, a stationary point is defined at f'=0
tepid hamlet
well it's necessary if we are only limiting ourselves to talking about differentiable functions, but an extremum can also occur at an undifferentiable spot (i.e. absolute value function)
willow urchin
by definition f'=0 is sufficient and necessary for a stationary point
so thats not the right question
granite breach
so thats not the right question
What did you mean by "turns out neither necessary nor sufficient, yall should try to find examples" then?
willow urchin
i think the right question is why f'=0 is necessary but not sufficient for a local extreme
granite breach
Yes, but how is it neither necessary nor sufficient?
tepid hamlet
Julian, can you plz ask a specific question on the point of confusion you are now having, if this hasn't answered your question? And specify "necessary and sufficient" for what?
willow urchin
i can give examples to show that but i invite you to try finding some yourself first
granite breach
Julian, can you plz ask a specific question on the point of confusion you are no...
Necessary and sufficient to determine a local extreme I assume. The conditions are named necessary/sufficient in the class notes but "necessary/sufficient for what" is not explicitly stated, hence I am wondering aswell in which context the conditions are necessary/sufficient. But as you already pointed out earlier you might be correct that the context is "for local extreme" which would in turn make sense that f'(x)=0 is only necessary and not sufficient. Right now I am still a bit confused about the input of roketsune though.
granite breach
i can give examples to show that but i invite you to try finding some yourself f...
If we assume a non-limited and differentiable function I cant think of any so Id be thankful if you could provide one.
tepid hamlet
Necessary and sufficient to determine a local extreme I assume. The conditions a...
what are we assuming about the function in the discussion? is it differentiable? or are we only assuming continuity?
because that changes the conditions
willow urchin
If we assume a non-limited and differentiable function I cant think of any so Id...
the kicker is we need not assume differentiable!
granite breach
what are we assuming about the function in the discussion? is it differentiable?...
This was not really specified, but most likely we can assume that both apply since thats the standard case for the level Im at.
granite breach
the kicker is we need not assume differentiable!
Oh okay I get it then I think.
tepid hamlet
the kicker is we need not assume differentiable!
yes but maybe his class discussion concerns only differentiable functions, it sounds to me like this might be more like calc in an economics context?
granite breach
Haha yes it is economics
tepid hamlet
thought so
willow urchin
even so i think its highly instructive to see what we can get away with vs what we cant by assuming certain conditions
tepid hamlet
well in short: local extremes can occur potentially at either places where the derivative is 0 or when it isn't defined. so if the function in discussion IS differentiable then yes we can conclude that it's necessary for the derivative to be = 0 for an extremum since the undifferentiable option is no longer an option
willow urchin
as an aside ive not met many calc students who know the math versions of necessity and sufficiency
tepid hamlet
so you kinda have to decide what properties of the function you are discussing are, otherwise you can't really make any conclusions
simplest example: absolute value function, continous for all real numbers, differentiable for all real numbers except x = 0, has a local (and global) minimum at x = 0, so that minimum occurs where it is undifferentiable
so that example shows it's not necessary to have f' = 0 for an extremum, but this is only if we are including undifferentiable functions in the discussions
granite breach
well in short: local extremes can occur potentially at either places where the d...
And in turn I think your take that it is not sufficient because f'(x) = 0 does not allow us to determine the type of the extremum is correct.
granite breach
so you kinda have to decide what properties of the function you are discussing a...
Thats a good example, thanks.
tepid hamlet
it doesn't allow us to determine if an extremum is even happening
that was the example of f(x) = x^3, it has a horizontal tangent at x = 0, but f is increasing for all nonzero x, both to the left and the right
granite breach
as an aside ive not met many calc students who know the math versions of necessi...
It is also far from important in the class context but it bugged me that the terms are always used to refer to these conditions without a lot of explanation.
granite breach
that was the example of f(x) = x^3, it has a horizontal tangent at x = 0, but f ...
So I guess the following conclusion would be correct?
- f'(x)=0 is necessary if we try to determine the type of a local extreme on a differentiable and unlimited function
- f'(x)=0 is necessary and sufficient if we try to determine a stationary point on a differentiable and unlimited function
willow urchin
what does unlimited mean
granite breach
what does unlimited mean
I lack the terminology, but what I mean is that we assume that x-values for -inf to +inf are allowed. Otherwise it would be possible to have an extreme at the end of the function where f'(x) would not necessarily be 0 right
tepid hamlet
what does f'(x) is necessary mean?
granite breach
what does f'(x) is necessary mean?
Necessary = If X is true, Y has to be true aswell (Y necessary for X)
Sufficient = If Y is true, X must be true aswell. But there might be other causes than Y that lead to X (Y is sufficient to assume X)
tepid hamlet
So I guess the following conclusion would be correct?
- f'(x)=0 is necessary if ...
yeah but literally what does f'(x) is necessary mean
granite breach
ah I meant f'(x) = 0
granite breach
it means I slacked
tepid hamlet
lemme see how we can summarize:
willow urchin
I lack the terminology, but what I mean is that we assume that x-values for -inf...
i think youre trying to say that the limit of f at +/- infty need not be finite?
in which case that has no relevance here
the thing about stationary points is boring. we DECLARE c to be a stationary point if and only if f'(c)=0, ie necessity and sufficiency is there already
if f is differentiable at c then f'(c)=0 is necessary but not sufficient for c to be a local extreme
granite breach
if f is differentiable at c then f'(c)=0 is necessary but not sufficient for c t...
Not suffcient because...?
willow urchin
you were already given a example to show that, f(x)=x^3
tepid hamlet
assuming f(x) is a differentiable function on some interval [p, q]. For local extremes in (p, q) the following is true:
- f'(x) = 0 is a necessary condition, but not sufficient, but this condition can be used to find "potential x values" which can be tested using either first derivative test or 2nd derivative test as below:
- first derivative test: if x = c is the potential x value examined, if there is some open interval (a, c) where f'(x) > 0 and some open interval (c, b) where f'(x) < 0 then x = c is a local max. (similar situation with local min with signs switched)
- alternatively you can do 2nd derivative test: if there is some open interval (a, b) where a < c < b and f''(x) > 0 on (a, b) then you have a local minimum
if f''(x) < 0 on (a,b) then you have a local maximum
willow urchin
f'(0)=0 but c=0 is not a local extreme
tepid hamlet
so basically the first derivative test is: are the signs of the derivative opposite on either side of the potential point?
2nd derivative test is it concave up or concave down on both sides of the potential point?
granite breach
you were already given a example to show that, f(x)=x^3
Okay so not sufficient for local extreme, but sufficient for stationary point.
granite breach
assuming f(x) is a differentiable function on some interval [p, q]. For local ex...
I think that sums it up yes.
tepid hamlet
stationary point is just a useless and unnecessary term that means derivative is 0, nothing else
just say f' = 0 instead of needless terms imo, but i guess that's what economics classes like to do : (
you can read many calculus textbooks without even coming across that needless term
this question is a prime example of how it just introduces needless confusion to begin with by introducing unnecessary terms
granite breach
this question is a prime example of how it just introduces needless confusion to...
It is a bit weird yeah but luckily not relevant at all to what we are doing in the end
But still wanted to dig a bit cause it bugged me
tepid hamlet
you can remember it just means derivative is 0 if you think about problems that come up often in calculus where you have some function of position, usually s(t) and then the derivative of that is velocity v(t) and well when v(t) = 0 you are stationary, not moving because your velocity is 0
i guess
granite breach
But still wanted to dig a bit cause it bugged me
Also the lack of context probably makes this task of exploring the terms quite a bit more daunting than it actually would be
Thanks
@tepid hamlet
@willow urchin
.close
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Available help channel!
rough citrus
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gusty bone
What do you think x and y should be?
rough citrus
yes
frail heron
May I see your progress?
rough citrus
rough citrus
no
rough citrus
yes
low verge
sorry
rough citrus
its 40 x for oinion and y is 75 for chicken
low verge
like you have to multiply the quantity of chicken wings to the calories
which gives 75y
75y = chicken wings
and 40x is onion rings
x and y are undefined which will have to be found
rough citrus
yes also this is off topic but ima need ur pfp
rough citrus
im gonna send it to Ukraine to bump up moral and let them know theyll just go back to lobby if they get hit
rough citrus
yes indeed we shall
rough citrus
yes
low verge
and all together there are 19 onion rings and chicken wings combined
rough citrus
yes
low verge
and then you add all of these together to get a combined calory total of 970
so
40x + 75y =970
rough citrus
is that equation
pearl tendon
Instead of just giving him the answer, maybe help him understand why a 2-variable system requires two equations to solve
rough citrus
no i got it
low verge
final question do you know how to substitute algebra
rough citrus
no
low verge
like you can make x the subject
rough citrus
idk
rough citrus
umm multiplying
rough citrus
yeah
low verge
so what would x equal
rough citrus
onion
low verge
ok
that is the number of onions
so I am assuming you don't know how to rearrange a formula
rough citrus
no not at all
low verge
ok
low verge
are you meant to solve for x and y or are you trying to just get the equasions
rough citrus
just getting equations
rough citrus
nah just eqautions
low verge
ok so the q has been solved
rough citrus
the q?
low verge
question
rough citrus
but theres two boxs
rough citrus
you gave me 40x+75y=970
rough citrus
x+y=970
low verge
can you eat 970 chicken wings and onion rings?
rough citrus
nickacadoavacado can
low verge
nice
low verge
I said 'combining'
rough citrus
wait wait wait would 970 be at the begging
low verge
970 is the amount of calories
not the amount of food
we are talking abt the number of rings and wings
rough citrus
okay so were finding the amount of food
rough citrus
so 19
low verge
good
rough citrus
x+y=19
low verge
yes but don't mix up what x is or y
like x is the rings
y is the wings
that should be it
rough citrus
okay
low verge
send a screenie before submitting
rough citrus
it was wrong
low verge
how?
rough citrus
i have one more chance
frail heron
What happened?
rough citrus
low verge
bro
frail heron
..
low verge
got it mixed
rough citrus
wait what
rough citrus
oh mb
rough citrus
yes
low verge
nice try
rough citrus
come onnn
rough citrus
40 x 75 y
low verge
40 or 75
so which one should be x and which one should be y
read the question
@rough citrus I'm losing you
rough citrus
75x 40y
rough citrus
=970
frail heron
and give him the answer
Were I you, I would definitely give him the answer directly 😂
low verge
ok
frail heron
It has taken too long and he doesn’t seem ambitious
frail heron
Congrats
low verge
yes
rough citrus
low verge
💀
now look at your answers and tell me it's wron
wrong
I think we should close this channel
@rough citrus
you can tell your teacher you got it correct
rough citrus
wait i put x and y when it should have been r and c
low verge
it says any letters can be used
rough citrus
wait fr
low verge
💀
rough citrus
i can make a case about this
rough citrus
they got my back fr
rough citrus
uhhhhh 2025
low verge
what?
rough citrus
no its 2024 lol
low verge
do you even go to school
rough citrus
yes im in ninth
low verge
grade?
rough citrus
and im only failing algebra
rough citrus
okaythank you for the help today
rough citrus
lol i need help agian
rough citrus
ye x and y
rough citrus
okay
low verge
let's x be small boxes and y be large boxes
rough citrus
okay lets define those
low verge
to find how many bars you get from the small box
what do you have to do to get the total number of bars in let's say 5 small boxes
@rough citrus
rough citrus
5 x8
rough citrus
okay
low verge
replace 1 number with x to find the total number of bars
rough citrus
okay x=8
rough citrus
x8
rough citrus
y=12
low verge
not equals
rough citrus
olay
rough citrus
72
rough citrus
8x+12y=72
low verge
good
now
in the problem it says there are 3 time as many small boxes as large boxes
how do we make an equasion out of that
what do you think it should be
@rough citrus
low verge
one sec lemme see if I'm right
ok
if I have 6 small boxes and 2 large boxes
idk how to word it
rough citrus
yea
rough citrus
no
rough citrus
no
low verge
might have to ping the helpers because idk how to help you without giving the answer
low verge
lol i need help agian
<@&286206848099549185> how do you teach ratios to a person to help them in this question
to find the relations with the boxes
rough citrus
just give answers
low verge
you need to learn not cheat
low verge
read the question and you will see where I'm going
devout drift
WHO HAS THE DUMB
rough citrus
me
low verge
nah don't be mean
devout drift
What's the question
gilded lava
read the question and you will see where I'm going
I am too lazy to read it....someone will do it
low verge
bro
devout drift
<@&286206848099549185> how do you teach ratios to a person to help them in this ...
So you are basically asking helpers to help how to teach a person so you can help them
rough citrus
low verge
lol i need help agian
here
yes
I'm so stuck
first time teaching and I'm still learning
rough citrus
so far i got this
gilded lava
U forgot there are 3 times small boxes
gilded lava
so far i got this
U already know number of gran per box
rough citrus
yes 12 and 8
gilded lava
So u took x wrong
low verge
oh
gilded lava
8x + 12y = 72
low verge
that is what he put
gilded lava
3y = x
low verge
so far i got this
.
gilded lava
Score good marks✅
low verge
3x=y
gilded lava
Bruh
rough citrus
okay so i put 3y=x
gilded lava
Take x as number of small boxes
.
rough citrus
okay
rough citrus
low verge
that was close
gilded lava
Don't waste more time
low verge
good
rough citrus
devout drift
You still there?
low verge
🥶cold
maybe try switch around the equasions into different boxes
because I am corrct
correct
devout drift
@rough citrus
low verge
I know I am
devout drift
Can you explain why you wrote that equation
rough citrus
wdym
devout drift
What logic went into that equation?
Why did you write 8x + 12y = 72
What is "x"
What is "y"
rough citrus
x is amount of bars in small box
devout drift
maybe try switch around the equasions into different boxes
Maybe first correct your spelling for equation
rough citrus
y is amount of bars in large box
devout drift
Yes
So the total number of small boxes
Is thrice the amount of large boxes yes?
If there are y number of boxes
There will be 3y small boxes
x = 3y
,w x - 3y = 0,8x + 12y = 72
low verge
surely it's the other way round
solid kilnBOT
devout drift
That would be wrong
rough citrus
so i will put x=3y
devout drift
Yes
low verge
see how that goes
gilded lava
U guys still at it
rough citrus
and 8x +12y= 72
low verge
yes
devout drift
x = 3y
low verge
let's see what it says
devout drift
let's see what it says
We all know what it is going to say
low verge
❎
gilded lava
🫵💀
devout drift
You still haven't corrected equasions
gilded lava
@rough citrus just change the x and y
devout drift
Bruh
gilded lava
Anyways gtg
rough citrus
now what
low verge
submit
devout drift
Submit
low verge
alt f4
devout drift
The fu
low verge
surely x and y are supposed to be the number of boxes
not the number of granola bars in the boxes
stiff cradle
y=2
low verge
nice one
rough citrus
low verge
YOU GOT THE FIRST TWO ANSWERS WRONG THAT'S WHY
rough citrus
ik
rough citrus
thats y i said lets define the variables
low verge
yeah
devout drift
Bruh
low verge
nvm
low verge
well done
stiff cradle
x=6, y=2
low verge
we are not solving
devout drift
Thanks a lot cedric
stiff cradle
ooh
rough citrus
stiff cradle
my bad
gilded lava
rough citrus
5
rough citrus
lol thats how we all feel with this algebra
rough citrus
low verge
we have 5 more questions
neon pine
hi
gilded lava
Child I have more work to do
rough citrus
soldiers prepare
low verge
fair
stiff cradle
u summoned me?
low verge
idk
neon pine
https://tenor.com/view/ww3-world-war3-ww2-hurry-soldiers-gif-15967119
When you forgave math work and you have to do 3 problems in 5 minutes
low verge
how much time can you spare
rough citrus
help the enemy is here
low verge
this took 30 minutes for one question
when is this die by
sdue
due
@rough citrus
devout drift
help the enemy is here
When the enemy is too strong, you gotta flee and come back strong to fight it again 
low verge
unless this is the last opportunity
rough citrus
its past due
neon pine
this took 30 minutes for one question
this type of problems let me on my mathematics competition. I had to do 25 problems in 90 minutes
devout drift
7s + 14l = 252
low verge
bro
devout drift
s + l = 21
low verge
you're a teach
rough citrus
thank you
low verge
💀
devout drift
,w 7s + 14l = 252,s + l = 21
solid kilnBOT
devout drift
Go for it
rough citrus
what are the variables
devout drift
Who exactly
low verge
how did you get the helpful role
devout drift
Oh
rough citrus
bro how are variables defiend
devout drift
Perhaps I have helped people too much now
low verge
fair
devout drift
@rough citrus
rough citrus
yes
low verge
🥱
rough citrus
thank you
rough citrus
lol hw won the war but the second wave is coming in perpare
devout drift
You know what s and l stand for right?
low verge
nah
rough citrus
rough citrus
devout drift
What are the options for the variable?
rough citrus
devout drift
They denote the volumes
low verge
but you have already define volumes in the 1st equation
devout drift
Volume of each small and large box respectively
low verge
nah
no way
am I going to go thru with this
it's the number of small boxes shipped and number of large boxes shipped respectively
devout drift
If you consider
low verge
which is 7s
low verge
look at the second equastion
devout drift
Not s
low verge
s+l=21
devout drift
But s would be defined as the volume of each box?
And also the number of small boxes shipped?
low verge
s is the number and 7 is the volume
low verge
it's the number of small boxes shipped and number of large boxes shipped respect...
@rough citrus put this in
as defining
low verge
TRUST ME😭
rough citrus
okay
rough citrus
so which is s small or large
low verge
s is small
devout drift
Well I get what you are trying to say
rough citrus
devout drift
Because it even asks the number of small and large boxes shipped
devout drift
So it would make sense
rough citrus
it was @low verge who i went with
devout drift
To find s and l as number of small box and large box
rough citrus
lol
devout drift
It also would be correct to say s and l is the volume of each small and large box respectively
rough citrus
wait do u hear that
low verge
I've been here for 2 and a half hrs
devout drift
Great work btw
low verge
I'm Asian I can do math for a long time
devout drift
So am I
rough citrus
im american i can grill
low verge
really!
devout drift
Ofcourse!
low verge
im american i can grill
and do unspeakable thing to you sibling
any way
let's get on with this work
rough citrus
no i race win wars and grill and shoot guns
low verge
ok bro
I see percentages😭 (those are the juggernauts)
can you give me 10 minutes
I need a break
low verge
I'm back
let's define the algebra
let's do x and y respectively
@rough citrus
and show me the options for defining the alsgebra
low verge
ok
I'm British
idk what commission is
can you explain it to me @rough citrus
is that profit
rough citrus
idk
low verge
it's is profit
rough citrus
low verge
I think
rough citrus
average american\
hoary pasture
Commission is money you earn after making a sale e.g selling a house earns a percentage of the sales as commision
low verge
so in the context it is profit
low verge
Commission is money you earn after making a sale e.g selling a house earns a pe...
thank you
let's start with the first equation
for profit
you will have to add the percentage onto the original price
@rough citrus
what is 9% as a decimal
low verge
ok
rough citrus
dude this isnt china u can not listen and still pass
low verge
I'm sorry
rough citrus
lol
low verge
I'm just tired
rough citrus
same
low verge
I'mma just give you the answers
rough citrus
please
low verge
isn't it like 10 am in America
low verge
where do you live
low verge
nice
shut moss
yo wassup
rough citrus
yeah
low verge
I'm in England rn
rough citrus
wspppp
low verge
no way a recruit
shut moss
Hw you guys ?
low verge
shellshocked
rough citrus
bro were at war with algebra
shut moss
Oh
low verge
we get through 1 question in 30 minutes and it is supposed to be easy
x is the number of dollars in phone sales
rough citrus
devout drift
@low verge is mathing
devout drift
Going for 3hrs straight
low verge
yessie
rough citrus
devout drift
Dedicated
rough citrus
wit i hear nuke warning
devout drift
your psychology
Are you asking in general?
shut moss
Oh sorry
rough citrus
okay
low verge
0.09x+0.06y=135
YESSSS
I THINK I'M RIGHT
but
don't submit yet
I'm not even teaching at this pint
point
low verge
he doesn't have a clue
low verge
135
rough citrus
lol
low verge
135 instead of 165
rough citrus
jk jk jk jk jk jk jk jk jk
devout drift
What is the question?
devout drift
Is this like your mutual improvement math study channel session
rough citrus
,w 7s + 14l = 252,s + l = 21
not supposed to give out answers guys
low verge
hahahah
devout drift
not supposed to give out answers guys
But you understood that part right
rough citrus
yes i understand it alll
devout drift
Then try making
rough citrus
lol
devout drift
Equations yourself this time
low verge
enter it in to see if it is right
low verge
low verge
@rough citrus can we do this all later
rough citrus
algebra teacher rn
low verge
bro I'm giving up
low verge
now close this channel and we can rest
rough citrus
.close
sullen sable
trim joltBOT
trim joltBOT
@sullen sable Has your question been resolved?
silk dawn
and these are the options for the drop down
weeks
silk dawn
seems good to me
trim joltBOT
trim joltBOT
Available help channel!
valid cave
trim joltBOT
valid cave
Is my calculation correct?
left oriole
rhs of first line equals -21I, not 21I
and then the 21 disappeared when you went from line 2 to line 3
aside from that, the idea is right
valid cave
I need to divide 21 to right side?
left oriole
yes
trim joltBOT
trim joltBOT
Available help channel!
quartz grotto
Greetings, given this system i must discuss for the non trivial solution, i tried to solve the problem using gaussian elemination but i am running into problems in the last part because i am left with two unknowns, how do i proceed? even if the calculations are incorrect how would one proceed here? thanks 🙂
eternal adder
you have 4 variables but only 3 equations
you won't be able to eliminate them all
so having 2 variables remaining is correct
quartz grotto
okay but how would i then solve for the other unknowns? i dont understand
eternal adder
so we have -9z = 10w, which you can rewrite to w = -9z/10
then replace w in all the other equations using that
then keep eliminating variables and get everything in terms of z
and that will parametrise the line of solutions
trim joltBOT
trim joltBOT
Available help channel!
lone elbow
hello! currently i am doing trigonometry inverses with a calculator, however i have no idea how to solve for sec(x)=undefined
lone elbow
ionic pendant
try rewriting sec(x) in terms of sin(x) or cos(x)
lone elbow
like cos-1(x)=und?
ionic pendant
we usually write it as 1/cos(x), to not confuse it with the inverse function, but yes
when would that be undefined?
lone elbow
im assuming infinity?
ionic pendant
we're dividing 1 by cos(x). when we divide by a number, when would that division be undefined?
lone elbow
whenever the denominator is 0?
ionic pendant
yes
lone elbow
however 1/cos(0) just comes out as 1
devout drift
however 1/cos(0) just comes out as 1
What's $\cos(\frac{\pi}{2})$?
solid kilnBOT
ColdTee
trim joltBOT
@lone elbow Has your question been resolved?
lone elbow
What's $\cos(\frac{\pi}{2})$?
0.9996
devout drift
,w \cos(\frac{\pi}{2}
solid kilnBOT
lone elbow
what
devout drift
hello! currently i am doing trigonometry inverses with a calculator, however i h...
Also you can easily solve this if you know the range of sec(x)
lone elbow
lone elbow
Also you can easily solve this if you know the range of sec(x)
i have a paper with the ranges of tan/cos/sin for graphs
devout drift
,w cos(1.57deg)
solid kilnBOT
lone elbow
but pretty sure i lost it somewhere
oh that’s probably why
this problem has to be in deg mode
devout drift
Radian
sec(x) is defined for all x in $R - (2n+1)\frac{\pi}{2},n \in Z$
It's range however is $\sec(x) \geq 1$ or $\sec(x) \leq -1$
solid kilnBOT
ColdTee
devout drift
$(-\infty,-1] \cup [1,\infty)$ in interval notation
solid kilnBOT
ColdTee
devout drift
Notice 0 doesn't lie in the range
lone elbow
does that mean i would need to plug in any value between $\sec(x) \geq 1$ or $\sec(x) \leq -1$?
solid kilnBOT
jupiter
solid kilnBOT
ColdTee
devout drift
does that mean i would need to plug in any value between $\sec(x) \geq 1$ or $\s...
No that's the range
What is $\sec(x)$ in terms of $\cos(x)$?
solid kilnBOT
ColdTee
trim joltBOT
devout drift
.reopen
trim joltBOT
✅
devout drift
$R - (2n+1)\frac{\pi}{2},n \in Z$
solid kilnBOT
ColdTee
devout drift
$\sec(x) = \frac{1}{\cos(x)}$
solid kilnBOT
ColdTee
devout drift
And $\cos(x) = 0 \implies x = (2n+1)\frac{\pi}{2}, n \in Z$
lone elbow
oh yeah also that
solid kilnBOT
ColdTee
devout drift
Put in any integer for n
You will always get 0
Since 1/0 is not defined
Therefore the domain won't contain those values of x when cos(x) = 0
lone elbow
would that mean cos(x) = 1/0??
