so idk
#help-33
scarlet wagon
regal coral
the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone.
marsh citrusBOT
@scarlet wagon Has your question been resolved?
scarlet wagon
> the Mohr–Mascheroni theorem states that any geometric construction that can be...
it can be performed by compass only
since the first two points generate the same construction (they're isomorphic)
scarlet wagon
this doesn't solve much
regal coral
it says the points have coordinates that are expressible with addition, subtraction, multiplication, division, and square roots
marsh citrusBOT
@scarlet wagon Has your question been resolved?
proper hemlock
Hello! I need help solving an ideal gas law equation, I think I may be stuck when it comes to units
marsh citrusBOT
Hello! I need help solving an ideal gas law equation, I think I may be stuck whe...
cunning fiber
#old-network - this server is for math, not sciences
proper hemlock
My bad! I thought that it might still be applicable because it's a simple equation uf you take away units
marsh citrusBOT
@proper hemlock Has your question been resolved?
broken pier
Can someone please help me
marsh citrusBOT
Can someone please help me
vagrant gull
!da2a
marsh citrusBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
void elm
do you have a specific question in mind?
it's not easy to help somebody when you don't know what they need help with 
ionic ferry
Yup, send it mate!
ionic ferry
Sure!
broken pier
11,12,13,14
ionic ferry
Alright, can be write monthly fee of Karate Klub as x and monthly fee of Kool Karate as y?
broken pier
Yeah
ionic ferry
I meant 25x and 35y, mb
ionic ferry
Ahhhhh I'm an idiot, just take x as the number of months, ignore y
broken pier
X=number of months?
ionic ferry
Yes
broken pier
Ah
ionic ferry
So what's the cost for each club if I go there for x months, the total cost
How would you write that as a function?
ionic ferry
Wait I'll help you with this one
broken pier
Thank you
broken pier
I don’t think we learnt that yet?
ionic ferry
Okay then, we'll try another approach, I'm sorry for not confirming this earlier
broken pier
No no all good! I appoligise for not mentioning!
ionic ferry
So basically, we want to know when the prices would be equal
broken pier
Correct
ionic ferry
And total prize of Karate Klub after x months is 200 + 25x, and Kool Karate is 100 + 35x
broken pier
Would we write it like this 200+25x=100+35x
broken pier
We collect our like terms
ionic ferry
We collect our like terms
Yes
broken pier
300=60
ionic ferry
Ahhh you made an error
Send me the equation after getting all like terms on one side
broken pier
ionic ferry
Okay, the equation after getting like terms on one side would be?
broken pier
-10
ionic ferry
And subtract 100 from both sides
ionic ferry
200-100 gives 100
Yes
broken pier
I have a paper yep
ionic ferry
Alright, subtract 25x and 100 from both sides, you'll get 0 on one side and a number on the other, what would the equation look like?
ionic ferry
Unfortunately no
broken pier
Oh
ionic ferry
Okay see, we have 200 + 25x = 100 + 35x
broken pier
Correct
ionic ferry
I subtract 100 from both sides
broken pier
Wait
ionic ferry
200 + 25x - 100 = 100 + 35x - 100
ionic ferry
200 + 25x - 100 = 100 + 35x - 100
What would this give?
ionic ferry
No no
Just subtract the 200 with 100 on left side, and 100 with 100 on right side
What equation does that give you?
broken pier
100-100=0
broken pier
200-100=100
broken pier
200+25=35
ionic ferry
You missed the x there
broken pier
35x and 25x
broken pier
200-25=175
ionic ferry
200-25=175
No no
It's 200 + 25x = 35x
200 won't be affected if we subtract variables
ionic ferry
Yes
broken pier
35-25=10
ionic ferry
Write the x too, so you don't get confused
ionic ferry
Wait
We subtracted 100 from 200 earlier
So it was 100 + 25x = 35x
So it's 100 = 10x
I missed that, apologies
So what should be x?
ionic ferry
You're confusing constants with variables
If we subtract 25x from 100, then it won't affect the 100, because they are not like terms
ionic ferry
So it's 100 = 10x
We got this equation
broken pier
Wait so
ionic ferry
So what should x be?
ionic ferry
Bingo!
ionic ferry
Okay, and?
ionic ferry
The value of X is 10
No no this is fine
So the number of months are?
Number of months was x, let me remind you
ionic ferry
That's correct, you've solved the first part
ionic ferry
No no forget y
broken pier
Ok
ionic ferry
David wants to save money, so he'll go to the one that charges lesser after 6 months, no Karate Klub charges 200 + 25x, substitue x with 6, what do you get?
ionic ferry
That's great
Now Kool Karate was 100 + 35x, so what would be the total charge there after 6 months?
broken pier
310
broken pier
The second one =310
ionic ferry
The second one =310
Okay, so David would join that club
ionic ferry
We solved and got 10 correct? What do we do with thr 10
In first part?
broken pier
Yea
ionic ferry
Alright, that's the number of months after which the total charge would be equal
Substitute x = 10 in 200 + 25x, you get 450
And x = 10 in 100 + 35x is also 450
So after 10 months, you'd have payed the same amount in both the clubs
ionic ferry
Sure, now do the thing you did in second part in third part, just replace x with 12 this time
broken pier
How would we write that
ionic ferry
Just write the equations for each club and replace the x with 12, write in brackets talking x = 12 as the number of months are 12
broken pier
100+200(12)
ionic ferry
100+200(12)
Wasn't it 100 + 35x and 200 + 25x?
broken pier
635
broken pier
Wait for 200*25
ionic ferry
Wait for 200*25
No no, why would be multiply 200 with 25
broken pier
Nvm sorry
ionic ferry
Well that's fine, take your time
broken pier
So 100 +35+200+25 x 12 would give us 650
ionic ferry
Yes, that's the total cost for second one
broken pier
Ok
ionic ferry
And the cost for the first one would be?
ionic ferry
It was 100 + 35x
broken pier
Right
ionic ferry
So what would it be, after 12 months
broken pier
520
broken pier
520
ionic ferry
520 is Kool Karate and 650 is Karate Klub
Alright, so he would join Karate Klub if he was joining for 6 months (second part) and Kool Karate if he was joining for 12 months (third part)
broken pier
Correct
ionic ferry
Okay, you need help with the others?
ionic ferry
Yeah it's fine
broken pier
Have a good day! Thank you so much again
ionic ferry
Have a good day! Thank you so much again
You too mate🫡
marsh citrusBOT
@broken pier Has your question been resolved?
keen wyvern
First did i draw this right and second im confused on if this is a washer or a disk
marsh citrusBOT
First did i draw this right and second im confused on if this is a washer or a d...
@keen wyvern Has your question been resolved?
silk sable
First did i draw this right and second im confused on if this is a washer or a d...
The parabola should extend into Q2 as well.
marsh citrusBOT
marsh citrusBOT
Available help channel!
lone anvil
im very confused on how to find sample variance and standard deviation, dont know how to use the formulas
marsh citrusBOT
im very confused on how to find sample variance and standard deviation, dont kno...
odd agate
welcome to the server!
lone anvil
thanks!
odd agate
please share a specific question you're stuck on for your problem here
would be better that way
lone anvil
it wants me to find s squared and o squared for a data set of 21, 3, 13, 7, 8. in my notes it says to create a table with two columns but how do i create two columns with five numbers?
stoic saddle
(sigma, not o)
odd agate
could you show the original problem, exactly as stated, please?
stoic saddle
that and show what youve got in notes
lone anvil
can i send pictures in here to make it easier?
indigo nest
Yes
odd agate
it wants me to find s squared and o squared for a data set of 21, 3, 13, 7, 8. i...
picture 4 shows how to make those two columns you need
lone anvil
how do i add it into the equation
odd agate
what equation? cuz you need to set up the table first (or, if you can hammer out the values you need, you can skip the table)
by the way
idk if the equation in pic 2 is entirely applicable. you may need to make some minor modification to it
lone anvil
what do you mean
odd agate
you are given the formula for the population standard deviation
however, in your question, you are asked to find the sample standard deviation
the formula is slightly different
i'm not sure if you have learnt about this, and from the mention of s it sounds like you have
but your notes shown here don't show that
if you have, proceed as usual as per picture 4
lone anvil
i cant find any notes on sample standard deviation, how much different is the equation for it?
lone anvil
ohh ok
odd agate
so would you know how to proceed using picture 4?
lone anvil
no but i can probably figure it out
odd agate
sure. a quick hint would be to think about how you would enter these scores in something like Excel
lone anvil
for the table?
odd agate
yes. enter the scores in one column
odd agate
would you like to keep this open for checking purposes, or are you done with your question?
lone anvil
i think im done with the question
odd agate
alright. if you're done, please .close the channel or mark it as .solved
and see you around!
lone anvil
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
ornate leaf
isnt integral 2cosx sinx just sin^2 (x) ?
marsh citrusBOT
isnt integral 2cosx sinx just sin^2 (x) ?
rose saffron
Why
ornate leaf
lots of different equivalent versions
but then how is -1/2 cos2x equal to sin^2
oh wait the c just differs
devout mauve
yes
ornate leaf
well dy/dx isnt really a fraction
why not
isnt dy a change in y
and dx a change in x
ornate leaf
wdym
when can i treat dx as a small change in x and when can i not treat it as a factor
because sometimes i ask and people tell me its just a small change in x and i can treat as a factor and in other cases i cant
but i havent understood when i can and when i cant
in substitution
dont we go from u=y => du/dx = dy/dx => du = dy/dx dx
marsh citrusBOT
@ornate leaf Has your question been resolved?
marsh citrusBOT
ornate leaf
.reopen
marsh citrusBOT
✅
ornate leaf
anyone?
serene bramble
Well, we could cancel, and it would get you the same result (note you'd have N(y) dy instead, but the integral is essentially the same)
The reason this is informal at best and mathematically illegal at worst is precisely because "dy/dx" as a fraction overlooks the property that both dy and dx represent infinitesimially small quantities
While the cancellation here can look legal here, that's more just a result of luck than anything
We want to rely on more than luck; hence the substitution
ornate leaf
We want to rely on more than luck; hence the substitution
why can i not treaat it as a factor
and why can i treat it as a factor in other cases
serene bramble
(I think you're confusing the words "factor" and "fraction")
ornate leaf
(I think you're confusing the words "factor" and "fraction")
sometimes
serene bramble
(which do you mean)
ornate leaf
you can use multiplication of dx
sometimes you cant
when can you and when cant you
amber birch
you can use multiplication of dx
$\frac{du}{dx} \ dx = du$ yes, always
elfin berryBOT
south
amber birch
but this is not to be justified as multiplication
ornate leaf
can i like divide by dx/ multiply by it sometimes always or what
amber birch
it follows from the chain rule
amber birch
can i like divide by dx/ multiply by it sometimes always or what
yes, it always gives the same result as the chain rule
if everything is differentiable and so on
serene bramble
Like, these AREN'T fractions (in the strict sense), though, which is the key point
ornate leaf
what isnt a fraction
serene bramble
dy/dx
ornate leaf
its a division of fractions
serene bramble
(You're confusing yourself again)
It just so HAPPENS that we notate them like so, which leads to the misconception that rules governing fraction arithmetic apply here too
And sometimes they do, but not for the same arithmetic reasons
serene bramble
yes
amber birch
and the derivative is a limit by definition
amber birch
if i had dx alone
it's an infinitesimal
it doesn't mean anything on its own formally speaking
ornate leaf
whats the difference
amber birch
you can think of it as "a tiny, tiny change in x"
ornate leaf
if dy/dx
serene bramble
"limit" refers to a point a sequence of points approaches
ornate leaf
is the limit of the division change in y and change to x
serene bramble
(You're getting that from the lim-def. of derivatives)
ornate leaf
then why isnt it infinitesimal dy /dx
serene bramble
?
We're explicitly telling you that dy and dx are infinitesimals
We can't let either be 0, because that results in a division by 0 problem
So we don't
ornate leaf
i dont see how the dy/dx in derivative
serene bramble
We literally let them be "infinitely small" (except "infinity" means "unobtainably massive" usually, so we use "infinitesimal" instead)
ornate leaf
is any different than lets say dy * (1/dx)
serene bramble
But I am telling you that the reasons behind them are not the same as the arithmetic examples
ornate leaf
to use dy and dx as a fraction
serene bramble
but why is it wrong
Because these are fokken tiny
ornate leaf
if its infinitesimal small isnt it the same as taking the limit
serene bramble
Arithmetic just doesn't function the same; we can't assume these rules to behave
[I recommend you read up on what infinitesimals are; you'll get a better understanding of what I mean by this]
ornate leaf
so the difference is
we cant distribute the limit
on a derivative
cause that will result in division by 0
serene bramble
generally yes
ornate leaf
[I recommend you read up on what infinitesimals are; you'll get a better underst...
what are they
ornate leaf
how is it not a real number
serene bramble
But I mean you need to read a short course on this; I'm not gonna write down a whole syllabus here
serene bramble
how is it not a real number
(by definition it is not a real number)
"because we say so"
vernal mantle
I mean tbh you could just try googling this
serene bramble
That's literally what I'm implying he do
vernal mantle
Ye
vernal mantle
That's literally what I'm implying he do
I'm just stating it ig
ornate leaf
this looks similar to limit defintion
amber birch
this looks similar to limit defintion
it's not
the limit definition only uses real numbers
ornate leaf
so
amber birch
in the real numbers, there is no infinitely smallest number
ornate leaf
in derivatives
amber birch
it just doesn't exist
ornate leaf
dy and dx arent infinitesemals?
serene bramble
ornate leaf
is it inside the limit
serene bramble
Personally I recommend the Iowa one
ornate leaf
we have lim Δx/Δy
when we write dy/dx
we cant mean the limit goes to both
cause that identity isnt true here
so what do we mean by dx
serene bramble
This is us literally leveraging infinitesimals
amber birch
when we write dy/dx
do you know that $\frac{d}{dx} f(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$
elfin berryBOT
south
amber birch
you can think of it as "a tiny, tiny change in x"
we mean this
we assert the existence of a number infinitely close to 0
and that's not a real number
ornate leaf
we assert the existence of a number infinitely close to 0
but inside a limit
dont we say that means the limit is 0
amber birch
dont we say that means the limit is 0
so that's different from what you're saying about dx
amber birch
**south**
this doesn't use any infinitesimals
we get to a point where we can just sub in h = 0 without dividing by 0
ornate leaf
yea i dont understand how we can use infinitesimals to represent a limit
how can dy/dx = lim Δy/Δx
one side is a limit
amber birch
one side is a limit
and that's no problem
ornate leaf
so left side cant be 0
but there are derivatives that are 0
ok so
define y = 5 , x in R
dy/dx = lim Δy/Δx <=> dy/dx = 0 <=> dy = 0
contradiction
since by defintion dy cant be 0
what went wrong
amber birch
dy/dx = lim Δy/Δx <=> dy/dx = 0 <=> dy = 0
cause you're not considering the limit
$\lim_{x \to 0} \frac{x}{1} = 0$
elfin berryBOT
south
amber birch
$\lim_{x \to 0} \frac{x^2}{x} = 0$
elfin berryBOT
south
amber birch
you cannot conclude dy = 0 if there's a limit
ornate leaf
i have a division of infinitesemals = 0
how can this be true if none of them are 0
how can a/b = 0 hold with a,b =/0
amber birch
how can a/b = 0 hold with a,b =/0
lim a/b = 0
there are many functions whose limit is 0
amber birch
dy and dx are infinitesemals
and so?
amber birch
ok so there is no limit
you would need to define a concept of a limit for non-real numbers
that is a valid point
ornate leaf
there is no limit
amber birch
you can define such a concept
amber birch
it doesn't work when you divide them
ornate leaf
what does a/b even mean
amber birch
dy/dx is undefined for dx, dy being infinitesimals
ornate leaf
dy/dx is undefined for dx, dy being infinitesimals
then if its undefined
amber birch
division doesn't mean anything here
ornate leaf
why are we using it to represent derivatives
amber birch
then if its undefined
we shouldn't use infinitesimals to represent dy/dx
that's my point
ornate leaf
since one side is infinitesimals and the other a limit
ornate leaf
you're using arithmetic on infinitesimals
but like dx you can find it inside expressions
if dx is an infinitesimal
and we cant use arethmitic
ornate leaf
then we cant use dx
amber birch
then we cant use dx
yes
amber birch
why do we write dy/dx * dx
you have to go back to the chain rule to understand this
it's a historical accident people discovered calculus
before it could be made rigorous
ornate leaf
isnt this arithmetic as in a multiplication of a derivative with an infinitesimal
well actually here there might be more confusion
cause the other dx is from the integral
amber birch
cause the other dx is from the integral
yes, that's also a historical accident
ornate leaf
yea icl man
amber birch
intuitively dx makes sense as the width of the infinitesimal rectangle
ornate leaf
im more confused than before i started asking
ornate leaf
so
wdym
the whole notation for integrals is wrong ?
and we just dont change it cause we historically used it in the past like this
amber birch
and we just dont change it cause we historically used it in the past like this
yeah...
you might want to search up Lebesgue integration
ornate leaf
so we can also not do arithmetic with the dx of the integral
amber birch
and we just dont change it cause we historically used it in the past like this
the current notation is the one that makes the most intuitive sense
we're technically not manipulating dx when we use the chain rule
ornate leaf
then why do some people write int 1 dx as int dx?
My mathematician in highschool said we should write int 1 dx because the dx goes with the integral as symbolisation
but tbf atp idk whats write or wrong
amber birch
then why do some people write int 1 dx as int dx?
My mathematician in highschool...
yeah, it comes from treating dx as a kind of number
so technically people shouldn't write that
but the meaning is clear enough
amber birch
its int 1 dx
yes
amber birch
yes
ornate leaf
is just a conventional thing
ornate leaf
ok thanks
amber birch
yeah I mean the whole history of calculus and analysis is insane
ornate leaf
ok
amber birch
there's also a concept in linguistics called pragmatics
which states "if I understand what you mean, even if it's technically wrong"
why bother fixing it?
if it ain't broke don't fix it mentality
think of the millions of students for whom calculus already doesn't make sense
and you could force the 'proper' notation on them
but they wouldn't understand anything
so this is a choice so that students learn what calculus is, then question every assumption about what they've learned later
that's how we can service all the engineers, physicists, and basically everyone who isn't a pure maths person
ornate leaf
that's how we can service all the engineers, physicists, and basically everyone ...
bro is offending me now
amber birch
otherwise you'd have to teach every 11th grade student what a measure is (in measure theory)
ornate leaf
i see how it is i cant study math because im going into engineering
amber birch
and a million more abstract concepts to learn something so useful
amber birch
i see how it is i cant study math because im going into engineering
you can
ornate leaf
yea ik just jk
amber birch
but pure maths and engineering are two completely different mindsets
ornate leaf
uni hasnt started yet
ornate leaf
but i was told in electrical engineering some stuff we write wrong
and we make a lot of conventions
amber birch
yes
ornate leaf
thats gonna piss me off fr
amber birch
there are certain subfields of engineering which are particularly egregious
ornate leaf
for example
on the differential equation for like metal moving with exponential function it doesnt go to 0 ever but we agree its 0 after some point
its I - e^r/L ... or some like that
sacred idol
its int 1 dx
i think its supposed to mean something like the sum of tiny rectangular areas in a cartesian graph
ornate leaf
and has asymptotic line y=0
anyways yea
@amber birch thanks a lot i understand it now
amber birch
no worries!
digital field
one argues that in physics, if two things are less than a certain constant (dim: length) apart, then they're actually the same thing
amber birch
so yeah the foundations of calculus are the real numbers
that's why it's called real analysis
digital field
very roughly anyways
amber birch
and then the real numbers are very very nice as a mathematical structure, so we can do a lot of cool things with them
like calculus
ornate leaf
no worries!
legend for answering to me doubting everything
i was getting mad of my own questions at some point
autumn vault
How do I even sketch that curve to begin with I know y=e^(x) but not that one
stoic saddle
you could isolate y in that eq
autumn vault
Y=1/x²
autumn vault
does that make it look more sketchable?
I'm not sure, maybe use intercepts from there to find 2 points
Does that work
marsh citrusBOT
@autumn vault Has your question been resolved?
marsh citrusBOT
@autumn vault Has your question been resolved?
echo scaffold
I’m really confused because this does not give me enough info. It does not give me an interest rate or time line besides 10 years.
marsh citrusBOT
I’m really confused because this does not give me enough info. It does not give ...
stark sandal
,rccw
elfin berryBOT
echo scaffold
And now I’m really confused because for the next one I’m getting the same number I started with
ancient ocean
I’m really confused because this does not give me enough info. It does not give ...
4 million over 10 years is 400,000 per year, I'm not sure if they want you to do anything else, it doesn't seem like it?
echo scaffold
4 million over 10 years is 400,000 per year, I'm not sure if they want you to do...
I have to use one of these equations
ancient ocean
I'd imagine if the interest is not specified it's just 1?
ancient ocean
I don't do financial math often, so I'm not really sure what to do here
echo scaffold
Kk no worries
The problem I’m running into is I either done have enough info or my equation gives me the same number I put in
stark sandal
RoR is just percent increase in value right
echo scaffold
I don’t know…
The problem is my finance teacher is a history teacher he doesn’t know how to teach math
But I don’t understand at all why Everytime I have been able to do a equation it equals the same thing I put in
stark sandal
in cuemath we trust
anyway so
initial value is 4m
final is 8m
theres no discussion to be had now
echo scaffold
The problem is my teacher said to only use the two formulas he gave us
Is my teacher just wrong? Like I won’t be surprised he’s a history teacher teaching personal finance …
marsh citrusBOT
@echo scaffold Has your question been resolved?
supple junco
Guys I don't understand when a function is neither increasing nor decreasing
indigo nest
Well look at something like f(x) = x²
It's decreasing when x is negative and increasing when x is positive
Overall it's neither
supple junco
What if I'm given a condition x ≥ 0
knotty trellis
What if I'm given a condition x ≥ 0
Then u can do e.g. sinx
It goes up then down then back up then down...
supple junco
Then u can do e.g. sinx
Wait I have a sum
For example this sun
The answer is neither
I don't understand why
The f'(x) is (-6+2x)/(x+2)^3
knotty trellis
The f'(x) is (-6+2x)/(x+2)^3
When is this positive? When is it negative
supple junco
When is this positive? When is it negative
I don't understand that
From what I know
if f'(x) is positive
It's increasing
And vice versa
vernal mantle
And what if both happen in the same domain
supple junco
And what if both happen in the same domain
I'm sorry I don't understand
vernal mantle
Do you think this function is increasing or decreasing or neither for x in (-inf,inf)
vernal mantle
Yes because there's a part where it's decreasing and part where it's increasing right
supple junco
Yes
vernal mantle
Wait I have a sum
So if f(x) is both increasing or decreasing
supple junco
So if f(x) is both increasing or decreasing
No matter the function?
vernal mantle
You can't call it an increasing or decreasing function
vernal mantle
No matter the function?
Yes
supple junco
So in the end it all comes down to the condition
vernal mantle
Yes
supple junco
Yes
Ok but what about this one
The condition is same here but the function is increasing
vernal mantle
I think you misunderstood
If the function is only increasing for the given domain
Then it's an increasing function
If the function is only decreasing for the given domain
It's a decreasing function
And if it does both it's neither
supple junco
I'm sorry but what do u mean by the domain
vernal mantle
I'm sorry but what do u mean by the domain
x>=0
supple junco
Oh I understand it now
calm harbor
.solved
midnight flower
hwkp
calm harbor
.solved
marsh citrusBOT
marsh citrusBOT
Available help channel!
tidal charm
Can I cancel these (x-5) and (x-3) without losing solutions?
marsh citrusBOT
Can I cancel these (x-5) and (x-3) without losing solutions?
tidal charm
And if not, I'm wondering how I'd go about solving this
stoic saddle
it's not that you lose solutions but rather that you risk gaining some
namely x=5 and x=3
whichever ones happen to be solutions afterwards
and indeed the one solution you got, x=3, must therefore be discarded as extraneous
tidal charm
Sorry how are solutions gained by doing that? Is it because x=3 wouldn't normally work because x-3 would be on the denominator if I hadn't canceled?
delicate prairie
Sorry how are solutions gained by doing that? Is it because x=3 wouldn't normall...
yes, same logic for x=5
tidal charm
Ok that makes sense!
What if I was doing a bunch of algebra to solve something, and midway through I had for example (x-7) on the denominator of an equation, but only because I did algebra to put it there. Would x=7 still be excluded as a solution? What if I removed the (x-7) afterward without cancelling it?
stoic saddle
if you put it there by algebra then it means you would have divided by (x-7) at some point
as in, divided both sides by (x-7)
this risks losing x=7 as a sol
stoic saddle
it's a risk. i can cook up an example where you're lucky and it is not lost.
but the best way to mitigate this risk is to just account for x=7 explicitly before doing it
tidal charm
it's a risk. i can cook up an example where you're lucky and it is not lost.
I would appreciate that if you feel like doing it!
stoic saddle
(x-7)^5 = 8(x-7)^4
tidal charm
but the best way to mitigate this risk is to just account for x=7 explicitly bef...
Like account for it by subbing it in and seeing what happens?
stoic saddle
dividing by just (x-7) gives (x-7)^4 = 8(x-7)^3
stoic saddle
Like account for it by subbing it in and seeing what happens?
yeah exactly
tidal charm
dividing by just (x-7) gives (x-7)^4 = 8(x-7)^3
So 15 and 7 are both valid answers here, and we can know 7 is valid by testing it before we divide (x-7)?
stoic saddle
yes
tidal charm
(x-7)^5 = 8(x-7)^4
We also could have lost a soln in this example if we immediately divide both sides by (x-7)^4 without accounting for x=7
Anyways I think I get it! Thanks so much @stoic saddle I really appreciate the help! 😄
@delicate prairie thank you as well for your help!
delicate prairie
marsh citrusBOT
marsh citrusBOT
Available help channel!
worn wadi
hi
stoic saddle
!status
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
okay
stoic saddle
and the eigenvectors to go with them
unkempt locust
Aren’t the eighenvectors orthogonal ?
You just need to normalize them and you’re done
stoic saddle
and the ones op just gave are.
stoic saddle
Aren’t the eighenvectors orthogonal ?
"eigenvector" has no h btw
unkempt locust
"eigenvector" has no h btw
My bad
stoic saddle
eignevectors are {-b/a, 1}, {a/b, 1}
wonderful now just normalize these as shakigras said
and youll have yourself a diagonalization
which really is all that the question asks for
worn wadi
which really is all that the question asks for
i still dont understand what O and D are
stoic saddle
ok do you know how diagonalization works
like $A = PDP^{-1}$ where $D$ is a diagonal matrix that holds the eigenvalues of $A$ and $P$ is the matrix whose cols are the corresponding eigenvectors
elfin berryBOT
Ann
worn wadi
like $A = PDP^{-1}$ where $D$ is a diagonal matrix that holds the eigenvalues of...
and here is O the P? but here it's the transpose?
waiit
oh ok
worn wadi
wonderful now just normalize these as shakigras said
why do we normalize O?
worn wadi
You just need to normalize them and you’re done
why do we normalize
delicate prairie
if the cols of P are orthonormal then P is orthogonal
unkempt locust
Because the matrix O is supposed to be orthogonal. Which means all its vectors need to be normalized
marsh citrusBOT
marsh citrusBOT
Available help channel!
deep dome
im stuck.
deep dome
i have 0 clue what to do further
i looked at it again and i think theres nothing more to do? its solved?
robust igloo
Consider a k such that x_k = k^2 + k
Then x_(k+1) = (k^2 + k) + 2k + 2 = k^2 + 3k + 2 = (k+1)(k+2) = (k+1)(k+1 + 1) = (k+1)^2 + (k+1)
Hence the relation between the serial number and the value of x for that serial number holds for the serial number k + 1 if it holds for the serial number k.
x_n = n^2 + n holds for n = 1 and hence it holds for n = 2 and so on.
deep dome
Consider a k such that x_k = k^2 + k
Then x_(k+1) = (k^2 + k) + 2k + 2 = k^2 + 3...
I understood that but did i do it correctly or was there something missing? can i just write that x_n = n^2 + n is the same as (k+1)^2 + (k+1)?
because i proved that its the same if u input 1, 2, 3 ,4 ?
oh wait they are legit the same...
<@&286206848099549185>
mild stratus
i dont know the exact meaning of mathematical induction
but i can help you solve this problem
deep dome
i dont know the exact meaning of mathematical induction
a proof technique to show a statement is true for all natural numbers
mild stratus
ok i think i can do that
deep dome
u kinda need mathematical induction to solve this haha
robust igloo
You don't need but you are required to use it here.
mild stratus
so its given that x_n+1=x_n+2n+2
consider x_n= x_n-1+ 2(n-1) + 2
and all terms all the way to x_2 = x_1 + 2 + 2
now define a sum S = x_1+x_2+x_3... x_n+1
mild stratus
and all terms all the way to x_2 = x_1 + 2 + 2
and add all the equations till here
that will give the value of x_n in terms of n, numbers, and x1
after a bit of simplification that is
lmk if you dont understand any of this
mild stratus
lmk if you dont understand any of this
ill write it down on paper and send it here
deep dome
hm i solved it and then checked this 😅
deep dome
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
leaden peak
marsh citrusBOT
leaden peak
I think a plane is just a line but it is also infinitely thick
So I'm kinda imagining this as two pieces of paper, one higher up that the other
and they are at the same slant
but I have no clue where to go from there
Also tried just doing 23.52 - -18.11 but that's wrong
the correct answer is 5.622 btw
BTW I can't really graph this, my calc only supports 2d on the grapher
cunning fiber
BTW I can't really graph this, my calc only supports 2d on the grapher
desmos
note that the planes are slanted, so this doesn't work
since the planes are parallel, ||I'd pick a point on one plane and use the formula for the distance from a point to a plane||
leaden peak
since the planes are parallel, ||I'd pick a point on one plane and use the formu...
Not really sure how to go about that
whats that formula?
wheat ridge
whats that formula?
this formula
leaden peak
Ok, and to pick a point I'm gussing I just assign random value to x, y, then solve for z?
wheat ridge
Ok, and to pick a point I'm gussing I just assign random value to x, y, then sol...
yes that right
leaden peak
marsh citrusBOT
leaden peak
I have a graphing calc and can also write programs to perform calculations
to actually find that full value directly is impossible, just returns infinity on my calc
I also graphed 2017^x and looked at the table, but I couldn't find any patterns with the first 5 numbers
leaden peak
oh yeah I just typed in python shell, returned 3906579...
How could I do this generally?
elfin cairn
modular arithemtic!
jagged relic
you can do 2017^2 mod 100000
Read the question again
leaden peak
and what do I do with that value?
jagged relic
... no
elfin cairn
$2017^{2017}=((2017)^2)^{1008} * 2017$
elfin berryBOT
ExpertEsquieESQUIE
jagged relic
Read it again, slowly
regal coral
i'm interested to find consecutive powers of 10 that it lies between
leaden peak
ok I understnad that, just splitting up the exponents
regal coral
ye
elfin cairn
mb @leaden peak
leaden peak
is it possible without python then?
jagged relic
With a decent calculator, yes
regal coral
i found $10^{6665} < 2017^{2017} < 10^{6666}$
elfin berryBOT
Axe
jagged relic
That just tells you it has 6666 digits
leaden peak
With a decent calculator, yes
I mean, Python is being run on my calc so
It's just the actual calculator app doesn't return the value
regal coral
then i think you want $\lfloor 2017^{2017} / 10^{6661}\rfloor$
elfin berryBOT
Axe
jagged relic
$2017^{2017} = 10^{2017 \cdot \log_{10}(2017)} = 10^{\lfloor 2017 \cdot \log_{10}(2017) \rfloor} \cdot 10^{{2017 \cdot \log_{10}(2017)}}$
regal coral
i got 39065
elfin berryBOT
Nel
jagged relic
All you need is the first 5 digits of $10^{{2017 \cdot \log_{10}(2017)}}$
elfin berryBOT
Nel
jagged relic
(where {x} is the fractional part)
regal coral
that's slightly different than what i did, but that also gives 39065
that's a good sign
jagged relic
(you only need the first 5 digits of {2017 log_10(2017)})
leaden peak
can anyone explain what this stuff means or how to get it?
oh I think its just log properties
regal coral
yeah mostly log properties
regal coral
$n=\lfloor n\rfloor + { n}$ for any n
jagged relic
$x = \lfloor x \rfloor + {x}$
elfin berryBOT
Axe
leaden peak
wait what does curly brace mean?
jagged relic
(where {x} is the fractional part)
.
leaden peak
oh yeah that makes sense
so ${n}=n-\lfloor n \rfloor$
why are the brackets not visible
jagged relic
The integer part doesn't contribute since it just ends up doing powers of 10
You need to write \{ and \}
Curly braces make groups in LaTeX
elfin berryBOT
UCYT5040
proud basin
marsh citrusBOT
proud basin
could someone explain the diagonal set definition? i dont get it
im p sure pi is treated like a permutation of S, so like for example {5,2,3,1,4}
what does pi(i) mean?
fervent rampart
a permutation of S can be thought of as a bijection from S to S
so (5,1,2,3,4) example could be phrased as a function pi(1) = 5, pi(2) = 1,...
fringe nacelle
a permutation of S can be thought of as a bijection from S to S
? what else could it be?
isnt that the default view?
fervent rampart
well that's the underlying definition but you don't have to write it in function notation
fringe nacelle
ah ,gotcha
marsh citrusBOT
tulip trail
need help
marsh citrusBOT
Available help channel!
marsh citrusBOT
sturdy python
A printing house must print a novel in two formats. This novel will be produced in at least 5000 copies but at most 8000. The number of pocket format novels must be less than the number of standard format novels, but must be at least 2000 copies. The pocket format novels cost $8 to print and will sell for $13, while the standard format novels cost $11 to print and will sell for $15. Knowing that the production costs amount to $1350 for printing, what maximum profit can this printing house expect?
x: number of pocket format novels
y: number of standard novels
x+y >= 5000
x + y =< 8000
x =< y
x >= 2000
i got troubles with this part
A printing house must print a novel in two formats. This novel will be produced in at least 5000 copies but at most 8000. The number of pocket format novels must be less than the number of standard format novels, but must be at least 2000 copies. The pocket format novels cost $8 to print and will sell for $13, while the standard format novels cost $11 to print and will sell for $15. Knowing that the production costs amount to $1350 for printing, what maximum profit can this printing house expect?
sturdy python
marsh citrusBOT
sturdy python
3000
queen sun
Then the coordinate is (2000,3000)
sturdy python
got it
queen sun
Do same with 8000 line
fallow jolt
why tis not 2
marsh citrusBOT
why tis not 2
bleak ledge
why tis not 2
Its asking you to find the function f(t)
you see it looks like a parabola shifted downwards
fallow jolt
Its asking you to find the function f(t)
yah i got it now i didn't know it want the function
.close
marsh citrusBOT
bleak ledge
lilac bane
Btw insane that parabolicinsanity is answering a parabola question
marsh citrusBOT
Available help channel!
woven chasm
excuse me, i'm trying to solve this question but i'm not really sure which direction to take. the decimals seem out of place where i am so far and i'm not sure if i'm taking the right approach. i'm doing this problem for fun so i may not have written my explanation in the best way 😓
marsh citrusBOT
excuse me, i'm trying to solve this question but i'm not really sure which direc...
woven chasm
i got stuck after 5.4 and i genuinely have no idea where to go after this or if calculating DE was even in the right direction 😭😭
zenith pasture
BD = DC is incorrect
lilac bane
AT THIS ECOND
!help
wanton frigate
Bro
marsh citrusBOT
AT THIS ECOND
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
lilac bane
!occupied
marsh citrusBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
wanton frigate
how do i not occupy it
woven chasm
BD = DC is incorrect
oh really??
woven chasm
uhhhh yes
unkempt locust
The ratio is 3
unkempt locust
So 4*A(BED) = A(DCA)
unkempt locust
The ratio is 3
3 to 9
woven chasm
Do you get this one too ?
i've been trying to understand it but where'd the 4 come from
unkempt locust
Ok let me write on a paper it’s hard to type
woven chasm
OKSY SURE!! thanx
elfin stone
,rccw
elfin berryBOT
unkempt locust
Thank you
woven chasm
thanks
marsh citrusBOT
Available help channel!
feral lagoon
marsh citrusBOT
feral lagoon
i found x y u and v, where to go from here?
i also notice that u=v^2 looks similar to x=y^2, but they are different variables in different dimensions no? how do i use this hint?
wary lichen
Ngl, this so much more convoluted than it really needs to be, ill try to tackle it
feral lagoon
a and b are my lagrange multipliers btw
wary lichen
This can be easily solved by differentiating regular f(x) functions tbh
Anyways, gimme a sec
wary lichen
actually whats a regular f(x) here?
as in, just recreate the problem to be easier
takes a little bit of geometry to come up with an answer, and tbh, i havent been able to get much progress on the method the problem asks for
marsh citrusBOT
@feral lagoon Has your question been resolved?
drifting goblet
What’s wrong with my working?
