sorry for disturbing 🫠
but it seems interesting
#help-4
ocean bloom
pure mirage
integrated 1/x to get ln(|x|), inside of the integral I multiplied numerator and denominator with 1 + log(x) of the second summand to get the numerator
pure mirage
$\frac 1x = \frac{1 + x\log(x)}{x + x^2 \log(x)}$ and now [\frac{1 - x}{x + x^2 \log(x)} - \frac 1x] can be simplified to [\frac{1 + \log(x)}{1 + x \log(x)}]
ocean bloom
after the subtraction thing in the integral in observation
it comes out to be
$\int\frac{1}{1+xlog(x)} dx $
opaque tiger
In the answer key the last term of the answer is negative
pure mirage
Wait a sec, maybe there is a sign error somewhere
ocean bloom
In the answer key the last term of the answer is negative
it will be for sure
as it comes out to be -x
pure mirage
Yes, actually that last integral should be - int 1 + log(x) / 1 + x log(x)
[\frac{1 - x}{x + x^2 \log(x)} - \frac 1x = \frac{1 - x}{x + x^2 \log(x)} - \frac{1 + x \log(x)}{x + x^2 \log(x)} = \frac{1 - x - 1 - x \log(x)}{x + x^2 \log(x)}] [= \frac{- x - x \log(x)}{x + x^2 \log(x)} = - \frac{1 + \log(x)}{1 + x \log(x)}]
rocky lotusBOT
Kepe
pure mirage
\begin{align*}
\int \frac{1+x^2\log(x)}{x+x^2\log(x)}\dd x &=\int \frac{1-x+x+x^2\log(x)}{x+x^2\log(x)} \dd x\
&=\int 1 \dd x + \int \frac{1-x}{x+x^2\log(x)}\dd x\
&=x + C +\int \left(\frac{1-x}{x+x^2\log(x)}-\frac1x\right)\dd x+\int \frac1x \dd x\
&=x + C' + \ln(|x|) + \int -\frac{1+\log(x)}{1+x\log(x)}\dd x\
&=x + \ln(|x|) - \log(1+x\log(x)) + C''
\end{align*}
rocky lotusBOT
Kepe
pure mirage
There
pure mirage
ocean bloom
nice solution there
pure mirage
np
opaque tiger
These questions are so hard bro idek if I'm making progress
pure mirage
Just do more of them
vale dockBOT
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sullen lagoon
Anyone can help with this problem: You submerge the iron sphere with diameter d and density 8000 kg/m3 into mercury with density 13500. How much of d is submerged?
vale dockBOT
Anyone can help with this problem: You submerge the iron sphere with diameter d ...
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
2
I integrated the submerged part and got a cubic but i have no idea how to continue
bright wind
Just... Show the work
vale dockBOT
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sullen lagoon
I will have to write everything again if I want to show it to you because it’s quite messy. Basically I equated the force of sphere and the force with which the mercury pushes the sphere up and the I integrated the submerged part and i got a cubic that I can’t solve
hardy coral
Archimedes' principle?
vale dockBOT
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sullen lagoon
Archimedes' principle?
Yes i think i used that
hardy coral
So the displaced volume, in mercury, weighs as much as the object
sullen lagoon
Exactly
vale dockBOT
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@sullen lagoon Has your question been resolved?
umbral cipher
"Give an example of a linear transformation which is left invertible but not right invertible"
umbral cipher
Could I get a hint 🥺
Oh I think I got it
Maybe T: R3 to R2 with (xyz) goes to (xy)
ruby sleet
So what would a left inverse of T be?
I'll be honest I think you mixed up left and right invertible
Because you now need to find $S:\bR^2\to \bR^3$ such that $S\circ T = Id_{\bR^3}$
rocky lotusBOT
Raphaelisius Maximus MMIII
ruby sleet
Maybe T: R3 to R2 with (xyz) goes to (xy)
So think about your example and if it works
umbral cipher
**Raphaelisius Maximus MMIII**
Why not = idR2?
Oh I see
Forgot which direction it goes
Ty
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bitter ice
I can’t wrap my head around why we are plugging 6 into y for the inverse function as the last step. I get how to implicitly differentiate but not this f inverse prime 6
frozen ledge
do you know the formula for the derivative of the inverse?
frozen ledge
if $f$ and $g$ are inverses then $g'(x) = \frac{1}{f'(g(x))}$
rocky lotusBOT
knief
bitter ice
yes I understand that
frozen ledge
ok so whats the issue
bitter ice
its the finding f inverse prime of 6
like what is that even asking
is it an x value
is it a y value?
frozen ledge
**knief**
plug in x = 6 here
its just 1/f'(f^-1(6)) and f^-1(6) is the solution to f(x) = 6
bitter ice
its just 1/f'(f^-1(6)) and f^-1(6) is the solution to f(x) = 6
but thats not the answer
and thats also not the question
its not asking f(x) = 6
frozen ledge
bro what
frozen ledge
but thats not the answer
what isnt the answer?
bitter ice
frozen ledge
💀
bitter ice
what isnt the answer?
1/5
frozen ledge
i never said it was
frozen ledge
,w solve x^3 + 2x + 3 = 6
rocky lotusBOT
frozen ledge
yea its 1/(3 + 2) = 1/5
bitter ice
im very confused
frozen ledge
f^{-1}(6) = 1
bitter ice
i cant wrap my head around why we plug in 6 to the original function for x
bitter ice
or y for the inverse
bitter ice
yes
frozen ledge
$g'(6) = \frac{1}{f'(g(6))}$
rocky lotusBOT
knief
bitter ice
yes sir
bitter ice
this is the part that trips me up
frozen ledge
by definition of inverse, g(6) is value such that f(x) = 6
^
bitter ice
yes i understand that part
bitter ice
the solution to the equation f(x) = 6 is g(6)
i understand this
bitter ice
so we can say g(6) is equal to f(x) = 6 right?
frozen ledge
not equal to an equation, equal to the real solution of the equation
frozen ledge
🤔
wdym?
think back to algebra when youd solve equations like f(x) = 0
to find the zeros of a function
bitter ice
mhm
frozen ledge
you found the values of x such that the equation was true
bitter ice
yeah
bitter ice
yeah i get that
bitter ice
mhm
frozen ledge
ok then as per the formula that is the value we plug into f'
we found g(6) = 1
so we plug 1 into f'
then the inverse is the reciprocal of that
frozen ledge
then the inverse is the reciprocal of that
inverses derivative
bitter ice
inverses derivative
last thing, when inversing a function like I need to do in this question. When doing implicit differentiation, should I change x's to y's and vice versa?
because I was taught when inversing to switch x and y then isolate for the new y
but in this case there is no isolating because we are doing it through implicit differentiation
frozen ledge
because I was taught when inversing to switch x and y then isolate for the new y
i mean you can just solve for x but generally in calculus you wont be asked to find the inverse function
oftentimes that algebraic technique wont work
they just ask you for the derivative at a point
bitter ice
mhm
bitter ice
they just ask you for the derivative at a point
wait but if f(x) =x^3 + 2x + 3, what is g(x)?
its still in respect of x
but then the variables cant switch
frozen ledge
,w plot x^3 + 2x + 3
frozen ledge
,w inverse of x^3 + 2x + 3
rocky lotusBOT
Sending query to Wolfram Alpha, please wait. 
bitter ice
,w plot x^3 + 2x + 3
yeah but without plotting
rocky lotusBOT
frozen ledge
its a nightmare expresssion
bitter ice
like I want to do this the way my prof is teaching it
bitter ice
its a nightmare expresssion
yeah but thats why im confused
like how would I do this the way hes teaching it
frozen ledge
I can’t wrap my head around why we are plugging 6 into **y** for the inverse fun...
he showed how he did it on the right side of the paper
bitter ice
like i did all the work but I jsut have no clue why we are plugging in 6 as the independant variable
frozen ledge
perhaps you're not understanding the formula
bitter ice
yeah probably not
frozen ledge
they asked you to find the derivative of the inverse at x = 6
bitter ice
but he never gave us the formula
frozen ledge
bitter ice
thank you
oh my god
im mad at myself
...
knief i got bad news
i was lookng at this trying to wrap my head around it for like an hour on the train
and didnt notice the theorem at the bottom of the page
frozen ledge
and didnt notice the theorem at the bottom of the page
😭
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heavy juniper
So when doing Q = A/B where Q is a quotient group, then B must be a normal subgroup of A?
next vortex
yes, quotient groups are only defined for normal subgroups
next vortex
if B is not normal, the group operation is not well-defined
vale dockBOT
@heavy juniper Has your question been resolved?
heavy juniper
if B is not normal, the group operation is not well-defined
Hmm makes sens e
Thanks
wary panther
What does the sum $\sum\limits_{k\geq1}(-1)^k\frac{(2\pi l)^{2k}}{(2k)!}, l\in \mathbb{Z}$ converge to?
rocky lotusBOT
Alrik
pure mirage
What does the sum $\sum\limits_{k\geq1}(-1)^k\frac{(2\pi l)^{2k}}{(2k)!}, l\in \...
Do you know the Taylor series of cos(x)?
wary panther
That makes a lot of sense
honest stone
Wolfram has a surprisingly simple answer but I haven’t a clue on how it would be dervied… 
wary panther
of the function exp(z)-1
yeah
the answer should be zero
and this should be the cosine function
for any l in Z
honest stone
Wolfram has a surprisingly simple answer but I haven’t a clue on how it would be...
scratch this I forgot about the alternation
wary panther
i do know about the taylor series of cos(x)
opaque stratus
here are 10 points marked on a circle, and chords are drawn form each pair of points if no three chords concur at a point strictly inside a circle find the number of intersections strictly inside the circle (which are meeting are meeting point of two chords)
wary panther
.close
vale dockBOT
pure mirage
I’m assuming you’re trying to find a formula for an integer value of 𝑙?
(the answer is there directly after plugging in x = 2pi l and subtracting off the k = 0 term)
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winter chasm
hi
queen rover
quasi dust
winter chasm
my question is the The Riemann Hypothesis
safe fulcrum
my question is the The Riemann Hypothesis
please don't troll
winter chasm
im not
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silk coral
my question is the The Riemann Hypothesis
Answer is 5
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signal chasm
part b
signal chasm
hollow rune
Depends on how much precision you want tbh, and there are a few ways, have you been taught any?
signal chasm
i know
that u use the expansion
and subsitute x=1/100 into it
but idk abt the find approximation for root 5
hollow rune
Ill take it you already know the method used for a)
You should be able to factorize out a (1-x)^1/2 instead of sqrt5
signal chasm
wdym
hollow rune
Ill take it you did the first a) by first factorizing out into a 1/2 . (1-20x)^1/2
Here you can do something similar
$\sqrt{5}=\sqrt{4+1}=\sqrt{4(1+\frac{1}{4})}=2\sqrt{1+\frac{1}{4}}$
rocky lotusBOT
∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴
signal chasm
ohhhhhh
hollow rune
From there you should be able to work out a good approximation
signal chasm
so we make the thing in the surds
equal to one another
and find x
sub back into approx?
hollow rune
Yeah. Theres a lot of good ways to find aproximations anyways
vale dockBOT
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zealous pendant
You shouldn’t find x here, just put 1/100 into x
You should have an approximation of (1/4-5x)^(1/2), if you put x=1/100 into that you get an approximation for 1/sqrt(5)
Then do 1/ it to get approximation for sqrt(5)
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orchid flower
I'm unsure if the part i solved is correct. If i remember correctly, integral of graph like this shouldn't give negative value. What part i did wrong?
hidden terrace
You can't integrate f(x) directly because you don't even know what it is
Right now you're treating it as f(x) = x
The solution lies in a relationship between the two integrals
Try drawing the relevant areas in the plane
orchid flower
One sec i think i found the connection
Is it like this
Because of it being an x function rather than y function
orchid flower
2 box right?
hidden terrace
Yeah
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shrewd chasm
any idea...how do i write this in a structured or short way (in understandable manner)..
stark wedge
ratio of girls to boys is 3:4 so there are 3n girls and 4n boys
boys' avg height is our goal so call it x
the entire group's avg height is x-3
coral nacelle
vale dockBOT
coral nacelle
Can anyone help
keen tundra
do you know how you rationalize a fraction like this?
||you multiply both denominator and numerator by the conjugate of the denominator||
coral nacelle
Ya I know that part I wanna check my answers if I’m correct tbo
Cuz I’m not sure if I’m missing some steps
keen tundra
show your work then
fossil warren
$(-\sqrt{7})(\sqrt{7}) \neq 7$
rocky lotusBOT
Kaladin.
deft hornet
then what
fossil warren
-7...?
coral nacelle
Ahhh my bad I didint see that part
keen tundra
fossil warren
also $6(3+\sqrt{7}) \neq 18-6\sqrt{7}$
rocky lotusBOT
Kaladin.
fossil warren
Nothing wrong with the second one.
coral nacelle
Alr I js have to make sure I look at the question again basically
Thank u guys
.close
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steel tundra
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steel tundra
This is one of the easier questions but have a hard time getting started, i kinda know how to factorise but i dont know how to start.
<@&286206848099549185>
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hardy coral
This is one of the easier questions but have a hard time getting started, i kind...
i kinda know how to factorise
Well, can you factorize 6x^2 + 92x + 352 ?
naive lotus
For a function ( f(x, y) ) developed around ( (2,2) ), the following holds:
$$
p_4(h, k) - p_3(h, k) = \frac{4h^4 - 32h^3k + 102h^2k^2 - 140hk^3 + 61k^4}{3}
$$
and
$$
f(3,3) - p_4(1,1) = \frac{17}{3} + 0.03002\ldots
$$
Which function is ( f(x, y) )?
rocky lotusBOT
Skiii
tawny moon
is this an MCQ?
naive lotus
is this an MCQ?
No
Been doing research online, came to conclusion theres more than 1 function have these requirments. But my teacher keep saying against lol
hazy pivot
What exactly is p_n
Are they related to f in any way or are they just arbitrary functions
ebon glade
!original
vale dockBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
naive lotus
What exactly is p_n
Pn(h,k) denotes the n-th degree taylor polynomial of f(x,y)
naive lotus
Please show the original problem, **exactly as it was stated to you**, with the ...
Swedish fyi ^
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@naive lotus Has your question been resolved?
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@naive lotus Has your question been resolved?
midnight pier
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@naive lotus Has your question been resolved?
tight trout
can you help me guys to do it without using integrals to find the expression of f(x)
sharp whale
d/dx both sides of f(x) = x
nvm this doesn’t work
inner path
The derivative is negative everywhere on R+, so as x increases f(x) decreases
In fact it is strictly decreasing
Oh to find the expression of f, no you just have to integrate it
sharp whale
the only way to find what f(x) is is by integrating
but the question only needs you to prove that f(x) = x has 1 solution, you don’t need to find it (in this case you likely can’t)
use that f(x) - x is strictly decreasing to prove there can only be up to 1 solution
inner path
Yea okay thats what I was going to sayc
And also note the existence is guaranteed by IVT
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steep scarab
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steep scarab
the test this is on is already finished and i have no more attemps this is soley for personal understanding
but i am confused on how to work out the second part where it asks
as in how the tension in EB affects the tension in the sperate ish system that BC is in
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silent dagger
just for fun;
how can i graph sin/cos of x that doesn't cross the x-axis?
what about sin/cos of x multiplied by x? log of x?
distant galleon
,w graph sin x + 2
rocky lotusBOT
tawny moon
,w graph sin x - 2
rocky lotusBOT
silent dagger
found one such case:
$f(x)\cdot\cos(x)+f(x)$
rocky lotusBOT
Weathers
silent dagger
.close
vale dockBOT
silent dagger
thanks y'all! o/
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onyx tusk
/e wave
stark wedge
hello, do you have a math question to ask?
stark wedge
ok first off, http://nohello.net/ and you should post the question as your first message usually.
now that that's out of the way
onyx tusk
ok first off, http://nohello.net/ and you should post the question as your _firs...
Alr mb
stark wedge
I'm genuinely clueless on how to do this
write down expressions for the perimeter and area of this shape in terms of x and y.
stark wedge
and you said you were clueless.
stark wedge
...where is the third y coming from in the perimeter tho
shouldn't it be 32x + 2y = 80?
onyx tusk
Oops
Careless mistake
Maybe that's why I didn't get my answer this whole time..
Wait gimme a while
to try redoing it
stark wedge
your area equation looks correct to me, for the record
onyx tusk
Ok I thought I figured it out but nvm
Ignore the oil stain I was eating chicken
I tried using sum of roots and product of roots to see if it can help me in some way but ehhhhhh
rocky lotusBOT
Ann
stark wedge
also (80-32x)/2 could have and should have been simplified
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dawn wigeon
Well, I’ve got this piece of crap as a problem. I’m applying the interpolation error theorem to solve it. I’ve determined that the number of nodes is 2, therefore 𝑛=1. By differentiating the expression twice, I end up with cos((pi * x) / 2) * pi * x. Knowing that the maximum value a cosine can take is 1 and that the maximum value of 𝑥 in the interval is 3, I approximated the expression to 3𝜋, taking this as the maximum value of the express.
dawn wigeon
For 𝑊𝑛(𝑥), I simply used the approximate expression ∣𝑏−𝑎∣^𝑛+1 resulting in 3^2. When substituting into the theorem’s expression, I realized I don’t know how to include the value of ℎ in the equation. I considered reformulating the 𝑊𝑛(𝑥) term to calculate the nodes according to the value of ℎ, but I’m completely lost.
Any help is appreciated 🙂
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sharp whale
Well, I’ve got this piece of crap as a problem. I’m applying the interpolation e...
you here?
sharp whale
you cant really use this to solve the problem, but the largest step length that ensures error of less than 10^-3 is h = 3/100 (i.e. from 100 subintervals)
this is from testing every value of f(x) so this isnt practical, thats just there if youre curious
if youre using this formula, the largest step length that ensures this is less than 10^-3 is h = 3/101 (i.e. from 101 subintervals)
this is from testing every value of f''(x) to find its max so its also not practical (you cannot solve for the max)
sharp whale
to get their solution, you have to use that, for 0 < x < 3,
as you can imagine this is a pretty bad bound on the max, you know this should be < 3, but using 12 here will get you the same answer that they have
lmk if you dont understand what Im doing here, I dont think what I did here is very standard
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valid vigil
for b do you just add all three varieence for do you subtract 1.5^2 and add 1.8^2 andfor mean do you just subtract and add the means?
vale dockBOT
for b do you just add all three varieence for do you subtract 1.5^2 and add 1.8^...
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valid vigil
@keen tundra
eager sleet
Hi guys
low ice
Question first please
robust wolf
No hi is crazy
honest stone
No hi is crazy
Lol. I have it as a text replacement on my laptop
eager sleet
I have a request no question
Can anyone dm me if you are student in college currently
robust wolf
I have a request no question
Can anyone dm me if you are student in college cur...
Bruh
honest stone
I have a request no question
Can anyone dm me if you are student in college cur...
Uh no.
wraith heart
I have a request no question
Can anyone dm me if you are student in college cur...
!done
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If you are done with this channel, please mark your problem as solved by typing .close
honest stone
Can someone .close this unless you have an actual question that doesn’t require dming?
bright wind
I have a request no question
Can anyone dm me if you are student in college cur...
Just ask math problem here or not at all. This's not a place to ask for DMs
eager sleet
.close
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dull cipher
to participate at an activity, each student needs to pay their part of the cost of transport by bus, which is of 300$, aswell as the entry at the insectarium, of 8$. Whats the equation of the amount that the students have to spend in fuction of the amount of students that participate at the activity
rocky lotusBOT
opal
hazy pivot
to participate at an activity, each student needs to pay their part of the cost ...
Well let's say there are x students
dull cipher
yeah
hazy pivot
How much is each student paying for the bus
dull cipher
300
hazy pivot
Yup
dull cipher
oh tysm
but it asks me aswell the equations of the asymptotes for the curve of the function defined by this equation
hazy pivot
Well what do you think the asymptotes will be
dull cipher
the h,k
dull cipher
asymptote isn't the coordinate at the half between both curves?
hazy pivot
Either the function approaches infinity at a point or the function approaches a value at infinity
hazy pivot
asymptote isn't the coordinate at the half between both curves?
I'm not aware of this notion of asymptote
dull cipher
ill show imahge
wait
i might be wrong then
i think the coordinate at the half is just (h,k)
dreamy scroll
asymptote isn't the coordinate at the half between both curves?
thats centre for a hyperbola
dull cipher
yeah h,k right
dreamy scroll
yeah h,k right
umm depends on the equation
but ye you can give it any variable value
dreamy scroll
its rational equation
whats h and k here ??
dull cipher
whats h and k here ??
didnt find yet
dreamy scroll
how can i find the equations for asymptotes
in such cases for the horizontal one just check the funtions convergence at infinity
and for the vertical one check when the denominator becomes 0
or the function becomes not defined
or aproaches any of the infinities whatever you wanna call it
dull cipher
the equation is f(x) = 300/x + 8 so i gotta replace x with 0
dreamy scroll
the equation is f(x) = 300/x + 8 so i gotta replace x with 0
ye
dull cipher
alright
dreamy scroll
the equation is f(x) = 300/x + 8 so i gotta replace x with 0
we're making the denominator of the expression zero
dull cipher
300/0 says math error
dreamy scroll
or the expression not defined
dreamy scroll
300/0 says math error
it's not defined at x=0 hence x=0 is an asymptote
dull cipher
oh
i dont understand so a asymptote can have a equation?
ah wait nvm i got it
thanks for ur help
.close
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silent bobcat
someone could speak a read in spanish? i dont know how do a problem :c
viscid spade
Post it and someone will probably come
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barren imp
I need someone good with word problems
vale dockBOT
I need someone good with word problems
barren imp
A company finds it can produce 25 heaters for $5950 , while producing 35 heaters cost $8250. Express the cost y as a linear function and the number of heaters as x. Determine the cost to produce 40 heaters.
How do we break this down?
I thought it was midpoint but I just kept getting stuck
This question has caught me off guard in my stuff twice now
...
<@&286206848099549185>
Anyone good at breaking down word problems?...
vale dockBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
robust wolf
I thought it was midpoint but I just kept getting stuck
It's not midpoint. Hint: try finding the slope
barren imp
Would the slope be the cost?
robust wolf
Would the slope be the cost?
Not necessarily, it would be the cost of each heater
fleet burrow
A company finds it can produce 25 heaters for $5950 , while producing 35 heaters...
y is a linear function, so y takes on the form y = mx + c, where m and c are constants to be determined. Substitute in x = 25, y = 5950 and x = 35, y = 8250. You should get a system of equations which is solvable.
(at least i think that's the solution)
robust wolf
y is a linear function, so y takes on the form y = mx + c, where m and c are con...
Don't need to do system of equations though
barren imp
So then the equation would be 5950=mx + 25?
barren imp
Don't need to do system of equations though
How many ways are there to solve this
robust wolf
So then the equation would be 5950=mx + 25?
Not quite
robust wolf
How many ways are there to solve this
Idk and idrk why or how you would use system of equations but finding the slope is the first move
barren imp
So (25+35)/(5950+8250)
robust wolf
So (25+35)/(5950+8250)
No that's not the slope formula
robust wolf
Yes
Wait
It's not y/x but you're close
The slope formula is $(y_{2} - y_{1})/(x_{2} - x_{1})$
rocky lotusBOT
డ్ర్యాగ్లొక్స్
barren imp
So its the opposite of midpoint but closer to distance
robust wolf
So its the opposite of midpoint but closer to distance
No I don't think it's either. The slope just tells how much the function is increasing
It's just change in y divided by change in x
fleet burrow
@barren imp i think you have some very big conceptual misunderstandings and you should probably revise your notes
barren imp
Slope has always been confusing for me...
Anyway so ok if I did the math right i got 2300/10
robust wolf
Slope has always been confusing for me...
Slope essentially is just a number that says how much a function is changing every time you change x
robust wolf
Anyway so ok if I did the math right i got 2300/10
Yes
The slope is 230 in this case
barren imp
Yes
robust wolf
And is the price of each heater
barren imp
So then 230...
robust wolf
Now you need to find the y-intercept
robust wolf
Where'd you get 40 from?
barren imp
A company finds it can produce 25 heaters for $5950 , while producing 35 heaters...
Here
robust wolf
No the 40 would be something to plug into x
You have some equation $5950 = 230(25) + b$ solve for b
Wait
rocky lotusBOT
డ్ర్యాగ్లొక్స్
barren imp
So where does the 40 come into play because I need to figure out the price of 4 heaters
robust wolf
So where does the 40 come into play because I need to figure out the price of 4 ...
Basically, you're given the price of 25 heaters and 35 heaters. You need to find the price of 40 heaters. Once you solve for b, you'll need to plug 40 into x to get y where y is the price of the heaters $y = 230x + b$
rocky lotusBOT
డ్ర్యాగ్లొక్స్
barren imp
Ah so y=230(40) + b?
robust wolf
Ah so y=230(40) + b?
Once you solve for b, and plug in x = 40, you'll get y at x = 40
Which is the price of 40 heaters
robust wolf
So in this case what would be 9200?
Very close, but you're missing the +b
robust wolf
**డ్ర్యాగ్లొక్స్**
.
barren imp
9200 + b
barren imp
So b = -9200?
robust wolf
No
barren imp
Im getting a little confused here:')
robust wolf
$5950 = 230(25) + b$ do some algebraic manipulation to get b
rocky lotusBOT
డ్ర్యాగ్లొక్స్
robust wolf
Im getting a little confused here:')
What exactly is confusing here?
barren imp
Oh we dont put the 40
barren imp
What exactly is confusing here?
My life (pun drum)
robust wolf
😭
robust wolf
Are you confused with perhaps why we are doing these steps?
barren imp
Ok so b is 200
rocky lotusBOT
డ్ర్యాగ్లొక్స్
barren imp
Ok
So then thats how to write the y
Im looking at some old notes and... there's point set formula?...
*slope
And solving for x... is -200/230?...
robust wolf
So then thats how to write the y
Yeah, just need to plug in the x value
robust wolf
And solving for x... is -200/230?...
No you don't need to solve for x
Plug in 40 for x
barren imp
Oh!
robust wolf
And then you'll get a certain y value
barren imp
Ok so ima check- if we plug in y= 230(25)+200
It makes 5950
Y=230(35) +200
It is also 8250
Ok so then we plug in y=230(40)+200
robust wolf
Can you help me with another area?
Sure in a second
barren imp
No problem I need to take 5 anyway
vale dockBOT
@barren imp Has your question been resolved?
vale dockBOT
barren imp
.reopen
vale dockBOT
✅ Original question: #help-4 message
mild kernel
sorry, youre just working on this root problem?
$\frac{ \sqrt{-35} \sqrt{ -5} }{ \sqrt 7 }$
rocky lotusBOT
jan Niku
mild kernel
@barren imp
forest lion
hello
mild kernel
what have you tried?
maybe you have a list of properties of roots that you can use?
if not we can find one
mild kernel
maybe you take an intermediate step there
$\frac{ \sqrt 7 \sqrt{-5} \sqrt{-5} }{ \sqrt 7 }$
rocky lotusBOT
jan Niku
barren imp
But now I have the (sqr)/-5 sitting next to it
mild kernel
this is after splitting the -35, but without taking out the i
do you notice anything?
barren imp
We can get rid of the 7s
barren imp
But what do we do with the 5s?
rocky lotusBOT
jan Niku
mild kernel
can you think of another way to write this?
mild kernel
how do we usually write a*a?
barren imp
Well I dont know with the sqr roots
mild kernel
but you know its a^2 yea?
barren imp
Yeah
mild kernel
$a \cdot a = a^2$
rocky lotusBOT
jan Niku
barren imp
They are both negative but would they make 25?
mild kernel
so then $\sqrt{-5} \sqrt{-5} = \qty( \sqrt{-5} )^2$
rocky lotusBOT
jan Niku
barren imp
Ohhh
mild kernel
what happens?
barren imp
So not 25
mild kernel
They cross eachother out?
the root and the square do, yea
barren imp
neat locust
So not 25
Your questions and confusion are valid. You really shouldn't ever have square root of a negative number because you get confused on how to distribute it.
mild kernel
well theyre doing complex numbers
neat locust
We still use the imaginary unit i
barren imp
Well earlier I thought I put the i out
rocky lotusBOT
jan Niku
mild kernel
looks like $i^2 \qty( \sqrt 5)^2$
neat locust
But (as far as i can recall), there should never be square roots of negative numbers
rocky lotusBOT
jan Niku
barren imp
So i turns to (-1)
mild kernel
in the front, yea
barren imp
But the 5...
neat locust
I'm not saying what you are doing here is wrong, it's just very unfortunate that it is presented to you this way
barren imp
Is it (-1)5?
barren imp
So then -5?
mild kernel
yup
barren imp
Ok thank you
mild kernel
I'm not saying what you are doing here is wrong, it's just very unfortunate that...
yea because
its hard to resist the temptation to combine them
int $\sqrt{ (-5)^2 }$
rocky lotusBOT
jan Niku
mild kernel
which seems like the most tempting thing to do
i think this is just a problem of 2 answers
barren imp
(I seemed to have made an error somewhere but I do not know where
barren imp
i think this is just a problem of 2 answers
I see
mild kernel
,calc 4*8
rocky lotusBOT
Result:
32
idk my table
mild kernel
(I seemed to have made an error somewhere but I do not know where
66 seems low
barren imp
I foiled it
mild kernel
we should get the 4*8 as the first contribution to the real part
and then 9*6
yea?
barren imp
Yes
robust wolf
and then 9*6
yeah this is it
mild kernel
sure
robust wolf
32-24i +72i-54i²
yes this is it
sorry i didnt come earlier, i was doing something and got carried away with it
robust wolf
yes but there's one more step
robust wolf
yeah
robust wolf
yeah
robust wolf
So then 86-48i is the result
Yep exactly
robust wolf
Do we simplify it?
It's already simplified
barren imp
Oh
robust wolf
Cuz you can't really reduce i
robust wolf
Wait what?
barren imp
mild kernel
,calc 48 + 96
rocky lotusBOT
Result:
86
,calc -46+98
rocky lotusBOT
Result:
48
barren imp
What did I do....
mild kernel
9 times 8 is bigger than 4 times 6
barren imp
Oh wait-
barren imp
Its +48i
mild kernel
it is, yea
barren imp
Not -48i
mild kernel
these problems are 100% just tricks to try to get you to mess up a sign
barren imp
Yayyy
robust wolf
these problems are 100% just tricks to try to get you to mess up a sign
ong
messing up signs is like 80% of all math mistakes
barren imp
True
mild kernel
$\frac{1}{a+b} = \frac 1a + \frac 1b$
rocky lotusBOT
jan Niku
mild kernel
the usual 
robust wolf
**jan Niku**
😭
robust wolf
yeah fractions are tedious to write sometimes ngl
mild kernel
once you realize fractions are just exponents it gets better
well, that is i guess if you are good with exponent problems
barren imp
I will take all of it over word problems though
mild kernel
fair, those are just like uhh
robust wolf
once you realize fractions are just exponents it gets better
aint nobody writing $a^{-1}$ instead of $\frac{1}{a}$
mild kernel
i mean you just have to see all the problems
rocky lotusBOT
డ్ర్యాగ్లొక్స్
mild kernel
aint nobody writing $a^{-1}$ instead of $\frac{1}{a}$
they absolutely do
barren imp
**డ్ర్యాగ్లొక్స్**
This is cursed
robust wolf
they absolutely do <:catthink:526983414226747393>
that's really weird then if so
like i know it's correct, but 1/a just feels more right
mild kernel
if you are just working with a big product
its nice to have everything on the same line
not a bunch of weird split up little pieces
barren imp
Fair
mild kernel
@barren imp got your question figured out?
rocky lotusBOT
jan Niku
mild kernel
but, you can just distribute here, youll get the same answer
barren imp
Uhhhh
fleet burrow
its called difference of square
sum? 
mild kernel
we get $\qty( \sqrt 7 )^2 - i \sqrt 7 + i \sqrt 7 - i^2$
rocky lotusBOT
jan Niku
mild kernel
_sum_? <:bleak:877093280905592842>
sum of difference of squares
the alliteration is so nice
barren imp
I guess
barren imp
Ok so simpied is it /7 ² -i²
mild kernel
yea
mild kernel
👀
barren imp
Is 6
mild kernel
7 minus negative 1
barren imp
But wair-
mild kernel
what is minus a negative
barren imp
It turns to positive
mild kernel
yea
barren imp
8
mild kernel
so seven plus one
mild kernel
you have a calculator?
barren imp
Yee
mild kernel
i mean genuine question
it has i and stuff
you might consider using it to check yourself
barren imp
I only have a science one
mild kernel
get comfortable using it with the parentheses and everything
science one works, it should have i
you got 8 which is the right answer
see if you can get 8 using your calculator
barren imp
Ok what do I do about i⁶¹
mild kernel
then you'll know how to type i on your calculator
mild kernel
you can use it to check yourself on this
marble arch
I can help you with this
barren imp
Thank yoy
barren imp
Ok
marble arch
because after every 4th power, it just repeats
i^5 = i
i^2 = i^6
i^3 = i^7
i^4 = i^8
then again
i^9 = i
and so on
barren imp
Wait really?
marble arch
because you see
i^4 is just 1
so i^5 is really 1*i
and i^6 is just 1*i^2
So look for multiples of 4 in power
like i^100 is just i^(4*25)
or 1^25
or just 1
mild kernel
its not supported 
marble arch
you get this?
mild kernel
you should get a ti 36x pro
barren imp
I see so then...
marble arch
okay so your first step is to look for the multiple of 4 before your power
barren imp
For 61 it would be...15 i?
marble arch
In 61, what is the multiple of 4 just before it?
marble arch
For 61 it would be...15 i?
no no, for now just look for the number divisible by 4
barren imp
60 is divisable by 4
marble arch
Nice!
barren imp
But 61 is not
marble arch
Okay so can we write i^61 as i*i^60?
barren imp
So what happens to the 60? Does it not turn to 15i
+i
Or does it completely cancle in the first place
Leaving just- i
marble arch
No no, it won't be like that
barren imp
Oh
marble arch
You'll see
marble arch
Okay so can we write i^61 as i*i^60?
Okay tell me this
barren imp
Its i×i?
barren imp
you should get a ti 36x pro <:catthink:526983414226747393>
Maybe so other time
barren imp
Sooo... 1+i?
barren imp
So it is just i
marble arch
Yes, do you get the process?
barren imp
I get it so i⁶⁰ =1
marble arch
Yes
barren imp
Which crosses it out leaving the remaining i?
barren imp
Ok so then i⁴⁷ makes... (1) and i⁷:?
marble arch
Well tried, you see you gotta look for the multiple JUST before your power, so it'd be 44, and not 40
you get it?
marble arch
Exactly
And we know that i^3 is just -i
Okay so tell me, what would be the value of i^155?
vale dockBOT
@barren imp Has your question been resolved?
barren imp
Okay so tell me, what would be the value of i^155?
So that makes -1?
marble arch
Well it'd be i^3, did you mean -i?
vale dockBOT
barren imp
.reopen
vale dockBOT
✅ Original question: #help-4 message
barren imp
Well it'd be i^3, did you mean -i?
Oh well- 154 > 152 +2
marble arch
Ahhh well I asked i^155, not 154
vale dockBOT
@barren imp Has your question been resolved?
barren imp
Sorry I lost wifi
This isnt on my stuff but What do we do if just its something like i‐⁵⁷
Imagine thats a -56
marble arch
i^(-57) right?
barren imp
Yes
marble arch
okay, just make it 1/i^(57) and do it normally
barren imp
I see so its...1/i?
vale dockBOT
marble arch
Yes
barren imp
.reopen
vale dockBOT
✅ Original question: #help-4 message
barren imp
Ok
honest stone
I see so its...1/i?
1/𝑖 = -𝑖 btw.
honest stone
Prolly cuz -𝑖 × 𝑖 = 1
robust wolf
1 = i⁴
honest stone
$-i \times i = -i^2=-(-1)=1$
rocky lotusBOT
𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³
