yea, im sorry
#help-13
violet flume
lunar lynx
Because i ruled out that it can't be a cube.
violet flume
but looking at your initial prompt made me even more doubtful. suprised youve come this far 
lunar lynx
yea, im sorry
No. I still learned that.
muted bear
Because i ruled out that it can't be a cube.
Why not a square prism?
lunar lynx
6a^2 = a^3 is only possible for 6 or 0. Both don't work.
muted bear
Ah ok
lunar lynx
Why not a square prism?
Umm... I didn't think of that. Give me a moment.
I can't seem to rule that out so far.
Maybe, i should consider that as well.
muted bear
$8x^3-cx^2+cx-c$ seems promising
wraith daggerBOT
GarlicB
muted bear
Tbh i thought it was cool that you used algebra
Did not think about that
But im still considering a geometric argument
muted bear
**GarlicB**
This is (2x-a)(2x-b)(2x-c) btw
lunar lynx
**GarlicB**
Is this for a square prism?
muted bear
Its for any cuboid
lunar lynx
a, b, c are sides of cuboid?
lunar lynx
I'm sorry. I'm kinda failing to see it.
Won't this have roots as (a/2, b/2, c/2) ? Are we trying to do that if those exist, there double would exist as well?
muted bear
We know that the roots for polynomial (x-a)(x-b)(x-c) and (2x-a)(2x-b)(2x-c) have the same sign
lunar lynx
Ah. Yes
muted bear
Which should be sufficient enough for the argument if ee find their signs are not all positive
Wait ok lemme try this
wlog a<=b<=c
lunar lynx
is that lambert w?
lunar lynx
Oh yes. Lol
muted bear
Not product log lol
lunar lynx
wlog means without loss of generality
I know. I just missed it there somehow.
muted bear
Ah ok
I tried bounding but i dont think it works
lets say abc=d
V=S=P=d
V+S+P+8=3d+8
V+S/2+P/4+1=7/4(d)+1
Wait im onto something maybe
No im not, its very easy to be circular here
lunar lynx
Umm... I have to go for lunch now. I hope it's fine. I'll be back in 25-30 minutes.
lunar lynx
Cool. I'll be trying to think on problem as well.
muted bear
8V+4S+2P=14d+8
7V+3S+P=11d
Ooh we do S/V, we get 1=1/a+1/b+1/c
Still using the wlog, we have a<=3
3 doesnt work
So a<3
have to find a way to include P
Ok lets try this
a+b+c=d
a^2+b^2+c^2=d^2-3d
a^3+b^3+c^3=d^3-6d-3(ab^2+...+bc^2)
Nah that wont work either
It just might actually
Ok ive got nothing sorry
cedar kilnBOT
@lunar lynx Has your question been resolved?
lunar lynx
Ok ive got nothing sorry
Thanks still.
snow bridge
If I have the function y=sqrt(x) and I’m proving whether the limit exists as x —> 0 using the epsilon-delta proof, how can I prove it doesn’t exist because I can certainly find an interval for every epsilon>0 such that if 0<|x|<delta then |sqrt(x)|<epsilon
snow bridge
More generally how does the epsilon-delta definition of limits account for the limit needing to be defined from both sides
And what about a function like f: Z —> Z, f(x)=0 (because I can interval 0<|x-a|<delta for every a and every epsilon>0 that works therefore is the limit everywhere 0?)
And what about something like this?
<@&286206848099549185>
Hi
Pls help me
It’s above
Yay 😀
Even more above
Check pinned messages
I thought that in order for a limit to be defined it had to exist from both sides
Really wow
Okay so then if you see the piece wise function I drew on the bottom of my original message, can you tell me whether the limit is defined at 0?
I can resend it if you can’t find it
Does the limit exist at 0?
Why not?
Btw the lines both touch the x axis
snow bridge
Yeah but using the epsilon-delta definition say that the x-ints are a and -a, then I can certainly find a delta for each epsilon>0 such that for all x in the domain of the function I drew, if 0<|x|<delta then |f(x)|<epsilon
I’ll just choose a delta that is really close to a and then it will be true
For any epsilon
upper ruin
Limits exist only for accumulation points, whereas from your drawing it looks like the origin is an isolated point
snow bridge
In your opinion does the function f: Z —> Z, f(x)=0 have a limit of zero at every x in the function or does the limit never exist
upper ruin
Ahn you were talking about sequences sorry
snow bridge
I’m probably not talking about sequences 😅 I haven’t learnt them in uni yet
upper ruin
If an f has Z or N as domain it's called a sequence, which have different behaviours for limits
snow bridge
I have an assignment about limits using the epsilon delta definition and there’s a continuous point at x=0, I’m trying to understand whether it is therefore required that there be a continuous interval in f including 0
upper ruin
If an f has Z or N as domain it's called a sequence, which have different behavi...
In particular, it makes sense only the limit as x -> +∞ for a sequence, since infinity is the only accumulation points
upper ruin
I have an assignment about limits using the epsilon delta definition and there’s...
Wdym with continuous point?
snow bridge
So these are the definitions we’ve learnt: limit L exists if epsilon-delta proof. a point x=a is continuous if the limit exists and the limit is f(a)
Those are our definitions
And using these definitions only I want to understand if the functions I’m describing have a defined limit or not
upper ruin
A point can't be continuous, I've never read nor heard this. Very weird, maybe your teacher has a definition I don't know
snow bridge
He has never explicitly stated that a point can’t be continuous but using this definition only I am lead to believe that it is possible
Because under this definition the limit at a point can be defined under certain circumstances such as the ones I have outlined above
I think
upper ruin
Ok, I get it now. The problem, as I said above, is that limits are defined only at accumulation points, which by definition means that every neighborhood if it contains at least one point of the domain different from the point you are calculating the limit at
upper ruin
https://www.youtube.com/watch?v=9D-ZlJUnNZM
I think this video helps
cedar kilnBOT
Available help channel!
tawdry mesa
(3-x)^2.x + (x-3)^2
cedar kilnBOT
(3-x)^2.x + (x-3)^2
tawdry mesa
factorizing
if i have to use the identity, how will i get rid of that x?
to get a^2-b^2
oh no its plus not minus, so idk what to use
low grove
hint: (3-x) = -(x-3)
tawdry mesa
so -(x-3)^2.x + (x-3)^2 if we change the places its (x-3)^2 -(x-3)^2.x and now we have to get rid of that x right?
low grove
both terms have a common factor
also (-(x-3))^2 = (-1)^2 (x-3)^2
and (-1)^2 = 1, not -1
tawdry mesa
so the answer is (x-3)^2 and (x-3)^2?
low grove
how did you get that?
we have $(3-x)^2 x+ (x-3)^2 = (x-3)^2 x+ (x-3)^2$. Now notice how $(x-3)^2$ appears in both terms
tawdry mesa
also (-(x-3))^2 = (-1)^2 (x-3)^2
by this and the problem
wraith daggerBOT
Toblerone
low grove
yes
tawdry mesa
is it solved then?
low grove
yes, that should be the answer
fringe moss
hello can anyone help me about this math
cedar kilnBOT
hello can anyone help me about this math
fringe moss
i get that in domain u need to get x
and in range u need to get y
i dont get when to use the
(x,x]
[x,x)
(x,x)
tawdry mesa
i don't know this stuff, but since you're not getting help, search a short 5 min vid or less in yt
in 8min ping @ helpers
primal lodge
(x,x]
[x,x)
(x,x)
[] means include the point
() means exclusive (u wouldn't include the point)
so basically for domain, you search for x values that gives you a defined value
fringe moss
so when should include the point
primal lodge
in your case, all x values from -3 to 2 gives you defined values
fringe moss
when its shaded?
primal lodge
when its shaded?
what value do you have when x = -3?
primal lodge
when its shaded?
yes
fringe moss
-4
fringe moss
2?
primal lodge
well that's not true
if it was shaded then yes
unshaded means that point is undefined
so we don't really know
static stirrup
and then the ] bracket at the range means the 5 value is included because we can see the value
static stirrup
and range is equal to y
ye u know ur range and domain gj
also know ur brackets
if the circle is shaded it means included, not shaded the not included so []
make sense?
fringe moss
okayy wait imma try a diff set of question
cedar kilnBOT
static stirrup
allg
buoyant latch
cedar kilnBOT
@crimson sedge Has your question been resolved?
sage rock
nvm im tweaking
cedar kilnBOT
sage rock
.close
cedar kilnBOT
Available help channel!
slim ice
cedar kilnBOT
slim ice
This is my question
tidal kernel
A classic!
slim ice
I've been trying to find the answer - but I don't know what the best possible steps are
tidal kernel
..or a variation
slim ice
Yes
tidal kernel
Yes
Have you figured it out?
We want to just race all the horses first because we can't race any horse for the second time without racing it once and gain any information if there still exist unraced horses.
We look for the fastest 3, so at each race we can eliminate two horses
So we had 5 races, leaving us with the order of the three fastest in each race
We then race the fastest horses from each previous race in the 6th race. We had 15 horses; this eliminates a further 6, since the 4 horses in the races with the two horses that came last in the 6th race can't be in the top 3.
We're left with 9 horses. Let's call them
a b c
d e f
g h i
where in the 6th race a was faster than d and d was faster than g (and a is faster than b, which is faster than c. etc). Now a, b, g are all faster than h, i, so h and i can be eliminated. a, d and e are all faster than f, so f can be eliminated. Finally we just need to race b c d e g to determine the top 2, since we know a is the fastest.
This takes 7 races. I think that's the best you can do
slim ice
We're left with 9 horses. Let's call them
a b c
d e f
g h i
where in the 6th ra...
Ohhhh that makes sense
Thanks
.close
brisk ferry
I understand that one of the definitions for identifying an inflection point is the point where the concavity changes, but the other definition for identifying an inflection point is that the second derivative equals zero. The graph f(x) or F prime in the image has undefined derivatives at x=0 and x=6 ( essentially F has undefined second derivatives at x=6 and x=0 ). So, why are x=6 and x=0 considered to be point of inflections when they don't have second derivatives equalling to zero at those points?
cedar kilnBOT
I understand that one of the definitions for identifying an inflection point is ...
@brisk ferry Has your question been resolved?
brisk ferry
<@&286206848099549185>
high coyote
The definition is the point where the curvature ("concavity") changes
What happens is that if the function is twice derivable at a point p and p its an inflection point then f''(p)=0
So the concept is the same only when the function is twice derivable at the point
Do you understand?
cedar kilnBOT
@brisk ferry Has your question been resolved?
eternal knot
why is this -1.2t?
cedar kilnBOT
why is this -1.2t?
wanton grove
have you tried simplifying the numerator
glass sky
show your work , what are you getting
unique isle
"what is the volume of this prism?"
cedar kilnBOT
"what is the volume of this prism?"
livid hound
what exacly are you multiplying
unique isle
length time width times height
livid hound
what numbers are you multiplying
unique isle
3* 3* 6.97
livid hound
the issue is that this isn't a rectangular prism
unique isle
oh
livid hound
the side with length 6.97 isn't the relative altititde to the base of 3
the actual altitude is indicated by that 4 near the bot right (with that right angle)
livid hound
well its a standard prism, so the more general formula
V = Bh
is applicable
(where B is the area of the base)
which here is a paralleleogram
livid hound
why are you still using the 6.97 despite me saying that isn't the relative altitude/hieght
livid hound
where's 20.91 cioming from
did you do something like 3*3.67?
forget about the 6.97
unique isle
i dont even know
livid hound
like just scribble it out, it is irrelevant to whats being asked
earnest verge
could someone pls tell me what they did here
cedar kilnBOT
could someone pls tell me what they did here
junior dome
divide the numerator and denominator by e^x
crimson sedge
multiplied by e^-x/e^-x
junior dome
or this ^^
earnest verge
but how can e^x + 1 * e^-x be 1+e^-x
crimson sedge
$e^{-x} e^x = e^{x + (-x)} = e^{0} = 1$
wraith daggerBOT
Renegade
earnest verge
ohhh okay okay that makes sense
may I ask, is this some kind of universal rules for integration?
I never get the thought to use those methods to solve the tasks
stiff totem
this isn't anything to do with the integral (as in, the manipulation with e isn't inherently tied to integration)
it's just rearranging the fraction
earnest verge
they continued like this
stiff totem
I never get the thought to use those methods to solve the tasks
as for this, it's just exposure -- just do more problems and you'll get used to spotting the patterns
earnest verge
junior dome
you dont need to convert into e^-x, but it is the faster way than just u-sub
stiff totem
the derivative of 1+e^{-x} has a - out front because of chain rule
so when you reverse chain rule it needs a minus back in
lemme write it out a bit more clearly
earnest verge
you dont need to convert into e^-x, but it is the faster way than just u-sub
I tried u sub but I just get complete bullshit
stiff totem
\begin{align*}
\int\frac{e^{-x}}{1+e^{-x}},dx&=-\int\frac{-e^{-x}}{1+e^{-x}},dx\
&=-[\ln(1+e^{-x})]
\end{align*}
wraith daggerBOT
Desync
stiff totem
it's only properly in the "top derivative of bottom" form with the minus there
earnest verge
but there wasnt a -e to begin with on top, or?
stiff totem
there's a minus in front of the integral as well after rearrangeing
junior dome
I tried u sub but I just get complete bullshit
you need to know partial fraction decomposition for that
earnest verge
there's a minus in front of the integral as well after rearrangeing
how? with the reverse rule there should be just ln(f(x))
stiff totem
\begin{align*}
\int\frac{e^{-x}}{1+e^{-x}},dx&=\textcolor{green}{-}\int\frac{\textcolor{green}{-}e^{-x}}{1+e^{-x}},dx\
&=-\int\frac{\frac{d}{dx}(1+e^{-x})}{1+e^{-x}}\
&=-[\ln(1+e^{-x})]
\end{align*}
wraith daggerBOT
Desync
stiff totem
what is the derivative of 1+e^(-x)
earnest verge
e^-x?
stiff totem
no
glass sky
-e?
stiff totem
-e^(-x)
stiff totem
so when you do reverse chain rule, you need the minus on top
but we can't just add one in
we need to cancel it back out outside the integral
earnest verge
you are literally the genius
all of you
😭
thank you so so much
I will take a moment to write this down before I close the channel
.close
lofty geyser
so I have this Hasse diagram
cedar kilnBOT
so I have this Hasse diagram
lofty geyser
and I want to write down all the antichains and their elements (I really just want to be able to draw the diagram for the downsets)
So I had
I will show the element and then its corresponding downset
b - b,a,c
a - a
d - d,c
c - c
b,d - b,a,d,c
a,d - d,a,c
a,c - a,c
Is that correct and should I be adding the empty set?
by elements i mean the antichains, for clarity
When i drew my hasse driagram i did get the principle downsets, but I'm unsure if this is correct still
I just realised that i need to include the empty set as one of the anticains
So, as a final note, I know I have the correct number of downsets, namely 8, but I just want clarification on my Hasse diagram, just to be extra sure.
sorry for the paint....
cedar kilnBOT
@lofty geyser Has your question been resolved?
cedar kilnBOT
@lofty geyser Has your question been resolved?
south tundra
What's your question?
No need to expand (x - 3)^2, there is only one obvious root to it
Yeah, for the rest you can just use the quadratic formula
upper ruin
$$a(x) \cdot b(x) = 0 \iff a(x) = 0 \vee b(x) = 0$$ (btw this doesn't work for all structures, but for things you've encountered now so far probably yes
wraith daggerBOT
Alberto Z.
wraith daggerBOT
Alberto Z.
upper ruin
If that's what you don't understand
remote creek
what is your math problem?
upper ruin
**Alberto Z.**
Can you identify the a(x) and b(x) I wrote here in your f(x)? @crimson sedge
Yes, not x = 0
upper ruin
**Alberto Z.**
No, the a(x) and b(x) I wrote here!
upper ruin
No, the a(x) and b(x) I wrote here!
If I write a*(x)*** and b*(x)*** it means they are functions of x, not coefficients
remote creek
the first factor (x - 3)² will be equal to zero when x - 3 = 0 so x = 3
upper ruin
What is your f(x)?
upper ruin
the first factor (x - 3)² will be equal to zero when x - 3 = 0 so x = 3
!nosols
cedar kilnBOT
the first factor (x - 3)² will be equal to zero when x - 3 = 0 so x = 3
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
upper ruin
So a(x) = (x - 3)² ...
And b(x) = 3x² + 7x + 5
I thought my question was trivial, but maybe it was not actually
I'm sorry for that
Either (x - 3)² = 0 or 3x² + 7x + 5 = 0
Yep
I don't know what synthetic division is, in my language I've never heard it to solve equations
Maybe someone here knows that and can help you
cedar kilnBOT
ocean garden
For y'= 3y + e^6t
I don't understand why is it
C' • e^3t + C • e^3t
in the left side
.close
stark quest
<@&268886789983436800>
stiff totem
<@&268886789983436800>
slim hearth
👍
stiff totem
.close
plain holly
how?
plain holly
how did we infer that from the question
i am very sleep deprived so that could be why i am not getting it
mind telling me something obvious i am missing
austere hull
how did we infer that from the question
wdym infer?
plain holly
yes i can see that
i am not sure how did that we know statement is valid
<@&286206848099549185>
stiff totem
how you know what statement is valid?
that lim x-> -2 x^2 is 4?
just plug in -2 into x^2
plain holly
just plug in -2 into x^2
gives lim f(-2)/4=1
plain holly
um
plain holly
no my question was how did this come from the question
stiff totem
we're given f(x)/x^2 and we want to isolate f(x), so we want to multiply both sides of the equation by x^2
before we do this, we need to make sure the limit of x^2 is well-defined at -2
so it's being checked there
plain holly
i understand the steps
i just done get the where is that coming from?
why is that 4? also i am lost as you write it the limits in text 😭
oh so that x^2 is the function here
fml i am need of sleep
.close
cedar kilnBOT
austere hull
sleep well
cedar kilnBOT
Available help channel!
potent sentinel
hello, dumb question but ion understand what this is asking, like do I js multiply 1/5 and 2/3?
potent sentinel
or add them
potent sentinel
yea
but what numbers do i multiply
cus its says in any order for black and red
granite ether
so you can have to do both possibilities for red and black
granite ether
yeah
granite ether
sure
potent sentinel
i asked this question on another channel but i didnt get it
so like do i add 4 to x then move down 5 for y
using the coordinates on the table?
actually
js ignore the question
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
shrewd reef
cedar kilnBOT
https://gyazo.com/2d512e4d4d44a6130260664fa6bb253f
shrewd reef
I don't know where to start with this question
deep oriole
try a u substitution
shrewd reef
that's what im trying to do
deep oriole
what sub did you use?
shrewd reef
would I use 1+1/t as u since it's the higher degree?
deep oriole
yeah
deep oriole
thats a good u sub
shrewd reef
i just checked and got the right answer
thank you
looks like i messed up the first time cuz I u subbed with 1/t^2 lol
.close
cosmic steppe
Like is there a better way
cedar kilnBOT
Like is there a better way
cosmic steppe
What the fuck
Dude college wifi sucks
It's sending
So my professor's in Japan and gave me no access to Mathematica or whatever so I've had to teach myself the beginning of ODEs
How the fuck do I do this without guessing
obsidian coral
Dude college wifi sucks
Yes
Get gig speed, my internet is like 700 mbs up and down
cosmic steppe
Heh
Well anyways help bevause like
Is there a nice Euler method error bound thing
obsidian coral
I don't know euler's method like that, maybe riemann or layla or hayley would know better
cosmic steppe
I'm just gonna leave this open then but I guess I'm testing each h value
Wait
Wait I can't do this manually what the fuck what if h needs to be 0.00003
That's gonna mean I have to manually click my stupid TI-84 300000 times
upper abyss
There's probably graphing software that can do it
Excel is actually pretty good at this too
cosmic steppe
I'm just gonna skip this then
So much for getting ahead on homework
Idk how to use excel
I really wanna use Mathematica but waaaah
runic garnet
Pro tip: Learn excel
upper abyss
Actually though Excel is bae and easy
I'm pretty sure even winplot can do a Euler method curve
obsidian coral
Pro tip: Learn excel
Pro tip learn vba
upper abyss
Know any programming languages? This is a nice programming practice problem
obsidian coral
Know any programming languages? This is a nice programming practice problem
Vba \s
upper abyss
If I was home I'd do this but I am not home so I cannot do this
slate lintel
javascript in the console 
untested code whee
y = 0.0;
x = 0.0;
d = 0.01; // step size
while (x < 1.0) {
y += (1 + x^2) * d; // derivative
x += d; // step size
}
console.log(y)
@cosmic steppe Has your question been resolved?
grand totem
it's mentioned that to calculate the rank of a rectangular matrix
I can take any subset of the matrix and calculate its determinant
but... what if a subset results in its determinant equaling 0 while the other subset results in a determinant equaling more or less than 0
flint plinth
yea i don't think that's true.. for example, consider this matrix:
$$\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 & 0 & 0 \ 0 & 0 & 1 & 0 & 0 & 0 \end{pmatrix}$$
wraith daggerBOT
Bungo
flint plinth
its rank is 3
if you took the submatrix consisting of the 1st 3 columns, the determinant is 1
if you took the submatrix consisting of the last 3 columns, the determinant is 0
now if you tried every 3x3 submatrix
and at least one of them had nonzero determinant, then you would know that the rank is 3
but even then, suppose i have the same matrix but replace the 3rd column with zeros
then all of the 3x3 submatrices will have determinant zero
that won't tell you that the rank is 2
you'd have to take all square submatrices of any size
cedar kilnBOT
@grand totem Has your question been resolved?
obtuse hinge
can someone double check my work
cedar kilnBOT
can someone double check my work
flint plinth
this is fine
i might suggest adding a line at the start that says that |f| = |g| implies that at each point x, either f(x) = g(x) or f(x) = -g(x).. of course you know this and use it in the proof, but if this is being graded, it's good to state it for the record
also, minor, "f is continuous", not "f(x) is continuous"
obtuse hinge
i might suggest adding a line at the start that says that |f| = |g| implies that...
i see thanks!
.close
haughty wadi
i started on some of the work, im just having trouble on this problem as of right now. i don’t know how to work “backwards” (i don’t think this is working backwards but as soon as it got easy for me it got hard)
regal oak
So you're basically trying to solve 3x+13=6x-2?
Converting this equation into the form 0=(something) might help
exotic furnace
i’d suggest to just solve for x lol, it’s linear anyway
cedar kilnBOT
@haughty wadi Has your question been resolved?
pastel temple
How to find range
cedar kilnBOT
How to find range
pastel temple
ok so basically I know how to do range and domain all that stuff
but my friend doesn't
I am really horrible at teaching people stuff
pastel temple
How to find range
Please just explain on how to find Range
he knows its y but doesnt know how to the (x, y)
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
shrewd crag
c)
shrewd crag
I know the turning point is (1/2, -25/4)
shrewd crag
ye ye
vestal bear
but theres also an a out front
for stretch factor
you can find that by plugging in a random point on the parabola
so y=a(x-h)^2+k where h and k are the coordinates of the turning point and x and y are an ordered pair on the parabola that isnt the vertex
vestal bear
yeah but write the rest
cedar kilnBOT
vestal bear
it is y=(x-1/2)^2-25/4
did you find the stretch factor
shrewd crag
.reopen
cedar kilnBOT
✅
dim tiger
hello everyone
cedar kilnBOT
hello everyone
dim tiger
how did he define the function to be always bijective in the first place and how did he continue to say that its not necessary to be bijective
solar vector
how did he define the function to be always bijective in the first place and how...
What do you mean?
The "for each x in X, there is one and only one y in Y" bit only guarantees no element of the domain can map to two things if that's what you mean.
solar vector
No it guarantees every element of the domain has a unique image.
You can have something like x mapping to y and x' also mapping to y.
dim tiger
oh wait i messed some things up
solar vector
Given x in the domain, the image y is unique, but two distinct x's can map to the same thing
dim tiger
yea you are right i was mistaken
solar vector
It's good to be aware of this stuff. Adding the injectivity and surjectivity requirements to this gives you a bijection but this is the bare minimum to just be a function.
dim tiger
yes ik but i messed up between each y has one and only one x and each x has one and only one y
tysm for your time and sorry for the stupid question XD
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cedar kilnBOT
dim tiger
.reopen
cedar kilnBOT
✅
solar vector
Was just gonna say no worries, it's not stupid, it's a subtle and important distinction.
Good luck!
wicked sphinx
So my math problem says
cedar kilnBOT
So my math problem says
wicked sphinx
-1 + 2x + 3x^-1 is not a polynomial
But isn’t 2x -1 already a polynomial?
Im so lost
Ooh
Nvm
The denomenator
Lol
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rotund vigil
Are these right ?
cedar kilnBOT
Are these right ?
fossil osprey
All good
cedar kilnBOT
@rotund vigil Has your question been resolved?
lament kelp
Question.. how is -(x-b)(x-2) = (x-b)(2-x)
cedar kilnBOT
Question.. how is -(x-b)(x-2) = (x-b)(2-x)
lament kelp
Should it not also change (x-b)
vague rapids
Should it not also change (x-b)
why do you think so?
small mist
Should it not also change (x-b)
either way is fine it's better to change the one with the constant though
small mist
it's just in practice it's better to have expressions with only variables unchanged
you can have (-x+b)(2-x) if that's your question
lament kelp
But here infront me we changed the variable
small mist
multiplication is associative
hollow lintel
either way is fine it's better to change the one with the constant though
yeah once you start doing harder factorising just use this habit
small mist
right
small mist
symmetry and constraint for example is where you would like to have similar looking expression
small mist
I was meant to factorise it
yea so it doesn't matter how you do it here
they're equivalent expressions
in any case
lament kelp
-ab
hollow lintel
what is -a * - b equal to
lament kelp
Ab
hollow lintel
alr
hollow lintel
correct
if there is one minus, you can only apply it to one variable, or bracket
two minuses create a plus
thus, -(x-b)(x-2) = -x^2 +2x + bx - 2b = (x-b)(2-x)
hollow lintel
-x^2 +2x + bx -2b = 2(x-b) - x(x-b)
hollow lintel
Why is it possible to only change 1 bracket and not 2
there is only 1 minus
grand totem
you'd have to take all square submatrices of any size
Oh dear, thanks
lament kelp
there is only 1 minus
Hmm
lament kelp
Isn’t it better to solve the brackets first and then multiply -1
hollow lintel
ie. -(8 * 9) = 8 * -9 = -8 * 9
lament kelp
If the brackets were a variable on their own
hollow lintel
yes?
lament kelp
ie. -(8 * 9) = 8 * -9 = -8 * 9
What
hollow lintel
is that correct
it is
just like brackets
the minus can go on any bracket/variable
lament kelp
That don’t make sense
hollow lintel
but only 1
hollow lintel
That don’t make sense
explain to me how
lament kelp
We have to do 8*9 first?
hollow lintel
no no im using an example
hollow lintel
what does this mean
lament kelp
Multiplication?
hollow lintel
@tropic oxide can you explain this question to @lament kelp i dont think they understand this well
lament kelp
- this thing gets rid of
hollow lintel
-1 = - in front of anything
lament kelp
No I understand
hollow lintel
all good then
lament kelp
But hold on
(X+b)(x+b)
This is xx + xb and so on
And if had -1(..) infront 1 bracket
lament kelp
(X+b)(x+b)
Shouldn’t I wait until I solved this
hollow lintel
you can
lament kelp
They will have the same answer?
hollow lintel
but minus in one bracket and minus in two brackets
hollow lintel
They will have the same answer?
no
if 1 minus, then it will have the negative complement
lament kelp
Ah ok
cedar kilnBOT
cedar kilnBOT
Available help channel!
eager wyvern
cedar kilnBOT
eager wyvern
how to solve for x?
versed fulcrum
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
versed fulcrum
However, but do log both sides first
versed fulcrum
Base doesn't matter here
eager wyvern
Do it for the other side likewise
i dont understand what it means to "take logs " ive heard it multiple times but non of the textbooks explain what it is and why i should do it
versed fulcrum
Oh
Alright
Logging both sides is just a similar concept to multiplying the same numbers/variables to each side
If you're adding 1 to both sides
It would still result the same value
For instance, changing the equation of x = y into x + 1 = y + 1
Won't alter the original equation
It's like a varied version of the equation
It's the same for taking the log
By taking the log, you can transform the base or even bring the exponent forward
Taking you a step closer to the solution
eager wyvern
Taking you a step closer to the solution
i see how it could help when you add or multiply but ive taken log and what am i supposed to do?
doesnt seem to bring my any closer i still got unkown on both side
versed fulcrum
$\log_{a}\left(b^{n}\right)=n\log_{a}\left(b\right)$
wraith daggerBOT
LE SSERAFIM
versed fulcrum
Have you learned this yet?
celest ledge
Divide by 4^x on both sides
eager wyvern
Divide by 4^x on both sides
which line
celest ledge
There is only one expression in your picture
4^(x+1)=3^(2x)
Divided by 4^x on both sides of it
eager wyvern
Divided by 4^x on both sides of it
so it will be log 1^1?
celest ledge
$4=(\frac{9}{4})^{x}$
wraith daggerBOT
Cogwheels of the mind
celest ledge
This is what you get
eager wyvern
how is 4 ^X+1 dived by 4^x 9 /4 x
eager wyvern
ok
eager wyvern
3^2x divided by 4^x is (9/4)^x
but what about the logs??
celest ledge
x=log(4)/log(9/4)=log(4)/(log(9)-log(4))=log(2)/(log(3)-log(2))
cedar kilnBOT
@eager wyvern Has your question been resolved?
celest ledge
Seems like you didn’t follow mine
eager wyvern
Seems like you didn’t follow mine
this is adifferent question
celest ledge
Oh I see
That’s not necessary
Remember 4=2^2
So simply
5-x=2(x+3)
(Because t->2^t is injective)
In general, for a question like this, m^(ax+b)=n^(cx+d)
You can always rewrite it as
r^x=s where
r=(n^c)/(m^a)
s=(m^b)/(n^d)
eager wyvern
What did you do after this
celest ledge
Then r and s are given meaning x=log(s)/log(r) for any base u: log_u you want
eager wyvern
R->R mapping t to 2^t is injective
Honestly i have no idea what that means
I heard mapping for engines before tho i dont think that's related😂
celest ledge
You don’t know what injectivity is?
You don’t know what a mapping / map is?
That’s high school stuff
Anyway, for your case
2^p=2^q implies p=q
eager wyvern
That’s high school stuff
I am equivalent of high school junior
celest ledge
a^p=a^q implies p=q for any a
wraith daggerBOT
BrotmitHonig
nimble mulch
For the derivative you can apply the rule for addition/subtraction
May we assume a is constant?
tropic oxide
then show us a screenshot of the problem
any and all uncertainty about what is to be done MUST be dispelled before we can proceed.
molten sage
Find a solution set for each rational equation
cedar kilnBOT
Find a solution set for each rational equation
molten sage
Pls help
crimson sedge
What have you tried
molten sage
Finding the LCM
versed fulcrum
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
molten sage
1
crimson sedge
Finding the LCM
Okay where did that take you
versed fulcrum
Multiply the LCM for the denom
molten sage
I’m not sure if I found the right LCM because I found different answers
crimson sedge
Send your work
molten sage
Sorry for blurry photo I’m in the car
cedar kilnBOT
@molten sage Has your question been resolved?
molten sage
<@&286206848099549185>
spice kraken
now that the denominators are the same you can combine the fractions
molten sage
10x - 18x - 18?
cinder venture
,rccw
wraith daggerBOT
molten sage
Multiplied first fraction by 2x and other fraction by 2x -2
cinder venture
Why didnt you cancel it out?
cinder venture
Not exactly
molten sage
Thank you
I got 10x/18(x-1)
I see online it says = -x(x-1) but I’m not sure how to get there
cinder venture
I got 10x/18(x-1)
You mean - not / yeah?
molten sage
Yes
cinder venture
I see online it says = -x(x-1) but I’m not sure how to get there
Multiply the last fraction by the LCM it will cancel out
molten sage
Would the lcm be 2x(2x -2?
molten sage
I see
molten sage
Multiply the last fraction by the LCM it will cancel out
The last fraction?
cinder venture
-1/4
molten sage
Oo I see thanks. How would you get two answers from this. I see online it says x=3 ,x=6
molten sage
?
cinder venture
Once you have multiplied through and cleared all the fractions
Just collect like terms
And solve
This is what it will look like
After clearing fractions
wraith daggerBOT
𝕏
cinder venture
No problem
cedar kilnBOT
Available help channel!
cedar kilnBOT
versed fulcrum
What do you not understand?
The volume of a sphere is given to you
Cubic meters, miles, kilometers makes the unit of a volume
All you need to do is substitute and change the units
Although the Earth isn't exactly a sphere
vocal laurel
That's the volume of an retangle
versed fulcrum
π is a ratio between the circumference and the diameter(?) I believe
But anyways yeah
r stands for radius here
Why is there a pi in the volume of a retangle?
cedar kilnBOT
@crimson sedge Has your question been resolved?
left valve
When I nest brackets in an equation I start with (), then [] and after that, {}. For ex: {[(5+5)+5]+5}+5
What bracket do I use when I nest further than that?
versed fulcrum
Just any is fine actually
tropic oxide
you can just cycle between (), [] and {}
versed fulcrum
But we normally just use () for all levels of brackets
tropic oxide
the only purpose served by these different bracketing styles is to make it clear which ones match to which
they do not really carry any special meaning besides that @left valve
left valve
they do not really carry any special meaning besides that <@455639170413494272>
in an academic paper, is there a preference?
tropic oxide
i don't think so.
versed fulcrum
Not all at
tropic oxide
i think all the academic papers i personally have seen don't even bother with [] or {} for those purposes
versed fulcrum
Unless you meet a pedagogue
tropic oxide
usually these symbols are reserved for other things like intervals and set notation
or whatever other field-specific stuff might be more needed
versed fulcrum
Is this correct?
lunar lynx
How is s 9?
junior dome
wrong
versed fulcrum
$\frac{-6\pm2\sqrt{6}}{9}$
wraith daggerBOT
LE SSERAFIM
lunar lynx
Also, you are supposed to remove the common factors.
versed fulcrum
Looks like
lunar lynx
Do that as well.
wraith daggerBOT
LE SSERAFIM
lunar lynx
Yeah
cedar kilnBOT
cedar kilnBOT
Available help channel!
eager wyvern
How to put this in terms of ln 3
cedar kilnBOT
How to put this in terms of ln 3
cedar kilnBOT
@eager wyvern Has your question been resolved?
dire geode
.close
crimson sedge
How to solve for n x^n + x^(n-1) + .... x^2 + x^1 = someNumber
crimson sedge
You know what geometric progression is??
Ig its copyrighted so (I took it from Google)
crimson sedge
You know what geometric progression is??
No
In a geometric progression of the form
a + ar + ar² + ar³ + ....+ ar^(n-1)
You get
a ({r^n} - 1)/(r-1)
So if you have like
2 + 4 + 8 + 16 + and so on
Can you see it's like
2 + 2(2) + 2(2)² + 2(2)³ + ....
So here you can use GP formula to find answer
Cuz you see there's a base term appearing in all terms, that is 2
And the term whose powers are being multiplied to the base terms, here 2, is also present
Understood?
Yes
Thank you
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
hot python
cedar kilnBOT
hot python
Shapes
16.76 cone
37.7 cylinder
27 cube
16 Prism rectangle
9 Triangle
33.51 sphere
6 right triangle
13.76 pentagon
is this all right?
glass sky
volume?
glass sky
no like idk how to calc last two
