$(x^2-1)(x^4+x^2+1)$
#help-0
fading nest
buoyant kayak
those are x's now, not u's
ocean sealBOT
Xerral
buoyant kayak
right, and both of those things are factorable as well
oak perch
Why (x^2)^3 not (x^3)^2 at the beginning 😂
fading nest
So difference of squares?
buoyant kayak
yes
buoyant kayak
Why (x^2)^3 not (x^3)^2 at the beginning 😂
hm that probably would've made things a bit easier huh 
would still have to do subs tho lol
fading nest
$(x-1)(x+1)(x^4+x^2+1)$
oak perch
It will be though… those two cubic functions have roots that can be easily spotted by eyes…
fading nest
It will be though… those two cubic functions have roots that can be easily spott...
Wdym?
buoyant kayak
that quartic function doesn't factor to (x^2+1)^2
fading nest
Oh Sorry
ocean sealBOT
Xerral
fading nest
Then how do i proceed
oak perch
…
oak perch
can you observe the root of x^3+1 or x^3-1 …?
Try
fading nest
No
fading nest
Soery gotta go
oak perch
x^3-1=0 also
Funny, you asked and you leave when it’s not solved
||x^6-1=(x^3+1)(x^3-1), x^3+1 has a root -1 so it’s divided by (x+1), so(x^3+1)=(x+1)(1-x+x^2), similarly (x^3-1)=(x-1)(1+x+x^2) since x^3-1 has a root 1 ||
lone heartBOT
@fading nest Has your question been resolved?
signal sable
Is there a way for one to determine the strength of a residual plot with a numerical value
signal sable
And how
lone heartBOT
@signal sable Has your question been resolved?
true eagle
leaden tiger
need help with part ii
lone heartBOT
need help with part ii
leaden tiger
the equation from the first half is
alpine sable
Hello
alpine sable
Question: Greg wants to open an account that is maturing 10,000 while using the initial investment of 8500 over the course of 5 years. assuming he does not do anything what is the interest rate?
so I did 10,000 = 8500e(r)(5)
first divided 8500
so i get 10,000/8500= e(r)(5)
- after this step im lost im not sure what to do from here
alpine sable
where is e?
ocean sealBOT
EndTimes
tight locust
Are you given that it is continuously compounding?
ocean sealBOT
EndTimes
alpine sable
I know but what do I do after having divided this
10,000/8500= e(r)(5)
my main problem
tight locust
Take the logarithm base e
That is how you inverse the exponentiation
Are you familiar with that?
tight locust
Yep
alpine sable
ok
after I did ln I got 0.1625189295
so I divide by 5
then I received 0.0325035
So when I plug this in, by doing 8500e^(0.0325035)(5)
I should get 10,000
i get an answer that isnt 10,000
@tight locust
tight locust
,calc 8500e^(0.0325035*5)
ocean sealBOT
Result:
9999.9857050325
oh
tight locust
Yeah thats just because the decimal representation isn't exact
alpine sable
lone heartBOT
alpine sable
can someone help me with the 2nd last question please
covert agate
can someone help me with the 2nd last question please
you have 2u • du/dx = 2x
then u du = x dx
solemn grove
nvm, i forgot that part,
solemn grove
substitute x dx for u du
and root of u^2 in the denominator
you should get either du or 1 du
i think
alpine sable
sorry but do you have any video recommendation of questions like this?
@solemn grove
alpine sable
you should get either du or 1 du
du isnt the answer
alpine sable
what would g(t) be?
alpine sable
x/sqrt(u^2)?
alpine sable
sorry g(u)
solemn grove
that’s the working
solemn grove
last one?, same substitution stuff?
did they accept du/ 1 du tho?
if not, email your lecturer/professor/ whoever is taking your lesson
solemn grove
yeah
alpine sable
did they accept du/ 1 du tho?
yeah du/1du didnt work
solemn grove
email them
and show your working
i could have made a mistake somewhere, just check for that too
alpine sable
okay all good ty for your help
alpine sable
yeah thats right
alpine sable
du/1 du is the same as du/du right?
steady echo
Oh my b, by that I mean either $$\int du$$ or $$\int 1 du$$
alpine sable
yeah du isnt the answer
ocean sealBOT
Name_me
steady echo
yeah du isnt the answer
Did they tell what the right ans is?
alpine sable
Did they tell what the right ans is?
nah they dont
isnt du=2*x?
because even 2*x is not right
@steady echo
steady echo
Idt du = 2x
We defined u = sqrt(x^2-25), did du/dx which gave us
du/dx = x/sqrt(x^2-25) = x/u
So u du = x dx
We took this into our initial integration, where x dx were together subsituted with u du
The u then simplified with the denominator (which was also u), to leave just 1 inside the integration
steady echo
Yess
brittle sun
Hey fellas, I just started studying fields.
I have this question: 3x^2 - 2x + 1 = 0 over Z(11)
I encountered the square root of 3 in one of my solutions, and I don't know how to translate it into a valid field value.
The question
What does the square root of a natural number equate to in a finite field?
lone heartBOT
Hey fellas, I just started studying fields.
I have this question: `3x^2 - 2x + 1...
@brittle sun Has your question been resolved?
brittle sun
<@&286206848099549185>
glass gale
the root of a number is a number such that when squared it gives that number
aka. the solution to x^2 = 3, which if my math is right are the numbers 5 and 6
brittle sun
aka. the solution to `x^2 = 3`, which if my math is right are the numbers 5 and ...
Ah I see. So in the context of Z11, the square root of 3 is pretty much this:
_^2 = 3
_ = ... 5 and 6, you're right.
Wait. so I need to split this equation into 2 equations, and check what happens for both the values of 5 and 6?
glass gale
6 is actually just -5
and the quadratic formula is already split into two cases where you've got either a plus or a minus in front of the root
brittle sun
and the quadratic formula is already split into two cases where you've got eithe...
Right, so what I found was something amongs the lines of:
(-9 +- 5) / 6
and
(-9 +- 6) / 6
So, 4 cases in total?
glass gale
and if you take into account 6 = -5
(-9 +- 5) / 6 and (-9 +- -5) / 6 are your 4 cases
which you can see are actually just two cases
since the first expression is the same as the second
brittle sun
since the first expression is the same as the second
Oh, so I can use either 5 or 6 and the solution should be identical? It's up to me? That's a little weird.
Oh no, you meant -5 = 6 and -6 = 5
Sorry, I misunderstood you
All clear. Thank you very much
.close
subtle raven
alright im stumped could someone help me please
lone heartBOT
alright im stumped could someone help me please
subtle raven
do I multiply by g on both sides first?
nevermind i got it wrong
this one
no clue either
how do I know where to start here?
glass gale
are all other letters constants?
subtle raven
the problem doesn't specify but we can assume that I think
it just wants me to single out h
glass gale
so just rearrange the equation such that h is on one side and everything else is on the other
glass gale
alright im stumped could someone help me please
here I'd multiply by 3+h both sides, then divide by F both sides, and subtract 3 from both sides
subtle raven
here I'd multiply by 3+h both sides, then divide by F both sides, and subtract 3...
thats what the explanation told me
i just dont see it
it's the first time I see a problem with 4 variables so it's kind of weird but i get the idea
glass gale
in reality you'd have to be careful for 0s in each of those multiplication and division steps, but here they just want the final equation so you can ignore all of that
glass gale
thats what the explanation told me
i just dont see it
it's the first time I se...
it's not 4 variables, it's 1 variable and 3 constants
subtle raven
right
glass gale
treat all other letters as if you know what they are
and you are just trying to find h
subtle raven
so on that second one I multiply by (h-f) on both sides first
correct
or can i just multiply the whole denominator at once
glass gale
so on that second one I multiply by (h-f) on both sides first
yep
if you have trouble imagining the problem try replacing all other letters with numbers
glass gale
good job
subtle raven
i've gotta do one more but it seems tricky
hold on
i'll try doing it myself
I got d= (b+4-ac)/a
glass gale
yep
loud grove
Yes but usually you can just leave it in one fraction
subtle raven
jesus christ that was stressful
thanks yall!
that saved a lot of headaches
.close
lone heartBOT
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lament cloak
can anyone help me with differential queatin
lone heartBOT
can anyone help me with differential queatin
lament cloak
abbout logistic growth
the place has an ability to host 10 000 animals
B = 10 000
The constant is
k = 0.0001
you can set a differential equtation equal to N' = k * N * (B-N)
but do you know what to do if 1000 animals are shot each year
somber escarp
just put -1000?
lament cloak
and N(0) = 2000
you cant do that
you need to find the new limit to the differntial equation
if x new animals are born each year, but 1000 is shot each year
fewer animals will get born
somber escarp
yes but the shots are constant so your new n+1 = n*k*(b-n) - 1000
somber escarp
yes i do, i folow civil engineering
lament cloak
i am 99% sure its wrong
somber escarp
but you could always try it yourself in geogebra
lament cloak
so the new limit will then be 9000
instead of B = 10 000
can you ask someone else
i am pretty sure thats wrong
somber escarp
no, the limit is not that, its a next cycle, in order to find the limit you must solve the eqation firsst
lament cloak
ohh
somber escarp
ye
lament cloak
dude
ur fcking amazing
i am having a math test currently
will be getting 100% because of that!!
Dj amparo the legend
somber escarp
haha yw!
lone heartBOT
@lament cloak Has your question been resolved?
harsh ocean
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harsh ocean
I need to know if this is correctly proven
I already sent this recently, but had no response in the matter
lone heartBOT
@harsh ocean Has your question been resolved?
glass gale
I think the problem is step 2
while that limit is indeed 0, the infinite product also contains infinitely many of the other terms that each approach 2, which multiply together to give something approaching infinity
so the mistake in step 2 is that it's assuming infinity*0 = 0
instead you'd have to solve a limit of the whole expression as n goes to infinity, and since at every step the expression is just x^a-b, the limit will also be x^a-b
@harsh ocean is everything clear now
lone heartBOT
@harsh ocean Has your question been resolved?
feral bridge
Hello, I have a latex band that I need to find the approximate weight and size of once rolled. This is not for any school assignment.
The band is 4 inches wide, 9 feet long, and 0.5 mm thick.
I calculated a volume of ~8.5 inches. However how can I find the approximate size of it rolled up? We would have to guess the diameter of the inner role, I assume its very small due to the thickness and material.
drifting hull
i would assume that there is no inner role (or it has diameter 0)
feral bridge
Correct, let's assume it has an inner diameter of 0.
So the width is easy, that won't change. 4 inches.
However how can I find the height and width
dim oasis
If you roll it into an approximate cylinder, the height of the cylinder is the width of the band
feral bridge
Why would that be the case?
The width is going to be a static 4 inches.
The height is going to change due to the length and thickness
dim oasis
Maybe I'm not visualizing the problem correctly then
I'm not entirely sure what this latex band looks like or what rolling it entails
feral bridge
Similar to a rubber workout band. 4 inches wide. 0.5 mm thick. 9 feet long.
How can I calculate how tall it will be once rolled
dim oasis
And if you roll it like this, the height wouldn't be its width?
feral bridge
Ok, so in that orientation, the height is a static 4 inches, always will be. The width is going to change based on length and material thickness
dim oasis
Correct
feral bridge
So how do I find out what that width will be.
I have the length the material thickness and can guess the inner diameter
dim oasis
That's the part I'm trying to work out rn but I love this problem
feral bridge
I can find lots of information of how to calculate the the length based on a roll. However I can't find the reverse..
dim oasis
You could approximate by ocnsecutively adding up washers (pi(R^2-r^2))
If you start rolling it such that the first roll has no hole through the top, it makes a cylinder with height 4 and radius 0.5
Then if you roll once more around you get a second washer with an inner radius of the sum of all previous washers (0.5 at this point) and an outer radius of that plus 0.5
So the first two iterations would yield:
pi(4)(0.5)^2
+
pi(4)((1)^2 - (0.5)^2)
As for the limits of that, I'll have to play around more
That would be calculating volume
I'm figuring out an integral right now but sorry if I haven't been as helpful as I could be
feral bridge
Not a problem. I am terrible at math. I am with a humanitarian organization and we are buying a large amount of compression wraps for hospitals in Ukraine. Unfortunately their data sheet is terrible and doesn't include how much volume 10 of these take up in a case. So just trying to figure it out.
dim oasis
I'll keep playing around but this is at least an integration problem and I'm relatively new to integration but I'd love to help however I can
feral bridge
Thank you!
lone heartBOT
@feral bridge Has your question been resolved?
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karmic rapids
when finding the zero crossings of a function, do you write $x = a \land x = b$ or $x = a \lor x = b$
ocean sealBOT
illuminator3
pale kestrel
then x=a=b
karmic rapids
when the function intersects the x axis
pale kestrel
x = a and x = b
<->
x = a = b
karmic rapids
let's say $x = \pm 1$
ocean sealBOT
illuminator3
karmic rapids
would you say $x = 1 \land x = -1$ or $x = 1 \lor x = -1$
ocean sealBOT
illuminator3
pale kestrel
??????????
karmic rapids
NO WAIT
pale kestrel
what
pale kestrel
lookup logic
compact axle
x = 1 and x = -1
<->
x = 1 = -1
1 = -1?
desert zephyr
What is the max of $\left(x-x_{0}\right)^{2}\left(x-x_{1}\right)^{2}$
ocean sealBOT
Yeetus
compact axle
is it $\left(x-x{0}\right)^{2} \times \left(x-x{1}\right)^{2}$?
ocean sealBOT
Charan
compact axle
yeah... I just copied it... markdown ignored it...
desert zephyr
Fair fair
compact axle
**Charan**
$(x - x_0)^2$ is always positive...
ocean sealBOT
Charan
desert zephyr
Yes the minimum is clearly 0
compact axle
yeah...
desert zephyr
But the maximum I have no clue
compact axle
we should maximize $\text{abs}(x - x_0)$
ocean sealBOT
Charan
compact axle
let's divide it into cases...
desert zephyr
Two cases. Furthest away from either a or b?
compact axle
if x < 0; x_0 = b
if x > 0; x_0 = a
I think... gotta check..
Is this question well defined? we need to know information about a and b, I guess..
What is the domain of $x$?
ocean sealBOT
Charan
compact axle
Okay, it's [a,b]... it is well defined..
lone heartBOT
@desert zephyr Has your question been resolved?
compact axle
Answer is
2 * (b - a)....
informal argument is... we want to maximise... abs(x - x_0).. to do that....
we want x to be as big as it can be... and we want to subtract as little as possible
b > a
big - small
so it is
b - a
or we want x to be as small as possible, and subtract as high as possible...
a < b
small - big
a - b
abs(a - b) = abs(b - a)
so answer is 2 * (b - a)...
it is an informal argument... I hope you got insight to prove it formally...
@desert zephyr
dull dove
lone heartBOT
dull dove
I'm lost, I don't know what to do from here
dull dove
Please could you write it down? I don't understand
median mauve
$h-\frac{h}{\sqrt{3}}=10$
ocean sealBOT
LittleMouse
dull dove
I'm trying to find h and x
median mauve
yea
lone heartBOT
@dull dove Has your question been resolved?
leaden aspen
I have a pretty basic question a bout Inverse Derivatives and the two rules... This is how my book shows these two different rules
leaden aspen
So for the problem f(x) = x^2 . If I use the top rule and put the derivative under 1 and then evaluate at say 4.... I get 1/8
if I evaluate with the bottom rule I get 1/ sqrt(4)*2 and I get 1/4
What gives? haha
oak perch
Let g=f^-1, so g(f(x))=x. Apply chain rule, take derivative both sides, g’(f(x))f’(x)=1 . This gives you that two results
oak perch
So for the problem f(x) = x^2 . If I use the top rule and put the derivative un...
No… 1/2sqrt(x). You let x=1 it gives you 1/2
f^-1’(1)=1/2
oak perch
1/4
leaden aspen
isn't 1 / derivative = 1 / 2x?
1 / 2sqrt(4) = 1/4 but 1 /2x = 1/8 - I'm not sure what I'm missing
lone heartBOT
@leaden aspen Has your question been resolved?
fallen rain
Is my calculation right for this question?
lone heartBOT
Is my calculation right for this question?
misty dagger
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plucky lynx
I am stuck proving the set of Natural number N is well-ordered using induction. If A is non-empty subset of N, then A has a least element. I tried using contradiction by assume A has no least element. I considered the set S of all natural number m such that m <= n for all n in A.
plucky lynx
Trying to use induction, 1 is clearly in S, I assumed m is in S for any m >= 1.
Now if m + 1 is not in S then n < m + 1 for some n in A.
This is where I am stuck on, I am not sure how to move on from here.
I have n-1 is in S, maybe I could use that?
hmm, if m + 1 is not in S then n < m + 1 for some n in A or equivalent n - 1 < m. By assuming m was in S we have m <= n which implies m - 1 < = n - 1. So combining that we have m - 1 <= n-1 < m.
Wouldn't that imply m - 1 = n - 1?
<@&286206848099549185>
any suggestions?
glass gale
try to think of the set of all subsets of N
and prove that every single one of them either has a least element or is empty using induction
(I'm suggesting a different line of thought but it leads to a really clean proof)
plucky lynx
thanks for helping. isn't that what I am doing already? Trying to show every non-empty subset of N has a least element using induction.
glass gale
I guess I need to give a bigger hint
plucky lynx
it's good, I think about it more.
glass gale
the hint: ||the thing I have in mind for the induction is to prove that, for any n, all subsets that contain at least one number between 0 and n have a least element.||
plucky lynx
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lone heartBOT
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brisk prairie
can someone help me with this
lone heartBOT
can someone help me with this
tacit arch
can someone help me with this
do you need help multiplying both sides by x^{1/2} ?
tacit arch
do you know the quadratic formula?
brisk prairie
yh
tacit arch
i guess you can just factor it
tacit arch
show the rest of your work so i don't keep telling you things you already know
tacit arch
what factors do the two terms have in common?
brisk prairie
no its right
tacit arch
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tacit arch
type .close
brisk prairie
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lone heartBOT
brisk prairie
.reopen
lone heartBOT
✅
brisk prairie
nah nah nah its wrong
tacit arch
no its right
?
tacit arch
what do you want help with then?
late lake
hello
late lake
anyone good at maths?
i need help with something
im learning how to find an area the circumferance of a circle..
i know a little bit of how to do it
just wondering how its useful?
tacit arch
help channels aren't really meant for telling you whether or not math is useful. that belongs in one of the #discussion channels or #math-discussion
glass lichen
With what?
glass lichen
Use the formula
pale kestrel
just wondering how its useful?
You want to bake a cake / make a pizza with a certain amount of dough
Such a formula would tell you the radius of the cake
and what size of baking mould you want
for the amount of dough you have
(or you could reverse this and figure out how much dough to make for the specific mould you have)
To give one application of such a formula.
late lake
You want to bake a cake / make a pizza with a certain amount of dough
i got an example of what i know
accidently done cm instead of m
lone heartBOT
@late lake Has your question been resolved?
late lake
i do have another question
how do you know the uhm
the number
in the circle
like
how u know theres 8.25cm
gray isle
late lake
how do u know theres 4m in this circle? or other shapes?
do u know how much cm or m is in this cup how do u measure it and then find out the circumferance or radius?
glass lichen
Ruler
Or any other length measuring device
You pick a chord (line segment in a circle) and if it passes through the center, you measured the diameter
late lake
oh thanks
lone heartBOT
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alpine sable
the population is positively skewed but the sampling distribution will be normal, why ? because of the Limit Theorim, but Why ?
alpine sable
mean, median, standard deviation, and the range, they all will be normally distributed because of the central Limit Theorim, but I cannot understand why and how this is True
the variance will be positively skewed
<@&286206848099549185>
lone heartBOT
@alpine sable Has your question been resolved?
olive oar
the population is positively skewed but the sampling distribution will be normal...
context?
alpine sable
even in uniform distribution when we get the means it will be normal
alpine sable
should I just memorize this ?
because I cannot understand why this True
is their a logic behind it ?
alpine sable
so its not a class just an online free course
olive oar
there definately is a reason, if i remember well you can show it with the poisson model
olive oar
so its not a class just an online free course
ah
alpine sable
should I search about poisson model ? Idk what is this
olive oar
id probably just remember it for now
dim oasis
$\pi \int_{-1}^{1} [(2)^2 - (x^2 + 1)^2] dx$
lone heartBOT
$\pi \int_{-1}^{1} [(2)^2 - (x^2 + 1)^2] dx$
ocean sealBOT
lexitorius
bright hedge
$\int 3 \dd x \neq 3$
ocean sealBOT
Brontochad (Shuri for honorable)
dim oasis
That should have been written 3x
But I followed that in the next step when I wrote 45x/15
bright hedge
then what is this step?
you have some quantity - itself
how did you not get 0?
,w integral from -1 to 1 of (4 - (x^2+1)^2)dx
ocean sealBOT
dim oasis
Well then everything would go to 0 and that would be wrong
brisk rune
I just did this in a quiz and I have no clue how to tackle it. I just know how to name it, but I dont get to figure it out how to prove it, counterprove it, or even find out if its T/F.
brisk rune
This is what I stated, but I just shot a triple:
A) False
The sumation of a specific rational number by every irrational number plus any irrational number by a specific rational number isnt a rational number.
B) True
The difference of every rational number by an irrational number by a specific irrational number minus a specific irrational number by a any irrational number is a rational number
For some reason I also dont fully "understand" how to prove rational and irrational things...
Yes, I see it, but no, I dont get it. I feel dumb as hell
This is some work done by the professor back in the day, but it doesnt really help me out
brisk rune
probably mainly because of me not grasping this^
Could we go over one of the followings given/done by the professor so I can fully understand "the simple part" and then jump to the ones I just did?
(Not fully sure if I should ask in #discrete-math or in here)
<@&286206848099549185> ? 🙂
kind wharf
halo
kind wharf
okay so I want to factor 24x(squared) + 18x - 15
I multiplied 24*-15
which equaled -360
and then my friend and I figured out -12 and 30 would multiply to -360 and add to 30
so we then went
24x(squared)-12 + 30x - 15
and so far we got
2(x-6)
but if we devide -15
we get -7.5
did we do something wrong?
here's a visual
serene sigil
im no expert but im pretty sure u cant do it just like that
use quadratic formula maybe
serene sigil
crimson dagger
hello
crimson dagger
We will prove the contraposotive. Suppose $x$\notin$B. $\forall$x((x$\in$A$\land$x$\notin$B)$\rightarrow$(x$\in$C$\land$x$\in$D)), so x$\in$D as required. Thus if x$\notin$B then x$\in$D. Therefore if x$\notin$D then x$\in$B
ocean sealBOT
Sir Raftalot
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crimson dagger
hows my syntax could you follow it?
lone heartBOT
@crimson dagger Has your question been resolved?
lone heartBOT
@crimson dagger Has your question been resolved?
crimson dagger
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strong wedge
lone heartBOT
strong wedge
I got part a but idk what to do in part b
Don't mind what I wrote
Nvm I got the ans ty
lone heartBOT
@strong wedge Has your question been resolved?
pine kettle
$y=\frac{4x}{(x^2+1)^2}+1$
lone heartBOT
$y=\frac{4x}{(x^2+1)^2}+1$
ocean sealBOT
sills
pine kettle
how do i find the range of this function
proven heart
You start with x
Which ranges from -infinity to +infinity
And then you slowly build your function from that
Adjusting the inequality
pine kettle
thats a lot of numbers
proven heart
Yes..anyway did you get what I said or should I explain how to actually adjust the inequality
?
pine kettle
im a bit confused on an inequality?
proven heart
Btw would you like to get into a VC or smth?would be easier to explain?if not ,that's ok
pine kettle
sure
proven heart
Ok
pine kettle
?
ur muted i think
@proven heart
d) Find the range of the solution found in part c).
,w find the general solution for dy/dx = x(y-1)^2
ocean sealBOT
pine kettle
@proven heart yeah i have the wrong function
proven heart
Ohh
alpine sable
so for question A would i set F(x) and g(x) = x = -2 for both functions and sub them in the Quadratic? my awnser came out to be f(x) = 20 and g(x) to be 5, so for b i would just sub these 2 and make d(x) = 15?
raven rover
?
raven rover
<@456226577798135808> <#488120190538743810>
^^
raven rover
Some integral theorem I misremembered
proven heart
lol
raven rover
¯_(ツ)_/¯
raven rover
Looks good to me
raven rover
it should just be -1/y-1
^^
proven heart
it should just be -1/y-1
Yeahh
I was like how is the integral just the negative version of the integrand?lol
proven heart
Okay...I guess I was actually kinda wrong when finding the range..
pine kettle
$y= \frac{-1}{\frac{x^2}{2}+\frac{1}{2}}+1$
ocean sealBOT
sills
proven heart
So get me the function actually as x as the subject?
pine kettle
so i solve for x
proven heart
Yeah
pine kettle
$y=\frac{x^2-1}{x^2+1}$
ocean sealBOT
sills
proven heart
Yeah...now solve it for x
pine kettle
BUT I JUST PUT ALL THAT EFFORT INTO SOLVING FOR Y
proven heart
so i solve for x
but?😅
raven rover
Don't ping random people
ocean sealBOT
sills
pine kettle
@proven heart
proven heart
Well.. great
proven heart
So...just let me think for a bit..btw .I'm just tryna help 😭
I don't know if I actually can
pine kettle
$x = \pm \sqrt{\frac{-y-1}{y-1}}$
ocean sealBOT
sills
pine kettle
so
proven heart
Yes...
pine kettle
the sqrt can not be negative
proven heart
You think what values of x are not allowed
pine kettle
or undefined
proven heart
There you go
pine kettle
so y = 1 is not included
pine kettle
wdym
proven heart
so y = 1 is not included
Yes..
pine kettle
now when is the sqrt negative
proven heart
No like do you notice that on the top...y has to be lesser than negative one
Or equal to negative one
pine kettle
true
so
im seeing that -2 and -3 make it negative
so i assume any value below -1 make it not an output
proven heart
No like ....y has to lesser than or equal to negative one.
pine kettle
oh
proven heart
That's for thetop restriction
pine kettle
so y >= -1
proven heart
Bottom restriction is y has to be greater than or equal to postive one
proven heart
so y >= -1
No I meant lesser than?😅
proven heart
So the range is ...(negative infinity to negative one] union [positive one to postive infinity)
proven heart
Ok
pine kettle
ok byee
proven heart
I hope I helped
pine kettle
you did
proven heart
I was trying 😅
pine kettle
thank you so much for your help
its ok
theres times where i really wanna help people with stuff but i forget completely
outer hearth
Did i factor this correctly?
outer hearth
<@&286206848099549185>
alpine sable
Is it not already factored? (x+1)^2 is as factored as something can be. Or are you trying to turn it into a polynomial?
outer hearth
Is it not already factored? (x+1)^2 is as factored as something can be. Or are y...
yeah but we can pull out a common factor of 1/2
out of both
alpine sable
Is the top equation the original?
There’s no more common factor after. You can’t pull out 1/2 from (x+1) because there’s no more variable attached to the 1
Well yea nvm you can do that
But the second half of the equation is wrong
What would benefit you the most is turning (x+1)^-1 into 1/(x+1)
Then multiplying both 1/(x+1) by their respective fractions.
(1/2)(1/(x+1)) + (3/2)(1/(x+1)) = 2/(x+1)
@outer hearth
outer hearth
looking
outer hearth
~~(1/2)(1/(x+1)) + (3/2)(1/(x+1)) = 2/(x+1)~~
how did you get the 1/2 to multiply by both
alpine sable
how did you get the 1/2 to multiply by both
How did you factor 1/2?
outer hearth
You know it's okay i'll just ask my teacher tomorrow. Thanks for trying to help
alpine sable
You can’t factor 1/2 from (x+1)^2
@outer hearth try using Desmos as you factor out an equation. Whether it’s factored or a polynomial they have to make the same graph. If not you messed up somewhere
lone heartBOT
@outer hearth Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
cold roost
Am I supposed to just combine the 2 numbers that match to find this percentile?
lone heartBOT
Am I supposed to just combine the 2 numbers that match to find this percentile?
@cold roost Has your question been resolved?
raven rover
Read this. It's not that hard.
hasty elk
raven rover
<@&268886789983436800>
dreamy cedar
fading zephyr
thanks
lone heartBOT
lone heartBOT
Available help channel!
peak stag
i have (x-6)(x-6) = 0. but to solve for x, i'll need to assume that x =! 6 because then i'll have 0/0, but at the end i'll still get x = 6 which is pretty obvious. so is my steps correct then?
peak stag
i know by the zero product property that x-6 has to equal 0. but now i'm stuck because i can't solve for x without getting 0/0
or does that mean i can't solve for x like this?
jovial breach
i have (x-6)(x-6) = 0. but to solve for x, i'll need to assume that x =! 6 becau...
You don't need to put (x-6) in denominator, it's simply states x= 6 is a factor of above quadratic equation
And both roots are same
,w calc (x-6)^2
ocean sealBOT
ocean sealBOT
jovial breach
It touches x axis at a single point x=6
jovial breach
peak stag
so does that mean i can't solve for x by putting x-6 in the denominator?
and then adding 6 to both sides
jovial breach
Nope we don't do it like that
peak stag
i guess that's what's confusing me a bit. since if i have 0/0 before, then the equation would be undefined and i wouldn't be able to solve for x or anything but here i can still solve for x even though i have 0/0
jovial breach
Yeah
peak stag
.close
topaz pumice
Im trying to convert this into a telescopic series, I tried using partial fraction decomposition but then there's no solution for n^2+n+1=0 so I'm kinda stuck, are there any other way or am I just thinking too much
topaz pumice
blissful whale
I assume you don't know complex numbers?
topaz pumice
well i do know a bit but not how to use them. U mean like imaginary number u get from quadratic equation?
ocean sealBOT
blissful whale
Ceveat: These are complex (besides the first)
Even with this is it is difficult though.
The culprit is that 1/(n-1) is not a convergence sum and has no pretty partial sum formula.
topaz pumice
so then I have these, well I'm supposed to plug in n ? according to organic chemistry tutor tho lol
ocean sealBOT
blissful whale
Wait a second, how do we even proceed after that?
Okay this is a very bad sign lol.
frozen stump
blissful whale
I mean here is a fun fact,
frozen stump
seeing 'euler-mascheroni constant' is how you know it's screwed
blissful whale
sum 1/n² is going to be pi²/6.
vale wigeon
TL;DR if you want to find the exact value of this then you are screwed
blissful whale
So these polynomial fraction sums can be pretty terrifying.
frozen stump
sum 1/n^3 is a constant with no elementary expression, afaik
blissful whale
It is possible Wolfy is missing a better representation.
vale wigeon
also
if you want to do partial fractions
it's A/(n-1) + (Bn+C)/(n^2+n+1)
and also plugging in values of n is not the only way to find the coefficients in a pfd
anyone who teaches you that and that alone and says that's the only way is a liar and a cheat
topaz pumice
I see
blissful whale
Where is this question from?
hardy geyser
lone heartBOT
hardy geyser
3/(3x) ain't x.
.
blissful whale
1/x
blissful whale
🙂
hardy geyser
ty
blissful whale
yes
use a/b + c/b = (a+c)/b
that is why you made the denominator equal in the first place.
hardy geyser
use a/b + c/b = (a+c)/b
i confused now
blissful whale
I typoed
hardy geyser
use a/b + c/b = (a+c)/b
ok i got it right but is this a formula
nvm
it’s not
ty
OK YES
TY
lone heartBOT
@hardy geyser Has your question been resolved?
empty hazel
can someone help me with this
lone heartBOT
can someone help me with this
oak perch
Polar coordinates
oak perch
Yeah,sin(2θ)r^2/2drdθ
oak perch
Np
empty hazel
.reopen
lone heartBOT
✅
empty hazel
.close
lone heartBOT
empty hazel
.reopen
lone heartBOT
✅
lone heartBOT
@empty hazel Has your question been resolved?
oak perch
You keep reopening it but you have no new question to ask…
errant dagger
lone heartBOT
errant dagger
exp((1+i)t) = e^t (cos(t)+i sin(t))
yep thats what i dunno how to get to
errant dagger
yes
vale wigeon
it's literally just that
errant dagger
huh
oh wait ur right im braindead
wtf is a logarithmic sprial
how do i know it is that
what does it do
blissful whale
what does it do
it spirals, logarithmically 
vague coral
vale wigeon
no that's just the defn of a spiral
errant dagger
its log cus it e
vale wigeon
a logarithmic spiral has the property that there is a scaling which maps it to itself
blissful whale
cos(x) = 1/2 (exp(ix) + exp(-ix))
blissful whale
e^(ix) = cos(x)+i sin(x)
since 
errant dagger
wait i think i did it
horrendous working
but i turned into cis form
and just used cos(-n) = cos(n) and sin(n) = - sin(-n)?
blissful whale
yes
errant dagger
tytytytytytytyytyt
now i try b
wait there is no common ratiop
😦
iis there?
am i braindead
is common ratio cos(n * theta)
blissful whale
$$\sum_{n=0}^N x^n = \frac{1 - x^{N+1}}{1 - x}$$
ocean sealBOT
M8732
errant dagger
so the common ratio is e^itheta
blissful whale
It looks like you applied this incorrectly.
I don't know what you mean by common ratio.
I do not see ratios.
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
pale kestrel
desmos
lilac orchid
Rohan went to market to purchase some fruits. Fruit seller said that the cost of 2 Kg apple = Cost of 5kg oranges. If you purchase 1kg each then the cost of apple will be 2.5 times the cost of orange
Ques - Cost of 3kg apples
Ques - Cost of 9kg oranges
Ques - Total cost of both the 2 fruit,1 kg each
Ques - Cost of orange is how much less than apple
solemn grove
let price of apple /kg = a, orange = o
2a = 5o
if a+o are purchased together
a = 2.5 o
5o = 2a
changes nothing
@lilac orchid does that sound right ?
solemn grove
let price of apple /kg = a, orange = o
2a = 5o
if a+o are purchased together
a =...
do you have any numbers
lilac orchid
do you have any numbers
nope... i have sent you the full quetsion
pls help
tomorrow is my exam
solemn grove
so do i get one in terms of the other?