it moved to (π/4,1)
so b = π/4 and c=1
now we look at another point
let's say (0,-1) is on the new graph, so we sub it back to find a
#help-0
nimble fern
nimble fern
got it?
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fresh parcel
can someone offer me an intuitive explanation of why if you have 3 vectors u, v, w, det(u, v, w) = sqrt(det((u, v, w)^2)
fresh parcel
i dont think this is proper notation but by (u, v, w)^2 i mean that the diagonal entries are u dot u, v dot v, and w dot w
quasi vector
what is det(u, v, w)??
fresh parcel
uhhh i dont know the notation either but its just taking those 3 vectors as columns
quasi vector
so u v and w are 3D vectors?
fresh parcel
yes
quasi vector
i dont think this is proper notation but by (u, v, w)^2 i mean that the diagonal...
what?
!xy
lone heartBOT
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.
fresh parcel
okay sure
mortal trellis
well thats true if they are orthogonal but I am not sure if its true otherwise
fresh parcel
quasi vector
well thats true if they are orthogonal but I am not sure if its true otherwise
that's what I thought
fresh parcel
quasi vector
the question also seems incomplete
fresh parcel
so what they did is they found the pairwise dot products between u, v, and w
quasi vector
so what they did is they found the pairwise dot products between u, v, and w
what vector does (u+v) represent?
fresh parcel
what vector does (u+v) represent?
vector with length sqrt(31)
quasi vector
so that's all they did
quasi vector
vector with length sqrt(31)
sqrt(21) or sqrt(31)
fresh parcel
yeah
mortal trellis
if you have a matrix A=(u,v,w) and multiply it by A^t from the left, then the entries of that product are all the pairwise dot products
fresh parcel
so that's all they did
sorry, im just confused as to why theyre taking the square root of the determinant
quasi vector
because of what denascite said
mortal trellis
and det(A^t A)=det(A^t) det(A)=det(A)^2
fresh parcel
if you have a matrix A=(u,v,w) and multiply it by A^t from the left, then the en...
ohhhh i see i see
mortal trellis
and you want to find det(A)
quasi vector
it's a pretty nice solution
fresh parcel
it's a pretty nice solution
yeah :)
i tried using vectors but got stuck because getting the exact values of u, v, w was too tedious
fresh parcel
and det(A^t A)=det(A^t) det(A)=det(A)^2
thanks!
mortal trellis
yeah very nice how they dodged around getting the values of u,v,w
quasi vector
you can probably do this with pure trigonometry too
fresh parcel
another good idea is to consider the tetrahedron thats formed by a point and its 3 neighbours because its 1/6 of the total
quasi vector
1/6 th or 1/2?
fresh parcel
you can probably do this with pure trigonometry too
I have terrible visualization tho ;-;
fresh parcel
1/6 th or 1/2?
the tetrahedron with 1/6 of the total area
quasi vector
ah okay I see what you are talking about now
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somber brook
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pulsar aspen
!status
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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
But it seems like a straightforward vector arithmetics.
clever folio
If you don't know that, then writing out the midpoint formula is a good place to start.
somber brook
If you don't know that, then writing out the midpoint formula is a good place to...
I just want to confirm it is the right answer like I need to answer
clever folio
People won't/can't give you the answer here
But they can help if you show your work and your thought process
Or if you show the answer you got sometimes people might be willing to confirm it.
But checking peoples work is incredibly boring and tedious so that can be hit or miss.
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halcyon mason
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halcyon mason
Could someone tell me what I'm doing wrong?
C be the curve of intersection of the hemisphere x^2+y^2+z^2=2ax and the cylinder x^2+y^2=2bx , where 0<b<a ; how to evaluate ∫C(y^2+z^2)dx+(x^2+z^2)dy+(x^2+y^2)dz using Stoke's theorem
Now I tried this way, but I'd really appreciate it if someone could explain how to do this using Stokes as well
lone heartBOT
@halcyon mason Has your question been resolved?
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@halcyon mason Has your question been resolved?
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@halcyon mason Has your question been resolved?
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@halcyon mason Has your question been resolved?
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@halcyon mason Has your question been resolved?
tight pier
C be the curve of intersection of the hemisphere x^2+y^2+z^2=2ax and the cylinde...
My guess is you would wanna turn this into a line integral and then by Stokes you can turn that line integral into a double integral, where you integrate over the intersection region and you'd need the curl
It looks curl f is turning out to be nice
(-4, -4, -4)
Now we would need a parameterization for the intersection region to calculate the normal vector
hardy pewter
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hardy pewter
i need to prove this eq.
i am stuck from step 1
can anyone send me a solved solution plz
ocean sealBOT
nimble fern
did you try using cot(A)=1/tan(A) for the first step?
lone heartBOT
@hardy pewter Has your question been resolved?
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proud falcon
I am unfamiliar of what (f/g) means would that entail that I need to devide the functions?
proud falcon
If I do need to devide the functions how would I do that?
dull lintel
I am unfamiliar of what (f/g) means would that entail that I need to devide the ...
It is $\frac{f(x)}{g(x)}$
ocean sealBOT
MetuMortis
proud falcon
Do I need to find the domain of each function individually?
Then write the period in which the value of x is okay for both functions f and g?
dull lintel
Find domain of f(x) and 1/g(x) then Intersection of those ranges is the answer
You can also do $h(x) = \frac{f(x)}{g(x)}$ and find the domain of the h(x)
ocean sealBOT
MetuMortis
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tired raft
If f and g are two polynomials in Z[x] and h is the gcd of the polynomials f and g over Z[x] then for every a integer number h(a)=gcd(f(a),g(a))?
lone heartBOT
If f and g are two polynomials in Z[x] and h is the gcd of the polynomials f and...
@tired raft Has your question been resolved?
pallid scarab
If f and g are two polynomials in Z[x] and h is the gcd of the polynomials f and...
the gcd is defined up to a multiplicative constant
and I think gcd(2,x+1) = 1 yet gcd(2,1+1) = 2
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raw jetty
a is a positive integers such thst 100a+64 and 201a+64 are squares less than 10000, find a
raw jetty
choices are 17,18,19,20,21
keen plinth
the gcd is defined up to a multiplicative constant
up to a unit ❗❗❗
plush needle
choices are 17,18,19,20,21
well if you're given choices you can just try them
but that's not the spirit I guess
raw jetty
well if you're given choices you can just try them
actually thats not a horrible idea
a right?
the only squares that end with 4 are 2 and 8
the only close numbers to ans choice are 42^2 only
plush needle
try to subtract the two equations
you end up with n² - m² = 101a
101 happens to be prime
maybe that's useful
lone heartBOT
woven hornet
actually thats not a horrible idea
Do you want the way that doesn't involve just checking all the options?
raw jetty
sure ig
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woven hornet
sure ig
100a+64=x^2
201a+64=y^2
(201a+64)-(100a+64)=y^2-x^2=101a
(y+x)(y-x)=101a
Note that 101 is prime. Do you see what you can do from there?
raw jetty
no ^_^
woven hornet
What does 101 being prime tell us about the possible values of the (y+x) and (y-x)?
fresh wedge
sour mica
What does 101 being prime tell us about the possible values of the (y+x) and (y-...
Also theres
squares less than 10000
that makes this even more specific
red pike
HOW MUCH IS 9720 x 20
vapid shuttle
HOW MUCH IS 9720 x 20
!occupied
lone heartBOT
HOW MUCH IS 9720 x 20
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@woven hornet Has your question been resolved?
raw jetty
What does 101 being prime tell us about the possible values of the (y+x) and (y-...
y-x=1 sorry didnt see
y+x=101
y=51 x=50
but that doesent work?
woven hornet
Where did y-x=1 come from? And why does y+x have to be the one that equals 101
You're right that one of them have to equal 101 (or rather one has to be a multiple of 101 and x and y have to be less than 100 which means that 101 is the only option)
raw jetty
Where did y-x=1 come from? And why does y+x have to be the one that equals 101
does it even make a diffrence? in the end its either (50,51) or (-50,51)
oh nvm
one of them has to be 101 times some factor a (it could be 1) nd the other to be a/the factor of a
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cerulean grove
Let ( f(x) ) be continuous on the interval [0,1], and ( f(0) = f(1) ). Prove that there exists at least one point ( \xi ) in [0,1] such that
[ f(\xi) = f\left(\xi + \frac{1}{n} \right). ]
ocean sealBOT
miyo
cerulean grove
status 1
ivory pivot
for every n ?
cerulean grove
n∈N*
ivory pivot
doesn t look to reasonable
verbal blaze
Let $f(x) = x + 1$. Clearly $f(0) = 1$ and $f$ is continuous. However, $$\forall n \in \mathbb{N} .\quad f(\zeta) \ne f(\zeta + \frac{1}{n})$$
ivory pivot
sorry, it say that for every n there is a \xi such that bla bla doesn't it ?
ocean sealBOT
Shuba
ivory pivot
Let $f(x) = x + 1$. Clearly $f(0) = 1$ and $f$ is continuous. However, $$\forall...
f(1) is not equal to f(0)
verbal blaze
Ah, I missteaad that.
ivory pivot
yes it is ... I was replaying to the prvious answer
cerulean grove
Misread
pallid scarab
**miyo**
if you don't know where to start, define the difference of those two quantities, find the domain and the values at the boundaries
verbal blaze
Oh, wait. you're asking this? $$\forall; n \in \mathbb{N} .; \exists; \xi \in [0,1] .; f(\xi) = f(\xi + \frac{1}{n})$$
ocean sealBOT
Shuba
verbal blaze
It's a "for all n, there exist a xi such that ...", not "there exists a xi such that for all n ..."
lone heartBOT
@cerulean grove Has your question been resolved?
cerulean grove
Oh, wait. you're asking this? $$\forall\; n \in \mathbb{N} .\; \exists\; \xi \in...
You can say that, but they didn't emphasize the behavior of n as you can see in the context of the question
n is just a random positive integer
lone heartBOT
@cerulean grove Has your question been resolved?
tawny condor
if you don't know where to start, define the difference of those two quantities,...
^
Also remember that f has a min/max at (0, 1) by rolles theorem
cerulean grove
Ok so the domain of F(x), the difference function, is [0,1-1/n]
F(0)=f(0)-f(1/n)
F(1-1/n)=f(1-1/n)-f(1)
Umm
So we want F(0)F(1-1/n)<0?
ivory pivot
miyo do you now a little bit of topology ?
ivory pivot
no but I find a tricy way ...actually every Q about continuos functions could be answered easier with topology
but if there is also some differential stuff inside the question then you need also some calculus stuff
I'll prove something stronger: $f\in C^0[0,1] $ such that $f(0)=f(1)$
ocean sealBOT
everg
ivory pivot
then for every $1>r>0 $ there exist $x, y\in [0,1] $ such that $|x-y|=r$ and $f(x)=f(y)$
ocean sealBOT
everg
cerulean grove
sure, how to prove it?
cerulean grove
ok i give it up
ivory pivot
ok i give it up<:monkaS:585602880434864138>
is there something not clear for you ?
cerulean grove
almost everything
what does this graph mean?
ivory pivot
is not a graph ... it is the set D inside R^2
however I translated this method for someone that know only calculus
I ll write it after my lunch
cerulean grove
Thank you !
ivory pivot
assume $f(x)\ge 0$, then let s define $g(x)=f(x)-f(x+r)$ with $x\in [0,1-r]$
ocean sealBOT
everg
ivory pivot
hence $g(0)=-f(r)\le 0$ (with equality we are done) wlog $g(0)<0$
ocean sealBOT
everg
ivory pivot
$g(1-r)=f(1-r)-0\ge 0 $ (with equality we are done again) wlog $g(1-r)>0$
ocean sealBOT
everg
ivory pivot
so there exist some $\xi$ between such that $g(\xi)=0$
ocean sealBOT
everg
ivory pivot
if is not clear why you can assume f >=0 ,ìlet me know... i ll write you later
lone heartBOT
@cerulean grove Has your question been resolved?
crisp kernel
vital blaze
sage shoal
how does a circle change if the equation is changed by -x or -y. For example what happens if the circle x^2+y^2=25 becomes x^2+y^2-x=25
modern sedge
how does a circle change if the equation is changed by -x or -y. For example wha...
Here is a little hint:
Add 1/4 to both sides
(x^2 - x + 1/4) + y^2 = 25 + 1/4
sage shoal
why are we adding 1/4
modern sedge
why are we adding 1/4
completing the square
note that x^2 - x + 1/4 is a perfect square
and we added the 1/4 to make it as such
modern sedge
+k?
sage shoal
i need to find it as a part b to the question
modern sedge
i need to find it as a part b to the question
I see, so they are asking for a circle of specific radius?
or whats the actual question?
sage shoal
yes a range
i have an idea on how to solve now though
first i need to find the centre of the circle first
so would I add 9 and 25 to complete a square
ok so (x-3)^2+(y+5)^2=36-k
so centre is 3,-5
modern sedge
ok so (x-3)^2+(y+5)^2=36-k
Wait 36?
sage shoal
34
stupid mistake
so it says that circle does not cut or touch the x axis
so radius must be less than 5
34-k<25
modern sedge
also in case you don't alllow degenerate circles (circles with radius <= 0) make sure to include lower bound on k as well
modern sedge
yw
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proud falcon
Would this be an okay method to solve this question?
lone heartBOT
Would this be an okay method to solve this question?
signal ice
multiply and divide by iota
twin nimbus
I think that's supposed to be the imaginary unit, i
if so,
then I have some interesting information
proud falcon
Go ahead
twin nimbus
i = sqrt(-1) right?
proud falcon
Yes
twin nimbus
and i^4?
proud falcon
i⁴=1
twin nimbus
ok, so here's another question
what's the defining property of a reciprocal?
in other words, if you have a number, let's call it x, what is 1/x?
as in what property does x * 1/x have?
proud falcon
=1
twin nimbus
ok
now i^4 = 1
which means i * i^3 = 1
which means -i = 1/i
so if you have 2/i, you actually have -2i
does this make sense?
thorny patio
Another way to see that is to take
1/i and multiply by i/i
signal ice
multiply and divide by iota
like i said
twin nimbus
The answer is 5-2i?
that's the answer that I arrived at
proud falcon
like i said
Yes thanks but I didn't understand u at first I'm not familiar to taking math in english
Using numbers helps me better understand
Thanks for ur efforts
.close
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strange dirge
Ive been struggeling with writing my own mathematical function and would like help to figure out how i write it on my own.
I have been given the following information:
The drug will be out of the system in 2.5 days.
One dosis is 25 mg.
The person stops taking the drug after one dosis.
I tried plotting it in geogebra but its not making sense in my mind.
my guess would be f(x)=-2.5x+25
strange dirge
but then the second task is to deem when the drug would not register in a testing if the testing doesnt register anything below 3mg
modern sedge
what is the function supposed to do?
rose sigil
MæthIsAlwaysRight
modern sedge
:bending_skull:
strange dirge
its supposed to "describe the amount of drug in a persons body(as mg) as a function of time (as days)"
modern sedge
its supposed to "describe the amount of drug in a persons body(as mg) as a funct...
wait so on the day 0, the person should have 25mg of thc in blood?
and on the day 2.5 the person should have 0mg?
modern sedge
and the drug escapes the system linearly?
strange dirge
it translates as "half-time"? idk if that makes sense
sorry im translating from danish
rose sigil
we need sir mikkel
strange dirge
modern sedge
we need sir mikkel
is sir mikkel awake ma'am?
rose sigil
@peak bough sir are you woke?
peak bough
<@965586576161771560> sir are you woke?
I am very awaken, yes.
modern sedge
that means that after 2.5 days, there will be only 25/2mg of thc in the system
rose sigil
I am very awaken, yes.
this ma'am has a question in danish
peak bough
Hej Byggemand Bob, hvad er din tvivl (don't translate this, Austin)? Så er sir Mikkel her for at hjælpe.
strange dirge
XD tak
strange dirge
jeg forstår ikke hvordan jeg skal opskrive en funktion for det her
peak bough
Okay, læser lige. 2 sekunder 
strange dirge
oki doki
peak bough
Okay. Begrebet "halveringstid" betegner hvor lang tid der går før mængden er halveret. Det vil sige, der går 2,5 døgn før personen går fra 25mg THC til 12,5mg THC. Bemærk at vi kommer fra 12,5 ved at sige 12,5 = 25 · ½. Det betyder så også at vi går fra 12,5 til 12,5 · ½ = 6,25 når der så går 2,5 døgn mere.
strange dirge
nåååh
peak bough
Bemærk her at anden halvering også kunne skrives som 6.25 = ½ · (½ · 25) = (½)² · 25, da vi jo blot har ganget med ½ for hver gang vi halverer!
Altså, vil vi gerne halverer n gange, så kan vi blot udregne (½)ⁿ · 25.
Vi vil nu gerne have at denne halvering sker hver 2,5 døgn!
Bemærk at hvis vi vælger n = x/2,5 (hvor x er antal døgn der er gået), så er n = 1 når der er gået 2,5 døgn (da 2,5/2,5 = 1), ligeså er n = 2 når der er går 5 døgn, n = 3 når der er gået 7,5 døgn, osv.
Kan du herfra se hvad det endelige udtryk for vores funktion bliver (hvor det er en funktion af x antal døgn)?
strange dirge
yessir jeg tror det giver bedre mening
peak bough
Du kan evt. prøve at skrive funktionen op hvis du lyster, så kan jeg bekræfte om det er rigtigt
peak bough
Næsten! Men hvad var det nu vi satte n til at være?
strange dirge
x/2.5?
peak bough
Lige med et komma mellem 2 og 5
strange dirge
NÅh ja T_T
rose sigil
T_T
peak bough
Go back to your cave, Layla.
strange dirge
min hjerne er på ferie måske skal jeg kigge på det imorgen tidlig T_T
rose sigil
i used to type T_T a lot i should do that more
strange dirge
you should
it gives me the will to cry bout math
w move
anywyas
tak for hjæpen jeg prøver at kigge på det med nogle nye hjerneceller imorgen så kan jeg vel bare skirve igen? C:
peak bough
thin saffron
can yall explain how to do sine/cosine rule i watched yotube videos i sitll dont understand still
lone heartBOT
can yall explain how to do sine/cosine rule i watched yotube videos i sitll dont...
forest marsh
You have that sin(A)/opposite of A = sin(B)/ opposite of B
So sin(A)/BC = sin(B)/AC
Just replace in and solve for sin(B)
lone heartBOT
@thin saffron Has your question been resolved?
lone heartBOT
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somber ridge
tacit arch
why are you even considering $a = \y$? What's $\mathbb{F}$
ocean sealBOT
riemann
somber ridge
$\mathbb{F}$ is a stand-in for either field $\mathbb{R}$ or $\mathbb{C}$
ocean sealBOT
Kapanda
tacit arch
yea so a = inf isn't even a scalar
when b is not zero, at least one of those 3 conditions aren't satisfied. find out which one.
somber ridge
Yes. I got help also from the linear algebra chat, and I got the same guidance. Thank you!
.close
alpine sable
hi
sharp plaza
hi
fickle sandal
:I
lone heartBOT
@alpine sable Has your question been resolved?
modest onyx
For applying L'Hopital's Rule on the sqrt function, is the sqrt function all one function or is it f(x)/g(x)?
modest onyx
wheren I'd apply quotient rule
modest onyx
But I can't
I have to do l'hopitals rule for the first part
Because then it turns to 0/0
Which isn't allowed
So can I do l'hopitals and then I don't have to do that for all functions?
lethal pelican
So can I do l'hopitals and then I don't have to do that for all functions?
and for this, I don’t think so. It’s gotta be f(x)/g(x)
acoustic sundial
For applying L'Hopital's Rule on the sqrt function, is the sqrt function all one...
look at the (x^2-1)/(x-1)
modest onyx
Does l'hopital have to apply for the whole function?
acoustic sundial
can you make that simpler
modest onyx
So if I do l'hopitals on the first part
acoustic sundial
So if I do l'hopitals on the first part
dont
modest onyx
I don't have to do it for the whole equation?
acoustic sundial
im telling you theres an easier way
how to simplify (x^2-1)/(x-1)
do you remember difference of squares
modest onyx
X+1 x-1?
acoustic sundial
you have to use a different channel
acoustic sundial
do the same for the radical part
you dont even need to lowkey
you can just evaluate at that point
lethal pelican
yes good point
modest onyx
Result is 0
2(sqrt (0/1)) = 2(sqrt(0)) = 0
Ok cool
for this I do do l'hopital's otherwise it's 1/0
and so
1+(0/1)
lim n- infinite (1)
=1?
lethal pelican
for this I do do l'hopital's otherwise it's 1/0
bruh did you just learn lhopital or smth
u spamming it on every problem lol 😞
modest onyx
It dne
acoustic sundial
for this I do do l'hopital's otherwise it's 1/0
you only need lhop when its 0/0 or inf/inf
modest onyx
Check limit of both sides
modest onyx
Or 1/0?
acoustic sundial
and 0^0
acoustic sundial
Or 1/0?
no
thats just always DNE
like 1/x
as x goes to 0
the limit does not exist
because its different on both sides
modest onyx
@acoustic sundial if there's a function that's in the form (fx/gx * (fx/gx) can I apply l'hopitals on one both not the other?
Given that the first fraction results in 1/0
lone heartBOT
@modest onyx Has your question been resolved?
flat prairie
guys
flat prairie
how do i do inequalities with fractions
sharp plaza
how do i do inequalities with fractions
can you give a specific question orrrrr
flat prairie
can you give a specific question orrrrr
yes one sdec
also I tried solving this but idk
@sharp plaza
sharp plaza
just isolate x
flat prairie
just isolate x
idk how for fractions
sharp plaza
idk how for fractions
x/3 is the same as x divided by 3
what is the opposite of divided by 3
flat prairie
times
sharp plaza
so multiply both sides by 3
sharp plaza
ye
flat prairie
epic
sharp plaza
also I tried solving this but idk
well you got the first part right
i actually think this inequality is wrong
1s
flat prairie
1s?
flat prairie
also I tried solving this but idk
0x > 2 is what im at right now
sharp plaza
1s = one second im gonna do something really quick
flat prairie
oh alright
sharp plaza
0x > 2 is what im at right now
also yeah the inequality is false thats why
you did it right
flat prairie
also yeah the inequality is false thats why
so then how would i graph it 😭
flat prairie
oh
nvm
the thing says can multi step inequalities have no solution or infinitely many solutions?
no solution im assuming
sorry for shitting handwriting
7x - 5 + x <= 4(2x + 1)
7x + 5 + 1x <= 8x + 4
7x + 11x <= 8x + 9
8x - 8x <= 9
idk what to do herte
<@&286206848099549185>
ocean whale
8x - 8x <= 9
Simplify the left side, what do you get?
flat prairie
Simplify the left side, what do you get?
nothing
ocean whale
Nothing meaning what?
ocean whale
And 0x <= 9 makes no sense, correct?
flat prairie
yes
ocean whale
And if it makes no logical sense, what would the answer be? No solution or infinitely many solutions?
flat prairie
no solution?
ocean whale
Yes
ocean whale
What are you having trouble with? It's the same process that you've been doing, it just involves fractions, with are numbers too
flat prairie
7x - 5 + 1x <= 8x + 4
7x + 1x <= 8x + 9
8x - 8x <= 8
wait
i think i solved it wrong on the other one
7x - 5 + x <= 4(2x + 1)
7x - 5 + x <= 8x + 4
7x + x <= 8x + 9
8x - 8x <= 9
nvm
flat prairie
What are you having trouble with? It's the same process that you've been doing, ...
i do not know how to do the fractions
ocean whale
Do you know how to distribute on the right side?
ocean whale
Yes exactly that
ocean whale
Now you have to get all the terms with x on one side and everything else on the other, right?
flat prairie
7x - 5 + x <= 4(2x + 1)
7x - 5 + x <= 8x + 4
7x + x <= 8x + 9
8x - 8x <= 9
7x−5+x≤4(2x+1)
combine like terms on the left side
8x−5≤4(2x+1)
distribute the 4 on the right side
8x−5≤8x+4
to get x isolated, subtract 8x from both sides
−5≤4
The statement -5≤4 is true
somebody said my answer was wrong
flat prairie
Now you have to get all the terms with x on one side and everything else on the ...
yes
ocean whale
It's the same process as the other problems
You have (3/8)x + (3/4) < (1/2)x + 2
You need to move the term with x on the right to the left, how would you do that?
flat prairie
(3/8)x - (1/2)x < (3/4) + 2 ?
flat prairie
yes
ocean whale
The left side was + (3/4) so what would you need to do to move it to the other?
flat prairie
2 + (3/4) ?
ocean whale
So what would you have as the inequality?
flat prairie
(3/8x) - (1/2)x < 2 - (3/4)
ocean whale
Now you simplify
flat prairie
idk
ocean whale
Well 2 = 2/1
ocean whale
1/8 < 16/8 - 6/8
Why did the x disappear?
ocean whale
And what's 3/8 - 4/8
ocean whale
1/8x < 16/8 - 6/8x
1/8x < 10/8x
Why is there an x on the right side now?
ocean whale
-1/8 or 1/8
Well, what's 3 - 4?
ocean whale
i dont know dude im not good with fractions 😭
The x has nothing to do with fractions
You started with 3/8x - 4/8x < 2 - 6/8
ocean whale
1/8 < 16/8 - 6/8
You made the x disappear here
ocean whale
1/8x < 16/8 - 6/8x
1/8x < 10/8x
Then it appears on both sides here?
flat prairie
You started with 3/8x - 4/8x < 2 - 6/8
1/8x < 2 - 6/8x
6/8x - 1/8x < 2
5/8x < 2
i have no clue where to go ffrom here
ocean whale
Where is the x on the right side coming from?
3/8x - 4/8x < 2 - 6/8
Is there an x on the right side at all?
ocean whale
We're not that that point anymore
flat prairie
3/8x + 6/8 < 1/2x + 2
flat prairie
We're not that that point anymore
yes but you asked if there was an x
ocean whale
You started here 3/8x + 3/4 < 1/2(x + 4)
Now we are at this step 3/8x - 4/8x < 2 - 6/8
You magically made the x appear on the right side here 1/8x < 2 - 6/8x
Why
flat prairie
3/8x + 6/8 < 1/2x + 2
man i dont know
i am just as confused as you are
idk how to do this
ocean whale
This problem is no different to the others
flat prairie
its been hours and i have to go back and show my work for like 80 answers
flat prairie
This problem is no different to the others
except the fact that i dont know how to do it
ocean whale
Are you able to solve something like 3x + 3 < 2(x + 8)?
ocean whale
It's no different, it's still the same process
Fractions and whole numbers are no different
flat prairie
explain
ocean whale
They're still numbers
ocean whale
It's the same process as the other problems
For something like this, what would you do?
3x + 3 < 2(x + 8)
flat prairie
() first
2x + 16
3x + 3 < 2x + 16
2x < 2x + 13
2x - 2x < 13
0x < 13
OK but howwwww do i do fractionsss
ocean whale
3x + 3 < 2x + 16 2x < 2x + 13
From here to here, you went from 3x to 2x somehow on the left
ocean whale
OK but howwwww do i do fractionsss
(3/8)x + (3/4) < (1/2)(x + 4)
You do the exact same steps with that example I just gave you
flat prairie
x = 13
ocean whale
Let's start over
(3/8)x + (3/4) < (1/2)(x + 4)
That's what you start with
The first step is ()
What do you get?
flat prairie
Let's start over
(3/8)x + (3/4) < (1/2)(x + 4)
That's what you start with
3/8x + 3/4 < 1/2x + 2
ocean whale
Good
Now you move terms around, getting terms with x on one side, and everything else on the other
Start with the terms with x
What do you need to do?
ocean whale
3/8x - 1/2x < -3/4 + 2
Yes that's it
Now you need to combine them
How would you do it to 3/8x - 1/2x ?
ocean whale
Why did you just move that to the left side
ocean whale
Is it a term with a variable
flat prairie
no
-1/8x < -3/4 + 2/1
4/2
8/4
16/8
-3/4 -6/8
-1/8x < -6/8 + 16/8
-1/8x < 10/8
?
idk dude this stuff confuses me so much
flat prairie
multiply.?
ocean whale
By what?
ocean whale
Almost
flat prairie
bleh
ocean whale
When you multiply or divide by a negative number, what happens to the inequality sign?
ocean whale
Yes
flat prairie
1x > -10
flat prairie
x = -10 for solving x
ocean whale
Why did the inequality change to equals?
The symbols stays the same
It doesn't change
flat prairie
x = -10 for solving x
x is -10
ocean whale
but not -10 itself
Yes
Now was that any different from a problem with whole numbers?
ocean whale
You did the same process that had whole numbers
flat prairie
ocean whale
There were just extra steps like finding a common denominator to add the fractions
flat prairie
4/5x + 2.4 >= x + 2
4/5x >= x -0.4
4/5x - x >= -0.4
4/5x - 1x >= -0.4
idk
maybe i add the x
idk
its still fractions so i dont know
i have trouble with fractions
normal stuff im fine but fractions no
ocean whale
Do you know how to do 4/5 - 1?
flat prairie
no, sorry
ocean whale
Well you need a common denominator, right?
ocean whale
Yes
ocean whale
Yes
ocean whale
So you multiplied by a negative number, what happens to the sign?
flat prairie
1X <= 2
flat prairie
thanks for all the help
ocean whale
Like I said, fractions are no different from the other problems
lone heartBOT
@flat prairie Has your question been resolved?
slow jolt
lone heartBOT
slow jolt
Can someone please help with question 2b
proven leaf
to test whether an integer sequence is a Geometric sequence or Arithmetic sequence, take the ratio/difference of successive terms and compare. If the differences are equal then you have an arithmetic sequence, if the ratios then you have a geometric sequence. I assuem you can do the rest from there :)
slow jolt
to test whether an integer sequence is a Geometric sequence or Arithmetic sequen...
Neither the ratios or differences are equal
slow jolt
to test whether an integer sequence is a Geometric sequence or Arithmetic sequen...
This is what I’ve got so far
slow jolt
I don’t think so
proven leaf
how did you get 35cm^2 for each new triange for 3 triangles turn into 65.22cm^2?
slow jolt
how did you get 35cm^2 for each new triange for 3 triangles turn into 65.22cm^2?
It says 105.22 cm^2
Sorry my handwriting is bad lol
proven leaf
I think for stage 3 the area of each new triangle is 11.69 not 3.90
that'd be the 4th stage
my logic is that the area of the first triangle is $\frac{27^2\sqrt{3}}{4}$ and then each iteration of triangle gets 1/3 smaller in side length, so then each other $n$th iteration would just be: $\frac{27^2\sqrt{3}}{4}\cdot\left(\frac{1}{3}\right)^n$
ocean sealBOT
PajamaMamaLlama
ocean sealBOT
slow jolt
**PajamaMamaLlama**
Why do you think the first triangle is that
proven leaf
,w 27^2sqrt(3)/4
ocean sealBOT
proven leaf
because if the area is 315.change then the side length is about 27, which in this case it probably is cause you're teacher I imagine wouldn't make the side length 27.00001 lol
proven leaf
Oh because sin120 is root 3 over 4?
root(3)/2 :) but yes
slow jolt
So it would be 2727sin120
proven leaf
A=1/2absin(C) = 1/2xx*sqrt(3)/2=x^2sqrt(3)/4
slow jolt
root(3)/2 :) but yes
Alright
proven leaf
so then the side length of each generational triangle gets 1/3 smaller, right?
slow jolt
Yep
proven leaf
so then the area of the new generation triangle would be $\frac{27^2\sqrt{3}}{4}\left(\frac{1}{3}\right)^{n}$
ocean sealBOT
PajamaMamaLlama
slow jolt
Why are you dividing by 4
proven leaf
because the initial area of the first triangle you divide by 4
slow jolt
I think so
proven leaf
no no that should be right
slow jolt
I’m confused
proven leaf
$\frac{\frac{27^2}{3^n}\sqrt{3}}{4}=\frac{27^2\sqrt{3}}{4}\left(\frac{1}{3}\right)^{n}$
ocean sealBOT
PajamaMamaLlama
proven leaf
I'm just complicating it my brain
slow jolt
**PajamaMamaLlama**
So this is the same as this?
Wait
No hang on
It’s the same as this
I think
proven leaf
yeah that's the same thing
slow jolt
Ok yes I understand now
slow jolt
**PajamaMamaLlama**
So is this the recursive or explicit formula
proven leaf
that's just an equality lol
proven leaf
Sooo I think what we have is: $\text{Area of New Triangle}=\frac{27^2\sqrt{3}}{4}\left(\frac{1}{3}\right)^{n}$?
proven leaf
For some reason, and I have no clue, it's only working for even integers in the 1/3 power
which is why I'm thinking did you calculate the area of each new triangle wrong?
ocean sealBOT
PajamaMamaLlama
proven leaf
ahh so it might be n in the power then
proven leaf
Then number of new triangles should be easier
slow jolt
Yeah
proven leaf
Then you multiply them together and that should finally give you an explicit formula 😭
slow jolt
Yep
I’m stuck on number of new triangles tho
Could you help me with that as well if you don’t mind
Sorry to be annoying haha
proven leaf
no worries sorry if I'm taking too long to asnwer this question, tbh I'm learning with you 😂
slow jolt
Oh haha
proven leaf
that's why I'm going all over the place
slow jolt
Fair enough
proven leaf
alr this is def geometric, ratios are the smae
proven leaf
so can you find this ratio? :)
slow jolt
Which is different from this
proven leaf
Yeah that's what I was saying before with the 2n in the number, plus in n=2 you get 35
you said you did the area formula wrong?
slow jolt
slow jolt
you said you did the area formula wrong?
But the teacher filled in stage 1 for us
proven leaf
But the teacher filled in stage 1 for us
honestly I'm looking at this and I have no clue, I'm sorry man :( you're gonna have to ping helper's
haven't a clue
slow jolt
Alright
Thanks for the help anyway
What you’ve said makes complete sense to me
I’m thinking the teacher might’ve made a mistake 🤷♂️
<@&286206848099549185>
proven leaf
What you’ve said makes complete sense to me
Makes sense to me too which is why I'm kinda upset I cannot get this 😭
proven leaf
😮
proven leaf
dang 😭
slow jolt
The only thing is now
proven leaf
so you're teacher was wrong?
slow jolt
Nope
proven leaf
oooh I got what you're saying
slow jolt
Yep
proven leaf
Yeah I think that should do it
slow jolt
I just need to find a rule for number of new triangles now
proven leaf
well that should be easier
slow jolt
But i can’t figure that out either 😭
proven leaf
need any help with that?
slow jolt
Yes please
proven leaf
For now ignore the stage 1 lol
he's making it difficult for us
what's 48/12 and 12/3?
slow jolt
4
proven leaf
there that's r
slow jolt
Yep
proven leaf
what's the first term of 3,12,48,...?
slow jolt
3
proven leaf
That’s smart
and combine those two formulae as you did above that should do it!! :)
proven leaf
lol see a learning process it is indeed
slow jolt
So is this right?
It doesn’t seem right
Because
It gives this
Which seems like a huge increase in area
lone heartBOT
@slow jolt Has your question been resolved?
slow jolt
<@&286206848099549185>
lone heartBOT
@slow jolt Has your question been resolved?
terse gull
@slow jolt
slow jolt
<@754654878915231784>
Yeah?
terse gull
u need help?
slow jolt
Yeah
terse gull
send question
slow jolt
What’s the explicit formula for this
terse gull
Send the entire question pls
slow jolt
slow jolt
What’s that got to do with anything
It’s asking for the explicit formula
Not the sum
slow jolt
It’s geometric
slow jolt
It’s geometric
slow jolt
I’ve literally sent it
slow jolt
Yes
slow jolt
Yes
terse gull
so what’s the issue
slow jolt
I need the explicit rule as well
slow jolt
What’s the explicit formula for this
??
slow jolt
Didn’t I do recursive?
