since we travel 10 meters in 0.5 seconds at 20m/s
#help-0
crude marten
gusty gorge
forget about trying to abuse some random formula
write the stopping distance in terms of the initial speed
it's not particularly hard to do
then you can see what initial speed corresponds to a stopping distance of 60 meters
gusty gorge
I haven't calculated anything at all, so numbers are meaningless to me
probably should describe, conceptually, what approach you took
crude marten
Ok Let me start from the beginning,
I used this formula as suggested,
but we had to consider reaction time, and using the point 5 second, I got a distance and subtracted it from the original 60. (the 48)
but that is also wrong, so Im wondering if this whole 48 thing is not going to work
the hint they gave is also confusing me
crude marten
Well I know what is going on with it
gusty gorge
what quantities are related to what
terse spruce
you can try to change delta X to 60- 0.5*v0 , if we consider reaction time
gusty gorge
what did you plug in for all of the unknowns in the formula
you can't just randomly plug shit in
some formulae are going to be part of the process, but it's more than just "I jammed everything into this formula"
crude marten
I get that, but I'm just trying to reverse this once I do get the answer
gusty gorge
reverse what?
crude marten
Ok so I think Im starting to get this
we use the constant velocity for the 0.5 part and since it starts decelerating we use the other one
terse spruce
Ok so I think Im starting to get this
try to submit 30m/s
terse spruce
🙂
lone heartBOT
crude marten
goodnight
terse spruce
u too
lone heartBOT
Available help channel!
finite robin
Are there any product rule or division rule for integrals? Like in differentiation? Or you just have to factorize as much as we can to simplify and then take integral for every question?
gusty gorge
integration by parts is sorta the product rule for integrals
serene junco
^this, but generally speaking, factored forms are not easier to integrate, so you don't usually want to factorize
finite robin
^this, but generally speaking, factored forms are not easier to integrate, so yo...
So there are no product rule for factors? You have to multiply and then take integral?
finite robin
integration by parts is sorta the product rule for integrals
And for division? is there any way? or just bring the denominator to the numinator and change it's power?
serene junco
Every integral is different
finite robin
no you're not getting my question
I mean is there any formula if we have factors or in p/q form?
gusty gorge
you mean like a quotient of polynomials or something?
finite robin
Yes
Do I have to find quotient first then find integral?
Or is there any other way?
gusty gorge
integrals of quotients of polynomials can be computed by doing polynomial division and then integrating the remainder I think
or you can literally just split it up
partial fraction decomposition might come in
but no, in general there's no formula for arbitrary quotients
knotty mountain
prove that a number is divisible by 6 if and only if it is divisible by both 2 and 3. (Remember to prove A implies B and B implies A)
rare goblet
n ⋮6 <=> n⋮2.3
rare goblet
divisible
knotty mountain
ah yea
but i'm just curious about the wording they'd want
if there's any formal way of saying it
rare goblet
there's a proof for it
so tell me
rare goblet
n ⋮6 <=> n⋮2.3
and (2,3)=1 is nessary, i forgot
gusty gorge
so tell me
what, you want the whole proof just laid out here?
-> is trivial
<- is let N = 2k = 3l
3 divides 2k
rare goblet
what, you want the whole proof just laid out here?
dont know how to find
gusty gorge
see if you can finish the proof from there
I think there's probably a fancy one involving bezout's identity too
rare goblet
if a⋮b1;b2;b3;.....bn and GCD(b1,b2,b3,....bn)=1 (b1,b2,b3,....bn are divisors of b)
then a⋮b
do you know how to prove this?
@gusty gorge general formula
lone heartBOT
@knotty mountain Has your question been resolved?
gusty gorge
I assume you just do induction on the two-number case
for example, if gcd(a, b, c) = 1, then gcd(ab, c) = 1, yeah?
astral briar
how do i take the derivative of both sides in g(x)=2f(x/2) + f(2-x)
median oar
Have you tried anything
astral briar
well, the problem is i dont really know what to try
i am used to solving things like f(x) = x^2
f'(x) = 2x
so now i dont know what g'(x) would be
robust vapor
try writing (x/2) and (2 - x) instead of x in function f
median oar
Do you know how to differentiate (2x + 3)²
astral briar
how do i take the derivative of both sides in g(x)=2f(x/2) + f(2-x)
g(2x)= 2f(x)+f(2-2x)
astral briar
Do you know how to differentiate (2x + 3)²
4x+10? 🤞
median oar
How did you do that
astral briar
ahh silly me 8x+12
astral briar
How did you do that
d/dx f(g(x))= f'(g(x))g'(x)
astral briar
Do you know how to differentiate (2x + 3)²
2* (2x+3)*2
median oar
d/dx [y] = dy/dx
astral briar
You should write d/dx f(g(x))
d/dx f(g(x)) = f'(g(x))g'(x)
median oar
d/dx f(g(x)) = f'(g(x))g'(x)
Ok so
median oar
how do i take the derivative of both sides in g(x)=2f(x/2) + f(2-x)
Look at this
Let h(x) = x/2
Let k(x) = 2-x
g(x) = 2f(h(x)) + f(k(x))
Find g’(x)
astral briar
g'(x)=2f'(h(x))h'(x) + f'(k(x))k'(x)
astral briar
g'(x)=2f'(h(x))1/2+ f'(k(x))-1
median oar
Put brackets around the -1
astral briar
g'(x)=f'(h(x))-f'(k(x))
astral briar
g'(x)=f'(x/2)-f'(2-x)
lone heartBOT
median oar
The trick is to see whatever is inside f() to just be some other function
That’s why the other guy said “chain rule”
lone heartBOT
Available help channel!
earnest lodge
lone heartBOT
earnest lodge
can anyone help me with qn22
I've tried it and I know I need to manipulate it by multiplying the integral by something but im not sure what I'm supposed to multiply it by
alpine sable
Long division
earnest lodge
I thought I can't do long division if the power of the numerator is lower than the power of the denominator
surreal meadow
I thought I can't do long division if the power of the numerator is lower than t...
you can think of it as dividing the inverse
median oar
Do you know about the integrals of the form f’(x)/f(x)
alpine sable
separate the fraction
Do this
median oar
What’s the integral of f’(x)/f(x) dx?
earnest lodge
what am I supposed to separate
earnest lodge
What’s the integral of f’(x)/f(x) dx?
ln
median oar
ln what
alpine sable
what am I supposed to separate
Like, $\int \frac{x+2}{3+4x^2} \dd{x} = \int \frac{x}{3+4x^2}\dd{x} + \int \frac{2}{3+4x^2} \dd{x}$
earnest lodge
X/3+4x^2
ocean sealBOT
Lixera
earnest lodge
**Lixera**
ahhh okay I get it I'll try it now again
surreal meadow
why is the integral of f’/f important
median oar
**Lixera**
Cos it helps you do the first one
alpine sable
Yeah the first integral is ln(something something) and the other is arctan(something something)
lone heartBOT
lone heartBOT
Available help channel!
dawn prism
Our teacher has given us holiday homework to complete to consolidate learning however, I'm really struggling to comprehend this word problem. I was wondering if someone could break down the question a bit as I've tried to wrap my head around it and can't come to any conclusion on how to progress
gusty gorge
surprisingly all of those italicised words are real words
wind geode
Our teacher has given us holiday homework to complete to consolidate learning ho...
looks hard
gusty gorge
oh yeah this one is really weird
how do they expect you to predict something in 2025
time series stuff is gross
dawn prism
how do they expect you to predict something in 2025
see you can predict the year with the Year/parts per billion to do it but I'm not sure how to move forward from there to find the density as the density is in the below data section and it's really confusing my mind
gusty gorge
huh? you can't
least squares assumes that the errors are iid
you can't just slap a line on the year vs bifenthrin concentration
the least squares estimator probably isn't consistent or unbiased
hell, that thing might not even be modeled well with a line
dawn prism
idk...
very lost, very confused
<@&286206848099549185> sorry for the ping but if you someone could help me out that would be extremely appreciated
lone heartBOT
@dawn prism Has your question been resolved?
lone heartBOT
@dawn prism Has your question been resolved?
lone heartBOT
@dawn prism Has your question been resolved?
lone heartBOT
@dawn prism Has your question been resolved?
elder wharf
<@&286206848099549185>
tardy nest
!help
lone heartBOT
Please read #❓how-to-get-help
tardy nest
I want to convert a Slope intercept equation to standard form, I managed to do this with every equation that doesn’t involve fractions, but when I do one that does involve fractions, and use a calculator to check, it doesn’t match up. When converting slope intercept to standard form, isn’t the goal to just get X and Y on one side? For example given: y=2/3x -3 <@&286206848099549185>
ocean sealBOT
.doc
barren portal
so, if you are trying to make it a slope-intercept form,
just isolate y, in one side
$y=\frac{c-ax}{b}$ which is $y=\frac{-ax}{b}+\frac{c}{b}$
ocean sealBOT
.doc
barren portal
sorry, can you explain how fractions comes as an issue to you here?
I didn't completely understood
dim hinge
hi i have a doubt in my math hw
does anyone know how to call each other and could i get some help
lone heartBOT
@dawn prism Has your question been resolved?
warm spruce
Hello guys! I need help. How do you guys factor 14c^3 - 42c^5 - 49c^4? My answer is 7c^2(2c- 6c^3 - 7c^2)
tidal mango
People I hope y’all having a nice day and fun and enjoyment learning math! 😃
sly yacht
Hello guys! I need help. How do you guys factor 14c^3 - 42c^5 - 49c^4? My answer...
should be 7c^3(2-6c^2-7c) and then I guess you could factor that part inside using a quadratic and factor it up even more
just think like this, how much c can i take out of member before I start making them into fractions, in this case its 3
lone heartBOT
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alpine sable
.close
alpine sable
tu'(t) = u(t) - t/u(t) where t > 0, u(1) = 1
I'm for some reason not able to solve this, could someone give me a hint on how to start?
lone heartBOT
tu'(t) = u(t) - t/u(t) where t > 0, u(1) = 1
I'm for some reason not able to so...
@alpine sable Has your question been resolved?
slow hound
tu'(t) = u(t) - t/u(t) where t > 0, u(1) = 1
I'm for some reason not able to so...
its clearly not separable so a substitution is the next best thing to try
alpine sable
What do I substitute? v = t/u(t)?
slow hound
yeah i did z = u(t)/t so yours should also work
alpine sable
okay, thanks! I tried a bit with that substitution already, but I probably made an error somewhere then
slow hound
which is indeed separable
alpine sable
thank you!
alpine sable
.close
lone heartBOT
lone heartBOT
Available help channel!
somber kiln
This question is from the heron's formula chapt, but I'm pretty sure it uses the formula 1/2bh
somber kiln
Tho i'm a bit confused on solving it, since there isn't an another number
minor needle
here, Heron's formula is an exaggeration
somber kiln
oh ok
minor needle
you can use 1/2bh (in fact 1/2b^2 - triangle is isosceles)
then hypotenuse from Pythaogrean or just diagonal of a square
fun fact is that if you know formula for the diagonal of a square, you can choose correct answer without doing anything
somber kiln
Should I multiply 72 with 2 and then find the sq. root?
minor needle
yes
somber kiln
fun fact is that if you know formula for the diagonal of a square, you can choos...
thanks I'll use it
alr
Yea I got my answer
its 12
thanks for ur help
somber kiln
oh shit ok
I need to find the sq root of 288, should I use the long division method or prime factorization?
minor needle
288 = 144 * 2
ocean sealBOT
Result:
576
starlight
alpine sable
144 is a perfect square
somber kiln
it would be 12
alpine sable
so if $\sqrt{144} = 12$ what would $\sqrt{144 \cdot 2}$ equal to
ocean sealBOT
starlight
somber kiln
so it would be V12^2*2
12*2?
since root 144 is already 12 and multiplying with root 2 would be root 12V2 right?
alpine sable
since root 144 is already 12 and multiplying with root 2 would be root 12V2 righ...
yes
dawn prism
.reopen
shell kindle
hello!
dawn prism
hi!
shell kindle
is this the place that I ask for help?
dawn prism
yes
shell kindle
ah ok
alpine sable
is this the place that I ask for help?
wary stream
is this the place that I ask for help?
Read #❓how-to-get-help
shell kindle
so
A(0,-3), B(a-4,0), C(6,a). out of these 3 points, what is a possibility for them to not make a triangle? other than on one straight line
alpine sable
you would usually open up your own channel
dawn prism
.close
lone heartBOT
lone heartBOT
Available help channel!
bleak pine
$\int_{\left( 0,1 \right]}^{}\frac{sinx}{x^8 + 2x^2}$
lone heartBOT
$\int_{\left( 0,1 \right]}^{}\frac{sinx}{x^8 + 2x^2}$
ocean sealBOT
draganb
bleak pine
How can I determine if this integral converges?
lone heartBOT
@bleak pine Has your question been resolved?
bleak pine
.close
bright remnant
anyone know how to integrate this monstrosity
lone heartBOT
anyone know how to integrate this monstrosity
lone heartBOT
@bright remnant Has your question been resolved?
lone heartBOT
@bright remnant Has your question been resolved?
half stream
you could maybe factor it
cursive badger
expand
then you can simply split it into like four integrals, that's the brute force method
not sure you can use a sub to do it all at once
@bright remnant
but expanding then integrating is definitely possible
half stream
that is probably the better option
but its always good to remember that if call cos(2x) something arbitrary like a, you get (1 - 3a + 3a^2 - a^3) which is like (1-a)^3 = 1 - 3a + 3a^2 - a^3
cursive badger
oh wait it's a cosx not cos2x being multiplied by
damn yeah factor like a cubic, then I think there's an identity for 1-cos2x?
half stream
damn yeah factor like a cubic, then I think there's an identity for 1-cos2x?
i think so too
cursive badger
yeah 1-cos2x is sin^2x
so you have (8sin^6x)cosx
which is a simple undo chain rule integral
cursive badger
just use cos2x = 2(cosx)^2-1 to get (1-cos2x)^3 = ((cosx)^2)^3
that doesn't make any sense?
cursive badger
look we have (1-cos2x)^3
half stream
left out the two and didnt negate the one
cursive badger
smh smh trig is hard
cursive badger
then diff by parts
no ;-;
you're overcomplicating this
32sin^6xcosx is a simple undo chain rule
a u sub at worst
lone heartBOT
@bright remnant Has your question been resolved?
distant flare
Both are same.
royal plank
lets put it mathematically
distant flare
Noo
woven plaza
It has higher density
woven plaza
It's not heavier
limpid turret
Old video meme reference
distant flare
Density is different but mass is same.... 1kg
alpine sable
Help
strong compass
Which bit are you stuck with
gray isle
the question wants you to do it by graphing
strong compass
It wants you to do it graphically I believe, so you first need to plot them
gray isle
were you able to graph the specified lines
alpine sable
I know you have to graph but how do you solve the equation
strong compass
The solution is at the intersection, because that’s when the x value produces the same y value for both functions
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
help
strong compass
By parts
alpine sable
Consider: IBP
sorry?
[\int_a^b \map f x \map {g'}{x} \dd{x} = \eval{\map f x \map g x - \int \map g x \map {f'}{x} \dd{x}}_a^b]
wary stream
Integration by parts
ocean sealBOT
alpine sable
Well I’ve only been taught how to do it without the rule ig?
tacit arch
Well I’ve only been taught how to do it without the rule ig?
What rule are you talking about
alpine sable
As in: figure out what to do to dy/dx to make it the same as the integration
I haven’t learned how to integrate the product rule by itself
tacit arch
Use part a
alpine sable
Ik but how?
tacit arch
Do you know the integral of a derivative?
alpine sable
Yes it’s the original equation
alpine sable
But idk what to change with dy/dx to get the integration
Oh ok
The equation on part a?
1-pi/2 is what I got
I’m so confused 😭
tacit arch
Show your work if you want it reviewed
alpine sable
lone heartBOT
alpine sable
Hello, I want some help with this question, and also, does it have to use Pythagorean theorem or can it be done via factorising alone
alpine sable
well I know that width is 10-x
hard patio
Yes
alpine sable
and so 8^2 = x^2+ (10-x)^2
hard patio
Yes
alpine sable
but what i dont get is how to expand this
hard patio
What is (10-x)^2
alpine sable
100-x^2
hard patio
You know binomial multiplication?
alpine sable
100-20x + x^2
alpine sable
which equals 64
hard patio
No, not exactly
hard patio
and so 8^2 = x^2+ (10-x)^2
You missed x^2
alpine sable
you too
vast tulip
If you don’t have any other questions, you should close the channel
can you help me in
#help-42 pls
last ether
<#948770026914213909> pls
Really bud? Don't do that
last ether
Doesn't matter
vast tulip
can you help me
alpine sable
how do i close channel
pearl saddle
.close
lone heartBOT
@alpine sable Has your question been resolved?
earnest carbon
hi can someone help me with this summation
lone heartBOT
hi can someone help me with this summation
earnest carbon
logn + (logn - 2) + (logn - 4) + (logn - 6) + (logn - 8).....
tacit arch
logn + (logn - 2) + (logn - 4) + (logn - 6) + (logn - 8).....
Show the original question. Screenshot or picture is best
heady pollen
earnest carbon
solving for the recurrence relation
and the log base is 2
i think the amount of terms here would be log_4 n right?
ionic trail
i think the amount of terms here would be log_4 n right?
Correct. And each term is at most log(n). With that you can make an estimation (upper bound) of the size of T(n).
You would get the "Big-O-Notation" of T(n).
earnest carbon
Correct. And each term is at most log(n). With that you can make an estimation (...
yeah im just not sure how to simplify the summation
i think i can group the log n's
so there would be log_4 n x (log_2 n)
ionic trail
Yep
earnest carbon
and i can group the subtractions
asymptotically can log_4 n x (log_2 n) be simplified to O(log^2 n)?
ionic trail
log_4(n) * log_2(n) is an upper bound of T(n), i.e. T(n) <= log_4(n) * log_2(n).
I don't know if we can actually do more here since we are only given an upper bound of T(n).
But we know that T(n)=O(log(n)²)
T(n) could be constant for all we know
lone heartBOT
@earnest carbon Has your question been resolved?
alpine sable
how do i solve for a line's equation with points
lone heartBOT
how do i solve for a line's equation with points
lone heartBOT
@alpine sable Has your question been resolved?
static depot
Is there anything else mentioned in the question
lone heartBOT
lone heartBOT
Available help channel!
open wharf
Need a step by step on how to solve
lone heartBOT
Need a step by step on how to solve
outer lark
do you know your kinematic equations?
open wharf
do you know your kinematic equations?
like formula?
outer lark
sure
open wharf
no
lone heartBOT
@open wharf Has your question been resolved?
open wharf
<@&286206848099549185>
keen pagoda
Uh not the expert
But
I would suggest trying to look over the things you're doing in class; it may give you some needed understanding
open wharf
I would suggest trying to look over the things you're doing in class; it may giv...
but could you just help me out here
like what to start off with
lone heartBOT
@open wharf Has your question been resolved?
open wharf
.close
north hemlock
I just need some help getting started on this
lone heartBOT
I just need some help getting started on this
north hemlock
Ironically, this wasn't actually discussed in class lol
u can expand it many times and then simplify, there isn't anything to "solve" though since there isnt an equals sign
oop
north hemlock
------------------
u can expand it many times and then simplify, there isn't any...
@dire thicket
dire thicket
lone heartBOT
@north hemlock Has your question been resolved?
north hemlock
sad
rich quiver
<@&268886789983436800>
native oasis
send probs
sly mantle
@spring anchor channel occupied, see #❓how-to-get-help
north hemlock
<@&286206848099549185> Anybody know how to prove this lol (I just need a push and then I'm sure I got it)
lone heartBOT
@north hemlock Has your question been resolved?
lone heartBOT
@north hemlock Has your question been resolved?
lone heartBOT
@north hemlock Has your question been resolved?
north hemlock
Rip me
smoky hedge
replace the k+1 terms with the recursive equations
you get s_k . t_k+1 - s_k+1 . t_k = - (s_k-1 . t_k - s_k . t_k-1)
In other words reducing the value of k by one changes the value by -1 * the original value
eventually you reach k = 0 and you can replace s0, t0, s1, t1 with the respective 1s and 0s and you'll get an eqn of the form -1^k+1
s_k . t_k+1 - s_k+1 . t_k = -1 ^k+1 (1+0) = -1^k+1
lone heartBOT
@north hemlock Has your question been resolved?
north hemlock
eventually you reach k = 0 and you can replace s0, t0, s1, t1 with the respectiv...
OHHH, I was trying that but maybe I miswrote something then
Thanks !
.close
lone heartBOT
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Available help channel!
tender stag
How would I do induction for n+1 in this case? Somewhere in the process I got: 6 | 5^2n+3 + 7^n+2..
Is that correct or did I screw up? and how to finish from here
raven haven
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
raven haven
yeah thats correct actually
raven haven
use your inductive hypothesis and see if you can put your current expression in terms of that
okay uh are you writing upside down lmao
tender stag
wdym haha
raven haven
"SmartLines" seems to be rotated
wind cloak
Probably going the other way round
raven haven
like
wind cloak
Manga style
raven haven
this is unrelated ik but lol
tender stag
oh yeah I am studying for finals so im going from the other side of the notebook xd
raven haven
yeah okay so use the inductive hypothesis
tender stag
dont I need to get the original expression to use the hypothesis?
wind cloak
Fields Medal
kindred anchor
no nobel prize in math tho <:soynoo:885331816322592809>
Yes 
raven haven
now you want 6 divides blahblahblah blah
so put blah blahblah in terms of blahblahblah blah
tender stag
but blah blah blah is different now from the starting expression
raven haven
yup but
you can still put it in terms of the original im sure
mess around with the algebraic manipulations
tender stag
and what do I do with whats left.. for example original is 5^2n+1 and now i got 5^2n+3
lone heartBOT
@tender stag Has your question been resolved?
untold rivet
hi, how i can make "24" using: 1,3,4,6 and using only: +,-,x,:
untold rivet
yes
alpine sable
can you repeat using them or can they only be used once
vague mirage
3+4+5=12+5=17+4=21+3
untold rivet
u can use once the numbers
alpine sable
u cant repaet
vague mirage
Oh
untold rivet
u can repeat only; +,-,×,:
untold rivet
what lmao
vague mirage
3×4×2+6-5-1☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️
untold rivet
u can use only: 1,3,4,6 for only one time lol
raven haven
I hope : is divide
untold rivet
yes
raven haven
is this even possible
raven haven
oh you can spam the operations
I thought you can only do it once
can you just not use some of the operations
weary wyvern
I think OP is trolling us
untold rivet
who
untold rivet
u must use all the numbers to make 24
raven haven
yeah
untold rivet
im not trollimg
raven haven
ok show us the original question
untold rivet
ok
weary wyvern
Closest I can get is 23
alpine sable
there is not a single combination that can make that true
vague mirage
(4×6)×3^-1×1
untold rivet
u can use only: x,:,+,-
vague mirage
😂
alpine sable
you can run it through python or something and figure out all combinations
vague mirage
alpine sable
but i am near certain there is no answer to that
trim wagon
keen plinth
untold rivet
itsright
keen plinth
untold rivet
lol
untold rivet
why it is impossibile
vague mirage
☠️
untold rivet
Nah 4×6 is 24 and 24/3 is just 8
i was ironic
wind cloak
limits moment
keen plinth
,w 6 / (1 - (3/4))
ocean sealBOT
untold rivet
,w 6 / (1 - (3/4))
u cant use fractions
keen plinth
im not sure what you think division is 
untold rivet
what
ocean sealBOT
untold rivet
division is :
untold rivet
lone heartBOT
@untold rivet Has your question been resolved?
lone heartBOT
@untold rivet Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
kindred jacinth
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rocky grove
Did i mess up somewhere ?
When you did a similarity for the oil, you should have used 15 instead of 5
After that, you get the volume of the 15 cm cone and subtract the 10 cm cone from it.
kindred jacinth
When you did a similarity for the oil, you should have used 15 instead of 5
i did use 15 no ?
rocky grove
For finding the similarity though
kindred jacinth
oh so 5/10 = x/4.5 ?
kindred jacinth
15/20 = x/9
Like this ?
rocky grove
Yeah
frosty leaf
Help!
2⋅3^(x+1)-4⋅3^(x-2)=450
lone heartBOT
Help!
2⋅3^(x+1)-4⋅3^(x-2)=450
frosty leaf
How do I get to x=4?
nimble fern
you can factor out the 3^(x-2) out of both terms in the LHS
frosty leaf
(2 * 3^3 -4) * 3^x-2 = 450?
nimble fern
yea, like that
frosty leaf
Why? I don't understand
nimble fern
Why? I don't understand
then it will become
50*3^(x-2)=450
nimble fern
yes
frosty leaf
I got to 50 * 3^x-2 = 450
Do I divide both sides by 50?
Do I always divide like this in this kind of situation?
I always do inverse operations right?
If It were -50 + 3^x-2 = 450 I would add 50 to both sides right?
vestal storm
help
vestal storm
can someone say an example
G is a group
and g is an element of G
what exactly is g?
could it be anything
if g is x
then x, x^2, x^3,... are all a subset of G
is that correct
@languid bolt
wary stream
<@483962566977126401>
One, that's a person, don't ping people
Two, if you were trying to ping helpers, you have to wait at least 15 minutes before pinging helpers
vestal storm
oh mb
ionic trail
<g> is a subgroup of G, called the cyclic subgroup generated by g.
If G = <g> for some element g€G then G is a cyclic group.
vestal storm
If G = <g> for some element g€G then G is a cyclic group.
isnt G a group tho
how does something equal that
ionic trail
isnt G a group tho
It is
vestal storm
oh g is another group which is a subset of G?
ionic trail
g is an element of G, and <g> is the set of all powers of g.
ionic trail
Let's say integers mod 5 under addition, so {[0],[1],[2],[3],[4]}, where [x] denotes the residual class of the number x mod 5.
The element "[1]" is a generator of that group. Note that a "power" of [1] is actually [1] + [1] + ... + [1] because we are under addition.
[1] = [1]
[2] = [1] + [1]
[3] = [1] + [1] + [1]
[4] = [1] + [1] + [1] + [1]
[0] = [1] + [1] + [1] + [1] + [1]
So <[1]> = {[0],[1],[2],[3],[4]} = G
lone heartBOT
@vestal storm Has your question been resolved?
vestal storm
oh sorry didnt see your message
vestal storm
So <[1]> = {[0],[1],[2],[3],[4]} = G
ohhh okk got it
tysm!
alpine sable
I cant do thissss
lone heartBOT
I cant do thissss
lone heartBOT
lone thunder
I have the topic of function templates and I have to set d second derivative to zero, but I have no idea how if the 2nd derivative is Fa ́ ́(x) 12x²-2k
lone heartBOT
Available help channel!
lone thunder
I have the topic of function templates and I have to set d second derivative to zero, but I have no idea how if the 2nd derivative is Fa ́ ́(x) 12x²-2k (not sure if this question goes in this channel)
wise ember
Can you send me a picture of the question? I’m afraid I didn’t understand your explanation
lone thunder
oh sorry i use google translate
The task is to examine the graph of FK for exrem- u inflection points. Sketch the graph for k= -2 and for k=2
fk= fa(x)
boreal verge
what language do you natively speak
lone thunder
german
lone thunder
i just have to underdstand how Functional chaars works
boreal verge
idk what you're referring to because google translate cant do its job at all
cedar pendant
lone heartBOT
astral briar
cedar pendant
interesting, can you elaborate?
astral briar
one sec
i just put this up here for my reference, i want to see if this table could help solve your problem
cedar pendant
okay no problem
astral briar
ahh now i see
for any number from 1 to 6, there are 11 pairs of dice rolls which have that number in them
so, if i got 4 for example, then there are 11 pairs with 4 in them
so the chance of reynold having a pair with 4 in it is 11/36
this is the same for all numbers 1-6
look!
astral briar
cedar pendant
but i dont see how i can relate it to this problem though
i mean it still makes sense to say 1/6 probability on first dice and 1/6 probability on second
why wouldnt this make sense to say?
harsh swallow
you look at that table
and calculate the chance that reynolds dice contain the number that you want
astral briar
i mean it still makes sense to say 1/6 probability on first dice and 1/6 probabi...
what does each chance represent
cedar pendant
what does each chance represent
number of possible outcomes
astral briar
1/6 + 1/6 = 2/6 or 12/36
no i meant like what does 1/6 + 1/6 represent
what are the two probabilities
harsh swallow
So the chance that reynolds gets the right number on the first die
is 1/6
correct
cedar pendant
yes
astral briar
harsh swallow
but the chance that reynold gets the right number on the second die
astral briar
look here
harsh swallow
requires the fact that he didn't get it on the first
astral briar
assume that reynold gets the dice right on the first try
1/6 chance
then after that first dice throw, he rolls again
cedar pendant
requires the fact that he didn't get it on the first
yes
astral briar
he has 1/6 chance of getting the correct number again
and has 5/6 chance of getting a wrong number
cedar pendant
ok 1 min let me think about it
astral briar
total chance is 1/6 * 1/6 + 1/6 * 5/6 = 6/36
chance of him getting the right number
given that the first dice roll was correct
now the second instance, the first dice roll was incorrect
harsh swallow
no 1/6 * 1 + 5/6 * 1/6
cedar pendant
omg
astral briar
no 1/6 * 1 + 5/6 * 1/6
wrong
cedar pendant
answer is 11/36
astral briar
5/36+ 6/36= 11/36
astral briar
yeah that's what i'm saying
i was talking about something else
when he initially gets the first dice roll correct
the second situation which i was about to discuss was when he gets the first dice roll wrong
@cedar pendant does it make sense now
lone heartBOT
astral briar
np cutiepie 💋
lone heartBOT
Available help channel!
jagged gulch
I'm trying to rationalize denominators right now. In my book it tells me that whenever I have: √A-√B I have to multiply it by √A+√B and vice versa. Why is it that in this picture they just change everything into positive?
median oar
,w expand (a+b-c-d)(a+b+c+d)
jagged gulch
I'm sorry, I still dont understand
ocean sealBOT
median oar
it looks like it squares all the terms plus a little extra
can do it another time to get rid of the remaining radicals
jagged gulch
I know how to rationalize, but I dont understand why in this instance I have to multiply everything in positive?
How do I know when to multiply by positive or negative?
median oar
,w expand (a+b-c-d)(a-b-c-d)
ocean sealBOT
fringe sleet
seems to be using hindsight unfortunately
like, they know this is the fastest way to do it so its the way they do it, not easy to tell yourself when you should be doing it differently
median oar
hmm idk this doesn't seem to have any reason
it just looks like you can factor and reduce it with these signs
fringe sleet
you wanna square b, c and d
median oar
you get c * d which is √3 * √15 = 3√5 which then simplifies with the √5 at the front from -2ac
actually that's a √3
fringe sleet
their way leaves 2 non squared terms, aka 2 square roots are left, most ways will leaves 3 square roots left
as far as i can see
alpine sable
translation: In the triangle ABC in the adjacent figure, the points M and N lie on the sides AB, respectively
AC, so that AM = 4cm, AB = 12cm,
1/3
YEAR
NEEDLE
= . If BC = 24cm, then the length
segment MN is equal to:
median oar
,w expand ((a+b)-(c-d))*((a+b)+(c-d))
ocean sealBOT
fringe sleet
ah yeah that one works as well
median oar
i'd go with this and then do it again if needed
jagged gulch
I'm super lost, sorry. I just want to understand when to multiply by positive or negative
median oar
if i were to do this i'd just group them up in 2's
((a+b)-(c-d))*((a+b)+(c-d))
like this
jagged gulch
why doesnt it flip the all the signs?
fringe sleet
why doesnt it flip the all the signs?
that only really works when there are only 2 terms
median oar
((a+b)-(c-d))*((a+b)+(c-d))
=(a+b)^2-(c-d)^2
second part is -2cd huh
jagged gulch
that only really works when there are only 2 terms
So when it's more than 2 terms do I just change everything to positive?
median oar
,w expand (-a+b-c)(a-b+c)
fringe sleet
So when it's more than 2 terms do I just change everything to positive?
unfortunately there isnt a straightforward way to do it when there are more than 2 terms, sometimes 1 minus sign will be the most efficient, sometimes all minus is the best, sometimes all positive is the best etc
jagged gulch
unfortunately there isnt a straightforward way to do it when there are more than...
Does this mean it doesnt matter what i change the sign to? It will give me the same answer at the end?
fringe sleet
Does this mean it doesnt matter what i change the sign to? It will give me the s...
it does still matter, only some will work
ocean sealBOT
fringe sleet
of course you can do it as many times as you like and eventually get there by chance
median oar
none of this looks good lol
jagged gulch
There is no sure way of getting the answer then?
fringe sleet
well im sure a table can be made which will say what is the most efficient depending on how many terms
jagged gulch
fringe sleet
but i sort of doubt someone has made that
jagged gulch
How would I go about rationalizing this then? The solver says I need to expand and multiply everything with a positive sign
after expanding the denominator how do I know what to multiply by
if the rule they gave me only works for 2 terms
fringe sleet
oh wait no its the same nvm, hmm. im not entirely sure if there is a nice way of doing these, seems to be mostly trial and error
jagged gulch
.close
lone heartBOT
median oar
.reopen
lone heartBOT
✅
median oar
,w expand (a+b+c)(a-b+c)(a-b-c)(a+b-c)
ocean sealBOT
median oar
that squares everything at 3 terms
fringe sleet
oh god
yeah the 4 one is not gonna be nice
i cant find anything online about tricks to do more than 2 terms
and ive never had to do this myself
median oar
it's just all the combinations of a b c d with different signs
jagged gulch
it doesnt help my question lol
median oar
well...it does, but it's not really doable
fringe sleet
technically this is a sure way of finding it, but yeah the amount of computations is just disgusting
wind cloak
I'm trying to rationalize denominators right now. In my book it tells me that wh...
Focusing on the denominator: $2(1 + \sqrt 5) - \sqrt 3(1 + \sqrt 5) = (1 + \sqrt 5)(2 - \sqrt 3)$
ocean sealBOT
NEONPerseus
wind cloak
In this factored form multiply by the rational conjugates of either of those terms
median oar
oh that is indeed very smart
wind cloak
Wait bruh you already did that 😔
wind cloak
Here 
median oar
oh wow i missed it
median oar
I'm trying to rationalize denominators right now. In my book it tells me that wh...
actually, this makes sense
it's grouped a + b - c - d into (a + b) - (c + d)
then multiplied it by (a + b) + (c + d)
which is why it looks like the signs all changed to positive
if you dont see the factoring this is probably the way to go
wind cloak
But that doesn't necessarily warrant the rationalization does it
I remember rationalizing stuff with three terms back in grade 9 or something but I forgor
median oar
But that doesn't necessarily warrant the rationalization does it <:thonk:4065757...
no but it makes you go from having 4 radicals to only 2
wind cloak
An improvement well
median oar
it expands to just 2ab and -2cd for non-squared terms
jagged gulch
it's grouped a + b - c - d into (a + b) - (c + d)
but to rationalize a+b you have to multiply by a-b
median oar
you can then redo it
median oar
but to rationalize a+b you have to multiply by a-b
yes but it's like step 1
you group them into x + y
then do * (x - y)
here x = a + b, y = c + d
x - y = (a + b) - (c + d)
x + y = (a + b) + (c + d)
restive token
.open
jagged gulch
.close
alpine sable
lone heartBOT
alpine sable
The proper answer is 2.06
I see it says "magnitude" so I guess ax != ay here
since the figure is not in equilibrium.
alpine sable
I think I go back to my equation m1g - m1ay = m2ax*sin50 and somehow figure out ax and ay then find the magnitude from there
But I'm not entirely sure..
Nor am I sure how I would even find ay or ax given this.
F = m*a, and if we applied that to find the force in the Y direction for m1, it would be ay = F/m1
however, our F in the y direction is, i assume, sum Fy. and that is FT = m1g - m1ay
so this is redundant.
Okay apparently its a = (m2*g*sin(theta) - m1*g)/(m1 + m2)
not sure how to get that from my equations, or if i got my original equations wrong, which i must have
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Okay apparently its `a = (m2*g*sin(theta) - m1*g)/(m1 + m2)`
This makes total sense, but I'm not sure how to get here from the equations i made. could someone tell me if my equations are wrong? Thanks
<@&286206848099549185>
rose peak
alpine sable
wrong chat homeboy
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Anyone?
lone heartBOT
@alpine sable Has your question been resolved?
worldly summit
Hi
I need two days for being a professional for deriving
I need a guide about this
alpine sable
lol
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
jade hollow
not sure what you’re doing with equating Fx and Fy
you just need to find the net force on both the objects which will give acceleration
like, on mass m1
net force is T-m1g which is giving an acceleration ‘a’ to the mass
find the equation for m2 and then you will get 2 equations and 2 unknowns (T and a)
lone heartBOT
@alpine sable Has your question been resolved?
ancient saddle
I think I go back to my equation `m1g - m1ay = m2ax*sin50` and somehow figure ou...
you don't have to take a component of acceleration a because it's already parallel to the body's movement
you have to get the equations following: sum of forces equal body's accelerations