why we doin natural log now 😭
#help-27
stable nymph
misty crest
logarithmic differentiation
misty crest
why we doin natural log now 😭
nah you’re cooked 😭😭
stable nymph
yeah na its jover
stable nymph
went for help
atomic dome
It is not that difficult
misty crest
mathmaxx
stable nymph
came back even more confused 💀
misty crest
😤😤
stable nymph
ong ts shi aint nothin to me
stable nymph
watch me get a 50 or sum
misty crest
50 more than zero
devout snowBOT
quaint citrus
why do triple product if u can do log diff ? clearly not chad
misty crest
"pick a random card from it"
frozen fractal
$$ y=u^3+4 $$
$$ u=x^2+2x$$
$$ \text{Use chain rule. }\frac{dy}{dx} = ? $$
woven radishBOT
Astro648
winter torrent
$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$
woven radishBOT
hayley is not layla
woven radishBOT
Astro648
woven radishBOT
Astro648
frozen fractal
Could someone please help me figure out how to get to this answer?
winter torrent
trying to figure out how you got yours
woven radishBOT
Astro648
frozen fractal
I may have screwed up 😭
winter torrent
is there a reason you expanded it out
winter torrent
it was factored to begin with i think
woven radishBOT
Astro648
woven radishBOT
Astro648
woven radishBOT
Astro648
frozen fractal
But the answer is missing an x on the outside
It's the exact same except the ( 6x ) in mine is a ( 6x^2 ) in the answer key
woven radishBOT
Astro648
frozen fractal
@winter torrent do you know why it ended up like this?
sorry for taking so much of your time 😭
winter torrent
$(x^2 + 2x)^2 = x^2\cdot(x+2)^2$
woven radishBOT
hayley is not layla
winter torrent
,tex .exp rules
woven radishBOT
hayley is not layla
winter torrent
distributivity
frozen fractal
**hayley is not layla**
Ohhhh
wait
Yo i got the right answer finally
thank you bro @winter torrent
🙏 have a good day
.close
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thorny raft
Ok so we know that the proportion of people on a website that click a link has a beta distribution with alpha = 8 and beta = 1, and we know the distribution has a mean of 0.89. If 1500 people visit the website, we need to know what the expected number of people who click the link is.
Somehow it's not 0.89 * 1500, so I'm not sure what it would be.
devout snowBOT
Ok so we know that the proportion of people on a website that click a link has a...
still elk
Ok so we know that the proportion of people on a website that click a link has a...
I don't understand how a distribution describes the probability of a probability. Anyway, have you considered if this could turn into a binomial distribution problem? That's what it looks like to me.
because 1500 people is 1500 individual trials, and success is clicking and failure is not.
thorny raft
hmm I wonder if we could treat the mean like a probability for a binomial
lemme try
wait
the mean of a binomial distribution is n * p lol
so it's the same
still elk
Yeah I realised but I thought you were doing something sophisticated
thorny raft
yeah idk, either there's something special about the beta distribution that makes the 1500 visits not independent, or the website is buggin
<@&286206848099549185> this one is stumping me a bit
nvm I'm dumb, I had calculated the mean earlier and forgot I rounded it when i inputted it, since it was correct I treated it like a given
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coral patrol
why can't t = -2? or any negative numbers?
devout snowBOT
why can't t = -2? or any negative numbers?
coral patrol
when i plot it in geoalgebra, the minimum t value is 0
thin basin
What does the angular bracket mean?
thorny raft
why can't t = -2? or any negative numbers?
I mean it probably can be negative but it's just being squared
but if it's greater than 2 it will make the square root negative
vast drift
i think u are finding minimum t^2 value
not minimum t value
from your geogebra graph
coral patrol
when i set t = -1 to t = 0
vast drift
it should be fine for any t as long as |t| <=2
wicked turtle
if you parameterize using both negative and positive values then you're gonna move in both directions along the line segment, probably not what you want
coral patrol
so when i parameterize something like this
i dont want to move both directions, so i just cut it in half?
wicked turtle
yea if you just want to make one pass in one direction then either do -2 to 0 or 0 to 2
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fresh basin
someone help me with 3-5.
devout snowBOT
someone help me with 3-5.
dapper egret
where are you stuck?
fresh basin
where are you stuck?
is this right?
dapper egret
perfect
woven radishBOT
ren
dapper egret
no you start by dividing
fresh basin
yea
dapper egret
5x³ with x ²
fresh basin
exactly
dapper egret
i mean 5x²
obsidian nebula
yes
fresh basin
then we multiply 5x^2 to x and 3?
obsidian nebula
yes
obsidian nebula
yes
fresh basin
obsidian nebula
you need to keep the minus sign infront of 18
obsidian nebula
and the powers doesn't add up
obsidian nebula
what does 3 multiplyed by 5x^2 gives you
obsidian nebula
yes 👍
fresh basin
fresh basin
okay
sand dove
be careful with parentheses
if you want to cancel -18x^2
you do +18x^2 and not -18x^2 again
fresh basin
fresh basin
fresh basin
but yes you might need to add another minus sign before 18x^2
which 18x^2?
obsidian nebula
which 18x^2?
the second one
obsidian nebula
yes
fresh basin
okay can u help me with #4 and #5?
obsidian nebula
yes
fresh basin
obsidian nebula
yes
fresh basin
obsidian nebula
no wait
obsidian nebula
when you multiply x by 37 you multiply 4 by 37 as well here
fresh basin
when you multiply x by 37 you multiply 4 by 37 as well here
yea
obsidian nebula
yes?
obsidian nebula
what do you get by multiplying x and -4 by 37
fresh basin
37x -148
obsidian nebula
put that down
fresh basin
wait im also confused with how i got -27x + 64x
obsidian nebula
thats from your previous subtraction
-27x - (-64x)
personnally I would just write it as one number cuz it can be confusing
fresh basin
is this right
obsidian nebula
yes
fresh basin
-27x - (-64x)
oh so i just brought both numbers down?
obsidian nebula
yes
fresh basin
but why
obsidian nebula
no as in rather in writing (-27x + 64x) -36 just write 37x -36
fresh basin
okay
last onee
#5
wait for #5 we have to organize it right?
@obsidian nebula
obsidian nebula
not necessarily, you can still do it but you might have to keep in mind of the powers as you will subtract even powers
you won't be able to just bring down the number every time
obsidian nebula
yes
because its different powers you will have to bring down seperately
so you should have -x6 -x5
obsidian nebula
yes
obsidian nebula
should be negative 2x4
obsidian nebula
this should ve negative
You have to multiply negative number by a positive number to get a negative number
obsidian nebula
you're subtracting a negative
it will become adding
rich dagger
Can someone help me?
devout snowBOT
Can someone help me?
rich dagger
I need to determine the radius, and need to get 2 values from the equation here. However, I can't get it resolved on a cas tool. Are there any others?
winter patrol
use . for decimal points
devout snowBOT
@rich dagger Has your question been resolved?
winter patrol
try wolfram
rich dagger
okay i try wait
rich dagger
try wolfram
but do you get a response from it when you try
Not work
<@&286206848099549185>
devout snowBOT
rich dagger
Eh
supple knot
What is the definition of a radius for a cubic polynomial
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Available help channel!
rich dagger
What is the definition of a radius for a cubic polynomial
What does this have to do with the answer…
devout snowBOT
What does this have to do with the answer…
rich dagger
I know the cas tool can figure it out, but I must be typing wrong.
supple knot
I need to determine the radius, and need to get 2 values from the equation her...
You're asking about radius
If you can't define radius, how can anyone tell you how to determine the radius
rich dagger
You're asking about radius
Yeah, I'll probably figure that out, but how do you clean the piece out?
I have the answers to the 2 x values, but need the intermediate calculation itself.
rich dagger
What does "clean the piece out" mean
I mean, solving the equation
rich dagger
Answer to what question?
The equation as you can see in the picture. How to solve it?
rich dagger
Also what is radius
Yessss
After solving the equation, we will get these answers: x = 2,934008 v x = 12,92806
But I just need to understand how to solve it first.
supple knot
After solving the equation, we will get these answers: x = 2,934008 v x = 12,928...
Are you finding the roots
rich dagger
Are you finding the roots
Yes, also called the limits.
How do you get them from the equation in the picture?
@supple knot are you using cas tool for that?
woven radishBOT
rich dagger
Shall we fix that?
The equation is in the picture
r(x) = -0,0029x^3 +0,069x^2 - 0,33x + 2,9 @supple knot
supple knot
use . for decimal points
.
supple knot
It doesn't work when I do it. Can you try?
Show your attempt
supple knot
,w roots x^3 - 1.4x^2 + 15
Following this message format
rich dagger
You have extra r(x)
What? You just have to elaborate on that, what am I doing wrong?
@supple knot
supple knot
What? You just have to elaborate on that, what am I doing wrong?
Extra means remove it
devout snowBOT
@rich dagger Has your question been resolved?
supple knot
no
rich dagger
Should I put it together?
supple knot
if you can't even copy paste, i don't know how to help
rich dagger
if you can't even copy paste, i don't know how to help
Yes, but I don't understand how to copy paste it?
I don't know how it should be?
Can anyone help me figure this out? WE just have to work out the equation?
<@&286206848099549185>
rich dagger
omg..
Okay, so how to solve the equation:
r(x) = -0,0029x^3 +0,069x^2 - 0,33x + 2,9
After solving the equation, we will get these answers: x = 2,934008 v x = 12,92806
winter patrol
that function doesn't have anything close to those roots you mentioned
and
use . for decimal points
supple knot
<@&268886789983436800> spam nonsense
devout snowBOT
@rich dagger Has your question been resolved?
rich dagger
that function doesn't have anything close to those roots you mentioned
Well, that's what you have to get?
I found out about it from my friends.
winter patrol
!original
devout snowBOT
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.
crude wasp
i realise this is a language thing, but most tools use . as a decimal point instead of ,
so you'll have to type 0.0029x^3 + 0.029x^2 + 0.33x + 2.9 instead
devout snowBOT
@rich dagger Has your question been resolved?
crude wasp
,w 0.0087x^2 + 0.138 - 0.33
woven radishBOT
rich dagger
no
huh?
I get this
These are the answers I was waiting for a long time to get answered about…
@crude wasp
I have to find the extreme points.
Local and maximum point
crude wasp
oh u missed a - sign in the msg up there
rich dagger
oh u missed a - sign in the msg up there
What have I missed?
crude wasp
0.0087x^2 + 0.138 - 0.33 = 0
as in u missed off a - sign in ur msg up there
rich dagger
as in u missed off a - sign in ur msg up there
Yes, but otherwise it's true, isn't it?
crude wasp
yh
devout snowBOT
@rich dagger Has your question been resolved?
strong igloo
why is it that
d/dx {0 if x = 0, x sin(1/x) if x!=0 is undefined when x=0? We can apply the squeeze theorem via -|x| <= xsin(1/x) <= |x| and then take the limit on both sides to get 0.
spiral geyser
why is it that
d/dx {0 if x = 0, x sin(1/x) if x!=0 is undefined when x=0? We ...
The limit at x = 0 is defined, but the derivative isn't
strong igloo
I think I just realized my mistake. I should be doing the limit of the difference quotient on -|x| when I'm only doing the limit on -|x|
wait so then
nvm i thin i got it
!close
or dont
.close
onyx glen
what does it mean when theres a x>0 and what should i subsitute
devout snowBOT
what does it mean when theres a x>0 and what should i subsitute
wise storm
what does it mean when theres a x>0 and what should i subsitute
not sure without more context but basically ln(x) isn't defined for x<=0
dapper fable
verbal coral
devout snowBOT
safe knoll
cant u use flemmings right hand and left hand rule for those?
verbal coral
cant u use flemmings right hand and left hand rule for those?
yeah im having trouble applying that
safe knoll
right hand for the motion of charges and left hand for force
verbal coral
bro whenever i try using the right hand rule it seems like im throwing gang signs
but what i think it is that the charge is moving left and force is out of the page
safe knoll
but what i think it is that the charge is moving left and force is out of the pa...
moving left?
current is going left
field is into the page
motion of particles ?
safe knoll
force is down btw
verbal coral
so down is into the page?
verbal coral
oh
safe knoll
bro im getting charges are moving up wards
ok these rules are dumb , let me try again wait
verbal coral
ya i asked ai to check and it said upwards too but one said downwards
safe knoll
ya i asked ai to check and it said upwards too but one said downwards
im getting charges motion upwards while force downwards
safe knoll
are those the only options?
verbal coral
yes
safe knoll
i would choose the last one
verbal coral
how are the charges moving right?
safe knoll
how are the charges moving right?
they are not
but charges flowing up isnt given , its 2nd or last
safe knoll
u can check ur self with flemming left hand rule
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Available help channel!
small meadow
I need help for this question, I don't understand what to do.
devout snowBOT
I need help for this question, I don't understand what to do.
lament tide
find its roots
lament kraken
So when f(x) is 0 there is an x intercept
lament tide
equate with 0
lament kraken
So what x makes f(x) 0
small meadow
ok
lament kraken
You can just try answer choices
small meadow
Oh its one of those that you can plug in and see
but how will I know if it is the right one?
lament kraken
Um yeah if you cant factorise the cubix
lament kraken
but how will I know if it is the right one?
Try each of the answer choices in f(x) and see which one makes f(x)=0
That's the answer
small meadow
Try each of the answer choices in f(x) and see which one makes f(x)=0
ok thank you
thank you so much
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lavish blade
can anyone help me on this?
devout snowBOT
can anyone help me on this?
lavish blade
please help me someone
like isnt it just this?
cause i dont get what they are asking
devout snowBOT
@lavish blade Has your question been resolved?
lavish blade
it says its still wrong
im guessing they want an y=ax^p
but not exactly sure how to format that
devout snowBOT
@lavish blade Has your question been resolved?
devout snowBOT
@lavish blade Has your question been resolved?
wheat pawn
im guessing they want an y=ax^p
they indeed want that form. so you'd write y=2x^3. You wrote the particular case instead of the general case
lavish blade
how do you close the help forum?
devout snowBOT
lavish blade
thanks
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Available help channel!
dense fable
Hey guys I need some clarification, I had a test today and the last question was “A water drop has a volume of 4 • 10^-6 then how many water drops is it in a glass of 100 ml). I answered with 10000 water drops since I divided 4 by 4 and added ^4 to 10^-6
devout snowBOT
Hey guys I need some clarification, I had a test today and the last question was...
twilit comet
4*10^-6 what
mL? L?
and your anwser would be incorrect anyway
the correct answer would be (100 mL)/(4 * 10^-6 whatever unit they used)
i.e. 25 * 10^7 mL/(unit they used)
dense fable
I was wrong I realized it now actually
twilit comet
if you're done, you might wanna close this channel (.close)
devout snowBOT
@dense fable Has your question been resolved?
left pulsar
Can someone explain why sin(arcsin(5)) is not 5?
devout snowBOT
Can someone explain why sin(arcsin(5)) is not 5?
upper crescent
The domain of ( \arcsin(x) ) is ( [-1, 1] ). This means that ( \arcsin(x) ) is only defined when ( x \in [-1, 1] ).
woven radishBOT
Trenton
upper crescent
The range of ( \arcsin(x) ) is ( \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] ), so ( \arcsin(x) ) returns an angle ( \theta ) such that ( -\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} ).
woven radishBOT
Trenton
spiral geyser
meaning (\sin(\arcsin(x)) = x) if and only if (x \in [-1, 1]) and (\arcsin(\sin(x)) = x) if and only if (x \in [-\pi/2, \pi/2])
woven radishBOT
Invariance
upper crescent
In fact, since the domain of the arcsine function is ( [-1, 1] ), the input ( 5 ) is outside the domain of ( \arcsin(x) ). Therefore, ( \arcsin(5) ) is undefined.
woven radishBOT
Trenton
upper crescent
So in short, it does not make sense.
spiral geyser
Conceptually, the problem here is that sin(x) has many duplicate values. Here's y = sin(x) and it's "inverse" x = sin(y):
but the blue curve is not a function
so we restrict arcsin(x) to a specific portion
or more simply: (\sin(0) = \sin(2 \pi) = 0), so does (\arcsin(0) = 0) or (\arcsin(0) = 2 \pi)? it can't be both
woven radishBOT
Invariance
uncut crow
when is invariance getting green
vivid topaz
hello
vivid topaz
Find an equation of this parabola. Then find the focus and the directrix.
i need help for this
spiral geyser
i need help for this
can you see where any interesting points are on the parabola?
you can see where both of the roots are
does that tell you anything?
spiral geyser
the equation is (x-2)²/2 -2 no ?
yeah, that's right
spiral geyser
did your teacher give you any information on how to do it?
vivid topaz
no
vivid topaz
how do u know that is the focus point
little gate
oh wait
its wrong
wait
here
you need to know the value of p k and h
C is the focus point
vivid topaz
how do i get them
little gate
u need to know the function first
vivid topaz
yes is (x-2)²/2 -2
devout snowBOT
@vivid topaz Has your question been resolved?
blazing crest
how does 1d work?
devout snowBOT
how does 1d work?
blazing crest
sullen island
which part of the answer specifically ? there's at least 3 different things going on there
@blazing crest
devout snowBOT
@blazing crest Has your question been resolved?
blazing crest
which part of the answer specifically ? there's at least 3 different things goin...
I dont understand why i would need to determine a the detA
And after then idk what they do in the third row of the answersheet
sullen island
they're using the fact that $A^{-1} = \frac{1}{\det A} \text{adj}(A)$, where $\text{adj}(A)$ is the cofactor matrix of A, transposed
woven radishBOT
aPlatypus
sullen island
so $(A^{-1}){3,1} = A^{-1} = \frac{1}{\det A} (\text{adj}(A)){3,1}$ but $(\text{adj}(A)){3,1}$ is just the cofactor of A at 1,3, so $C{1,3}$
woven radishBOT
aPlatypus
blazing crest
😂
sullen island
solid osprey
find all positive integers n such that (n^6-n^5+n^4-n^3+n^2-n+1)/(n^2+n+1) is also a positive integer
devout snowBOT
find all positive integers n such that (n^6-n^5+n^4-n^3+n^2-n+1)/(n^2+n+1) is al...
solid osprey
wolfram shows that remainder is 1, so n^2+n+1=1 for it to filly divide, which is n=-1 or n=0 which arent positive integers, so is the answer 0?
uncut crow
makes sense to me
the second alternate form makes it pretty clear
1/(n^2 + n + 1) is not an integer if n >= 1
devout snowBOT
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Available help channel!
oblique mulch
I’m not sure how to go about this. How do I find the mass of one slice and how to find the force for one slice?
devout snowBOT
I’m not sure how to go about this. How do I find the mass of one slice and how t...
@oblique mulch Has your question been resolved?
devout snowBOT
@oblique mulch Has your question been resolved?
solid osprey
for positive integer number k and n>=2. prove that (n-1)^2 | n^k-1 if and only if n-1 | k
devout snowBOT
for positive integer number k and n>=2. prove that (n-1)^2 | n^k-1 if and only i...
solid osprey
status 1
thin basin
Skill issue 
sand dove
for positive integer number k and n>=2. prove that (n-1)^2 | n^k-1 if and only i...
k a real number??
thin basin
I think Integer
solid osprey
er whoops i accidentally translated directly
devout snowBOT
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).
solid osprey
hmm i swear ive seen you somewhere
thin basin
for positive integer number k and n>=2. prove that (n-1)^2 | n^k-1 if and only i...
Let's say that k = 10 and n= 3
n-1 divides k
But 3¹⁰ is not divisible by 2²
Or have i misunderstood the ques?
sand dove
yeah so n-1 | (n^k-1+n^k-2+...+n+1)
can you do division algorithm like last time
solid osprey
wdym
sand dove
remember when you had n^2 + 2n + 2 | n^3 + ...
crude wasp
for positive integer number k and n>=2. prove that (n-1)^2 | n^k-1 if and only i...
as an aside, if you know lifting the exponent this problem is pretty easy and is basically directly LTE
solid osprey
i dont :D
crude wasp
i love lifting the exponent <3
crude wasp
should i learn it
u could
what sort of level of olympiad r u currently aiming for?
basically from my UK experience
it becomes quite useful for like early international competitions/tsts level
solid osprey
maybe im around amc10 rn, im trying to go to amc12/aime ish if that made sense somehow lmao
crude wasp
maybe im around amc10 rn, im trying to go to amc12/aime ish if that made sense s...
unfortunately i have no clue how the american system works so i can't help u lol
basically if ur kinda on the level of IMO P1/P4 then i think it would be beneficial to learn it
solid osprey
basically if ur kinda on the level of IMO P1/P4 then i think it would be benefic...
nah i can only dream of doing my first imo question alone 😭
alright then im going to go to sleep, byee
thanks
.close
devout snowBOT
crude wasp
nah i can only dream of doing my first imo question alone 😭
ah right ic
in which case i'd say it's probably quite early to learn it
when u get more experience, it'll be worth slowly picking up facts like these
crude wasp
alright then im going to go to sleep, byee
gn!
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Available help channel!
fervent hedge
just wondering if i did my chain rule correctly,
devout snowBOT
just wondering if i did my chain rule correctly,
fervent hedge
looked up answer and they got this
not sure if its the same (?)
and if it is how do i convert it to that form
vast drift
looked up answer and they got this
u made a small algebraic error
on the right column of your working out, first line
to the 2nd line
knotty sage
just wondering if i did my chain rule correctly,
1/2(1+e^x)^-1/2=?(1+e^x/2)^-1/2
vast drift
u made an algebraic error which detracted u from the right answer
vast drift
not quite what i was referring to
you shoulddn't have included 1/2 into your power of -1/2
should have kept it ouside the brackets
which would have been correct
knotty sage
so like this it is okay?
it is acceptable but some people want it simplified
knotty sage
yep
fervent hedge
then the 2 at the bottom since its divided by 2
knotty sage
since its to -1/2
but it’s negative
knotty sage
So what you are referring to should be
1/(2sqrt[1+e^x])
fervent hedge
yuh
devout snowBOT
@fervent hedge Has your question been resolved?
midnight seal
do it by either using substitution or by parts
I hope you remember the formula of integration by parts
fervent hedge
wait no
its asking for
square root of
oops
that equal shoudlnt be there
this is th ewhole integral
its the surface area formula
midnight seal
bruh
midnight seal
great
devout snowBOT
@fervent hedge Has your question been resolved?
fossil locust
they somehow turn the top in 2 + e^x)^2
if you let $e^x = u$, you have $4 + 4u + u^2 = (u + 2)^2$
woven radishBOT
higher's secret twin brother
devout snowBOT
fervent hedge
if you let $e^x = u$, you have $4 + 4u + u^2 = (u + 2)^2$
ty
devout snowBOT
Available help channel!
lethal holly
🤔 how would we integrate over the surface of a sphere?
devout snowBOT
🤔 how would we integrate over the surface of a sphere?
lethal holly
what does it mean to do that?
acoustic leaf
for the ordinary riemann integral, we cut up an interval of the number line into sections, evaluate the function at a point in each of those sections, multiply the function value by the size (length) of the section, and add up for every section. this gives the riemann sum, the integral is the limit of that as the sections get smaller and smaller.
for a surface integral we again divide into sections, evaluate the function at each section, and add up. the only difference is that we instead multiply by the surface area of each section
fossil locust
also there are different types of integrals we can do on 3D surfaces!
we can measure the flux, like the amount of a gas passing in - gas passing out
and we can integrate the flux over the sphere, by adding up many infinitesimally small rectangular regions on the surface
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olive raptor
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olive raptor
for this question, i've approached it two different ways and obtained 2 different answers
the first way i've tried is to say that z = a + bi and then evaluate, but this comes to 4 values of a
then i've triend using exponential form, but these answers seem wrong too as when substituted in, dont satisfy the statement
polar chasm
the first way i've tried is to say that z = a + bi and then evaluate, but this c...
How so?
olive raptor
i manage to get a^4 - 3a^2 -1 = 0
fossil locust
i manage to get a^4 - 3a^2 -1 = 0
right, but by assumption a and b are real numbers
olive raptor
right, but by assumption a and b are real numbers
yes, thats what i've missed
fossil locust
so there are only 2 real values of a
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polar chasm
,w a^4 - 3a^2 -1 = 0
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old timber
Hello. My assignment was to prove by contradiction that if m² is divisible by 7 then m is divisible by 7. I'm not sure how to do that
devout snowBOT
Hello. My assignment was to prove by contradiction that if m² is divisible by 7 ...
supple knot
proof by contradiction is a simple counterexample
although this one i'm not sure if it's even false
old timber
although this one i'm not sure if it's even false
The statement itself should be true but I have to prove it
old timber
And m² is still divisible by 7?
supple knot
well you'll contradict m^2 is divisible by 7
supple knot
if m is not divisible by 7, then m is not congruent to 0 mod 7
old timber
if m is not divisible by 7, then m is not congruent to 0 mod 7
I haven't been taught what 0 mod 7 is
brisk panther
Hello. My assignment was to prove by contradiction that if m² is divisible by 7 ...
if m^2 is divisible by 7 but m is not divisible by 7, then m is either congruent to 1,2,3,4,5,6 mod 7
m^2 is congruent to 1^2, 2^2, 3^2, ... mod 7
see if any of these are divisible by 7
old timber
m^2 is congruent to 1^2, 2^2, 3^2, ... mod 7
what does mod 7 mean tho
brisk panther
what does mod 7 mean tho
the remainder when you divide by 7
for example 15 is congruent to 1 mod 7
because 15 / 7 has a remainder of 1
old timber
the remainder when you divide by 7
Ohh
old timber
m=7 something +1 to 6?
brisk panther
then m^2 is congruent to n^2 mod 7
old timber
Ok let write this out and see if it's what I was supposed to do I guess
brisk panther
m=7 something +1 to 6?
then check the remainder when you divide m^2 by 7
for example
m/7 has a remainder of 1
so
m^2/7 has a remainder of 1^2 = 1
check each case
if you get a remainder that is a multiple of 7
old timber
So it will have a remainder each time that can't be a multiple of 7
brisk panther
then m^2 is divisible by 7
old timber
I see
brisk panther
yes
old timber
I don't think I was supposed to do this given that I wasn't taught all this
But this is pretty much flawless fr
brisk panther
hmm
then you can use the fact that 7 is a prime number
if m is not divisible by 7
then m = p1 ^ a * p2 ^ b * p3 ^ c ...
old timber
Yeah that's what I was trying to do originally and it's obvious but idk how to write that out
brisk panther
where p1, p2, p3 are the prime factors
old timber
Yeah that's what I was trying to do originally and it's obvious but idk how to w...
Also I don't remember the original wording of the question so if it mentions m being a rational number
brisk panther
and a, b and c are the powers
brisk panther
Also I don't remember the original wording of the question so if it mentions m b...
i mean divisibility wont make sense if m isnt an integer right
old timber
Also I don't remember the original wording of the question so if it mentions m b...
Cant I do something like
brisk panther
then m = p1 ^ a * p2 ^ b * p3 ^ c ...
do you understand this
old timber
where p1, p2, p3 are the prime factors
Yeah and it will end up with 7 somewhere
brisk panther
not really
you see m isnt divisible by 7
that means none of these prime factors are 7
or powers of 7
old timber
you see m isnt divisible by 7
yeah but m² is and that's just mxm
brisk panther
now if you square both sides
the exponents a
b
c
will become
2a
2b
2c
right
old timber
This seems even more out of what I am meant to write 😭
brisk panther
thats just notation
what im saying is that
m is a product of prime factors
none of these are 7
then m^2
also is a product of prime factors
old timber
and one of those is 7
brisk panther
but since 7 is a prime number
you cant multiply to prime numbers to create 7
so if m isnt divisible by 7
then m^2 cant be
brisk panther
yes because 7 is a prime number
the prime numbers in m^2
cannot multiply to create 7 or a multiple of 7
old timber
😭🙏
old timber
😭🙏
Idk how to notate this and stuff but that's not demanded of me either
I can number them m1 and stuff for each case I guess?
old timber
you forgot the 2ab term in (a+b)^2
Ohhh
brisk panther
also
old timber
Yeah I'm dumb
brisk panther
when you divide both sides by 7
notice that
the first term
7^2a^2
is divisible by 7
and the 2ab also has a factor of 7
so you can ignore it
and focus on the remainder squared
old timber
and the 2ab also has a factor of 7
Bro idk wtf I was meant to use
As proof
But this shit is far more complicated than what I thought
Thanks anyways either of these should work I guess
I just wonder wtf the intended solution was here
old timber
and focus on the remainder squared
Ok so I have another one which is proof by conjunction which should be easier
basically 1+4+7+...+(3n-2)=3n²/2-n/2
Imma try that
fluid flax
Decompose the following matrix into the sum of a symmetric matrix S and an antisymmetric matrix T
devout snowBOT
Decompose the following matrix into the sum of a symmetric matrix S and an antis...
fluid flax
I don't understand the statement
supple knot
A = S + T. Find S such that S = S transpose and T = - T transpose
observe that (A + Atranspose) is symmetric
fluid flax
oh ok i got it, thank you!!
but i have another problem
Consider the matrices according to the angles of the interval [0,2π).
- Discover if the product of M i N ́is commutatiu.
b. Explain what relationship there is between N i N^−1
<@&286206848099549185>
supple knot
well use the definition of commuting to do the multiplication and see
fluid flax
can u give me one more clue, im lost
supple knot
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tawny spoke
Hello I’m a bit stuck - I’m not sure why the three expressions are equivalent
tawny spoke
Is F_y(y) = F_X^2(y)? I’m not certain what the subscripts denote either
<@&286206848099549185>
supple knot
Is F_y(y) = F_X^2(y)? I’m not certain what the subscripts denote either
Yes because Y=X^2
sterile flame
I need help on whether these two quadrangles are similar in any scale or nah? I have some geometry knowledge but a total solar eclipse on my mind has come, while I need this to move onto with my other problems. Any help would be apreciated
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I need help on whether these two quadrangles are similar in any scale or nah? I ...
sterile flame
from other info the angle is a random angle and the two lines on the edges are parallel to each other
the yellow intersect line is at a 90 degree angle from the bottom part of the angle
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austere echo
They are definitely similar, not only that they are cyclic quadrilaterals as well
inner zenith
They are definitely similar, not only that they are cyclic quadrilaterals as wel...
and why is that?
(sorry im not the one asking but just curious)
austere echo
All of them have 2 opposite 90 degrees angles with an angle of defined size in between
So basically all their angles are equal (a-a-a)
@inner zenith The cyclic quad part is because two of their opposite angles are 90 degrees, which have the sum of 180
inner zenith
So basically all their angles are equal (a-a-a)
equal angles doesnt mean similar figures
for quadrilaterals
austere echo
yeah, you need the lengths as well
inner zenith
ye
austere echo
why did I forget that
inner zenith
I did too and then I thought that it couldnt be that simple
austere echo
Well in that case we can pull the yellow line back and make them not similar
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restive river
hi
restive river
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steep fractal
How do I do this?
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steep fractal
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cyan axle
I was doing this problem but ended up dead end
That’s where I ended but idk where I went wrong, I’ll write out my work again so it’s more readable
I think I went wrong somewhere after this
Shoot
It’s taken
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hidden sapphire
I am doing the factor theorem/integral zero theorem.
one example question is: Factor x^4 + 3x^3 - 7x^2 - 27x - 18.
I know i need to make the equation equal zero by using a factor of -18 and inputting it as the x-value which would be +/- 1,2,6,9,18
Instead of doing trial and error is there a method so I do not need to input those into the equation 1 by 1
if its confusing i can send a picture to clarify
solid hull
I am doing the factor theorem/integral zero theorem.
one example question is: ...
I thought 3 would also be a factor here
hidden sapphire
I thought 3 would also be a factor here
oops, yes it is
solid hull
from my understanding there isn't a faster way to do it without using a calculator/other supporting material
But that's only from my teaching
hidden sapphire
i see, yea ive been looking everywhere i cant seem to find one either
graceful cosmos
It's any factor of 18, over any factor of 3. So note ±1/3, ±2/3 are also in there
hidden sapphire
so you're saying +/- 1/3, 2/3, 3/3, 6/3, 9/3, 18/3?
graceful cosmos
It can be smart to "approximate the graph" to find roots. It's kind of like 3x³ - 18, which has a root at cuberoot(6), so searching near there is a good start
graceful cosmos
so you're saying +/- 1/3, 2/3, 3/3, 6/3, 9/3, 18/3?
Yes, but you've got most of those already
graceful cosmos
Doing this can be very difficult
hidden sapphire
yes, but this or a calculator seem to be the quickest methods though
this rly helps tho
thank you
graceful cosmos
@hidden sapphire
I'm so sorry, I didn't see the x⁴ at the start. I was wrong, don't include the 3 in the denominators
It's all factors of 18 over all factors of 1
hidden sapphire
its totally fine, but what difference does the exponent of the leading coefficient make?
graceful cosmos
What I said would have been true if it were 3x³ - 7x² - 27x - 18 like I misread
hidden sapphire
for instance what if it was x^2?
graceful cosmos
None. All that matters is the leading coefficient, and the constant term
hidden sapphire
so if it was 2x^4 then it would be all factors of 18 over 2?
i see
ill go test it out rn on some practice questions
thank you for the help!
.close
plain turtle
Sorry just need to confirm something, online isn't giving the right answer. Are 7a and 5. The same process ?
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Sorry just need to confirm something, online isn't giving the right answer. Are ...
novel pivot
The lease contract terms are as follows: Annual lease = P1.5M, 1st payment upon the start of the lease, annual lease increase by 10% each for 4 years. A single lump sum payment is acceptable at the beginning of the lease based on an interest rate of 14% compounded semi-monthly. Find the amount of this lump sum.
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spiral scaffold
Sorry just need to confirm something, online isn't giving the right answer. Are ...
Technically yes. For 5, they're asking you to show the work using the definition of inverse function, ie, y := f(x) = arcsin(x) implies sin(y) = x and then you differentiate both sides and simplify.
For 7a, you can use the result from 5 and just apply chain rule (x -> x/2)
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sly willow
Can someone help me solve this?
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Can someone help me solve this?
spiral scaffold
Can someone help me solve this?
You tried anything yourself?
sly willow
You tried anything yourself?
im not that good at math becuase i have dyslexia , so im trying to help my friend With these as much as i can, im not even sure where to start hahaha
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muted lark
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neon shard
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eager nova
!noans
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neon shard
Okay help me on how to solve then
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orchid torrent
claim
orchid torrent
I would like to check this first
"How many ways can the letters in the word TELEPHONE be arranged in a row"
answer is 9!/3! right?
solid osprey
lools correct
orchid torrent
okay so what if I change it so that the question is "how many ways can the letters in the word TELEPHONE be arranged if the letters TO must remain next to each other"
is it as simple as 8!/3! ?
winged bone
is it as simple as 8!/3! ?
- 2 if im not wrong
as TO can be arranged as TO and OT
two ways
orchid torrent
what is it (8!÷3!)÷2! or (8! ÷ 2!)÷3! ?