hmmmmmmmm
#help-27
stuck field
stuck field
I see.
worthy quest
doesn't jive with the wording of the problem imo
i'm just going to report it for incorrect answer and move on
thanks for the help 
.close
soft shore
find b/a where 2a^2=(a+b)^2
devout snowBOT
find b/a where 2a^2=(a+b)^2
woven radishBOT
soft shore
<@&286206848099549185>
devout snowBOT
@soft shore Has your question been resolved?
devout snowBOT
@soft shore Has your question been resolved?
devout snowBOT
@soft shore Has your question been resolved?
main gull
find b/a where 2a^2=(a+b)^2
FYI, I can help you with this
soft shore
soft shore
a^2=2ab+b^2
soft shore
ohh
main gull
Now quadratic formula
main gull
Hopefully from there, you should get it
delicate galleon
is this assumption correct?
$gcd(2a,2b) = 2 \implies gcd(a, 2b) \leq 2$
woven radishBOT
Crown
devout snowBOT
@delicate galleon Has your question been resolved?
delicate galleon
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plucky solar
Can someone explain how to convert 31,680 ft and 5 in to miles? I know the answer is 6.00094696969697 but I don't know how to get there.
devout snowBOT
Can someone explain how to convert 31,680 ft and 5 in to miles? I know the answe...
supple knot
1 mile = 5280 feet
plucky solar
thanks
supple knot
.close
devout snowBOT
devout snowBOT
Available help channel!
restive river
I sketched S but I'm stuck on the second part of the question
devout snowBOT
I sketched S but I'm stuck on the second part of the question
pseudo basin
@restive river z2 is the point in S furthest away from the origin
for z1, imagine an idealized, perfectly straight windshield wiper hinged at the origin and rotating counterclockwise; z1 is the first point in S that it hits.
devout snowBOT
@restive river Has your question been resolved?
restive river
devout snowBOT
restive river
Thought of factoring 324 as 2^2 * 3^4 (since 324 is in every pair) rewrite the equation to see where's going but can't see anything
or maybe highlight the common factors?
mild marsh
I can only see completing the square as $324 = 18^2$
woven radishBOT
वाह्य
mild marsh
$a^2 + b^2 = (a-b)^2 + 2ab$
woven radishBOT
वाह्य
carmine jacinth
search up sophie-germain identity
carmine jacinth
I can only see completing the square as $324 = 18^2$
If this doesn't work
restive river
But if I wanted to use sophie-garmain identity I should change 18^2 to x^4
woven radishBOT
felipee
mild marsh
$10^4 = (10^2)^2$
woven radishBOT
वाह्य
mild marsh
search up sophie-germain identity
I think you need this tbh
woven radishBOT
felipee
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
restive river
still leaving 10^2
restive river
I think you need this tbh
okay
I'm a bit confused how to use the method
knowing that I have to transform 18^2 to x^4
(3^2 * 2)^2
carmine jacinth
324/4=81=3^4
restive river
Oh....
Sorry for that I'm dumb
okay so I did the formula
and so, I have to do it with the 5 pairs and simplify everything?
restive river
Noticed that right now
I'll do the latex 1 minute
Actually nevermind, too big
1 question
4*3^4 = (2b^2) = (2.3^2)
or is it (3^4)^2
carmine jacinth
Where did you get 4*3^4=(2b^2) from?
carmine jacinth
Right so you would want to find the b term from 4*3^4 and plug that into (a^2 + 2b^2 - 2ab)
carmine jacinth
Sorry I'm not exactly sure what you're asking
Are you asking if it's (2b)^2 vs 2(b^2)?
restive river
${2b^{2} = 2.3^{2} or 2.(3^{4})^{2}}$
woven radishBOT
felipee
restive river
I'm asking if a^4 will stick to it
restive river
okay
carmine jacinth
Remember that you set 4b^4=324 so b^4=81
main gull
${2b^{2} = 2.3^{2} or 2.(3^{4})^{2}}$
Are you using . as multiplication? Because I suggest not to do that, because that looks like a decimal
restive river
Oh sorry
placid rover
\cdot
restive river
thank you
placid rover
in latex
main gull
or \times
odd saddle
I still don’t know where I’m going wrong so I’d appreciate any help. I don’t even know what the max and min is 🤦♂️
devout snowBOT
I still don’t know where I’m going wrong so I’d appreciate any help. I don’t eve...
mild marsh
Maximum distance both vectors pointing in opposite directions
min distance when both pointing in the same direction
woven radishBOT
वाह्य
mild marsh
correct me if I am wrong
devout snowBOT
@odd saddle Has your question been resolved?
odd saddle
Thank you, but how would I even begin to answer it? Someone told me I should do the square length of v and w separately with cos
restive river
I choose a random integer $n$ between $1$ and $10$ inclusive. What is the probability that for the $n$ I chose, there exist no real solutions to the equation $x(x+5) = -n$? Express your answer as a common fraction.
woven radishBOT
crabbo
devout snowBOT
I choose a random integer $n$ between $1$ and $10$ inclusive. What is the probab...
restive river
my answer is that every n will have a real solution
carmine jacinth
my answer is that every n will have a real solution
and your reasoning for this?
restive river
and your reasoning for this?
thats sortof my answer
placid rover
???
Well ok, and I tell you I'm not convinced at all by your reasoning.
There is none.
Reason in a way that would leave me with no doubts there are real solutions no matter what n is.
Brute force, logic, whatever.
pseudo basin
@restive river what is the probability of an event that is guaranteed to happen?
actually wait
i think you may have screwed up since the last time you came here w/ this problem and none of us noticed
you calculated the discriminant of x(x+5) = -n, yes?
...ping me when/if you reply
devout snowBOT
@restive river Has your question been resolved?
pseudo basin
devout snowBOT
pseudo basin
.reopen
devout snowBOT
✅
slender mirage
you calculated the discriminant of `x(x+5) = -n`, yes?
@restive river when does a quadratic have no real solutions?
oak harness
Hint: It has to do with the discriminant of a quadratic
pseudo basin
they already calculated the discriminant earlier
but i think they did so incorrectly and so i'm asking them to restate what they got
just to be sure
but crabbo is intentionally refusing to provide
copper mango
shock
oak harness
f
copper mango
shock they're not posting their working / answering the question(s)
pseudo basin
genuine shock or sarcastic shock?
copper mango
genuine shock or sarcastic shock?
latter
Thought the \s was implied from the crossout.
oak harness
Thought the \s was implied from the crossout.
I mean that's how I parsed it
pseudo basin
right
devout snowBOT
@restive river Has your question been resolved?
oak harness
You can't force someone to learn 🤷
The public education system tries hard enough as it is
pseudo basin
they came here to get help
it's disrespectful on their part to completely ignore ppl trying to hep them
oak harness
they came here to get help
I wonder whether they wanted help or solutions
We'll never know for sure I guess
devout snowBOT
devout snowBOT
Available help channel!
iron cedar
I am confuse confused understanding frequency distribution and understanding contingency table
devout snowBOT
I am confuse confused understanding frequency distribution and understanding con...
crisp plume
I need help with this (I will translate if needed)
devout snowBOT
I need help with this (I will translate if needed)
gaunt quiver
so.. you're looking for the amount of value gained?
crisp plume
The percentage of value gained
I will be doing other questions so please ping me if u have anything I really need help with this one
<@&286206848099549185>
devout snowBOT
@crisp plume Has your question been resolved?
devout snowBOT
crisp plume
.reopen
devout snowBOT
✅
devout snowBOT
@crisp plume Has your question been resolved?
devout snowBOT
@crisp plume Has your question been resolved?
fresh cairn
so here's the problem, I gotta turn into a + bi
devout snowBOT
so here's the problem, I gotta turn into a + bi
fresh cairn
I used euler's formular twice
to get this for a
and this for b
my question is if I messed up the calculation or if the conceptual idea is wrong
I did euler's to the upper exponential
to get 7(cos(pi/3) + isin(pi/3))
then separated my new one into two exponentials being multiplied by each other
and did euler's again
fresh cairn
and this for b
realizing now I forgot to distribute the seven to b
cool
that'll do it
you know sometimes all I need is someone to talk out my answer to
so thanks for existing, server
.close
devout snowBOT
devout snowBOT
Available help channel!
half bolt
there are four married couples at a party, how many ways can they sit around a circular table where the couples cannot sit next to each other? i know that the amount of ways they can sit around the table without restrictions is 5040, but how do i put it where the couples cannot sit next to each other when everyone in the party as a spouse? i cannot find a way to figure it out
devout snowBOT
there are four married couples at a party, how many ways can they sit around a c...
torn vessel
Use the compliment. Figure out how many ways at least one couple is sitting together and take that away from the total number of ways they can sit
devout snowBOT
@half bolt Has your question been resolved?
tight crypt
devout snowBOT
devout snowBOT
@tight crypt Has your question been resolved?
devout snowBOT
@tight crypt Has your question been resolved?
devout snowBOT
tight crypt
.reopen
devout snowBOT
✅
devout snowBOT
@tight crypt Has your question been resolved?
restive river
<@&286206848099549185>
devout snowBOT
<@&286206848099549185>
main gull
<@&286206848099549185>
You have to wait at least 15 minutes before pinging
Also, you pinged before even asking anything
restive river
You have to wait at least 15 minutes before pinging
Also, you pinged before even...
sorry im very confused on the ssytem
can you help me tho
how can i solve this im stuck on it
h(x) = x^4-x^3+2x^2-4x-8
i got -1,0,-2,6
as the zeros
but that isnt right
i tried doing it like with quadratic formula
and it wasnt working
it keeps giving me these numbers
main gull
Can you provide your work?
main gull
You see that expression at the end, after doing synthetic division? The x^3 - 2x^2...
Apply factor by grouping
restive river
i havent been taught that
what is that
my goal is to get it into that little like criss cross thingy
that happend on nuimhber 1
but idk how
main gull
I'm pretty sure that you've been taught it, it's a factoring method for cubics
restive river
I'm pretty sure that you've been taught it, it's a factoring method for cubics
bro im being so serious idek wat cubics is
im in alg 2
my teacher doenst teach like "normal" he teaches his own way but idk how to do it
main gull
Cubics is the name of an expression that has power of 3
restive river
oh okay
main gull
Yes
devout snowBOT
Available help channel!
quasi wind
I have a few math questions that need to be done... if anyone is free can you help? (pls ping me @quasi wind )
devout snowBOT
I have a few math questions that need to be done... if anyone is free can you he...
copper mango
I have a few math questions that need to be done... if anyone is free can you he...
Dont ask to ask.
copper mango
Solution set
find the solutions to that system
then give them the largest y value.
quasi wind
find the solutions to that system
So just solve for x?
copper mango
yes.
quasi wind
Ok
copper mango
then find the largest y value.
warped crest
is this a multiple choice question
quasi wind
Where are they getting "y" from...
What do they mean by "y" though...
warped crest
they are trying to say y(x) = highest value
so solve for the equation set
what x solutions did you get
copper mango
What do they mean by "y" though...
the y value of the points of intersection..
polar oyster
y-intercept?
copper mango
nowhere did I say intercept, so no.
polar oyster
oh, so 3.782
copper mango
This should be correct right?
why do you think it's correct?
quasi wind
I graphed the equations in desmos
copper mango
Yeah but the actual point of intersection clearly isn't useful
cause they don't ask about anything quantitative
copper mango
what does the point of intersection represent here?
copper mango
what happens when revenue=expense?
quasi wind
No profit.
copper mango
yes.
quasi wind
The graph is constant
copper mango
No
quasi wind
(a perfect line)
copper mango
Still no
quasi wind
Wha
copper mango
That picture has no meaning whatsoever
quasi wind
Oh
copper mango
Nor, should you be graphing anything.
revenue = expense at the POI as I said already
so they break even at the POI.
quasi wind
revenue = expense at the POI as I said already
So yeah, I get this. The more the revenue goes past the expense, the higher the earnings.
quasi wind
so they break even at the POI.
But what does that mean?
quasi wind
Ohh
copper mango
You made back exactly how much you spent.
copper mango
yes
quasi wind
Ok
reef pebble
hello
reef pebble
so im given the function and have to find the derivative and then the value when x = 2pi/3
$$f(x)=\frac{sin(2x)}{cos(x)}$$
woven radishBOT
heep
reef pebble
i start buy doing quotient rule
$$f'(x) =\frac{cos(x)*(cos(2x) * 2 - sin(2x)*sin(x)}{cos^{2}(x)}$$
woven radishBOT
heep
reef pebble
i think plug in 2pi/3 and got -1/2 / (1/4) which is not correct
so i was wondering if my calc was right and just the angles i was incorrect with
slender mirage
.
old plank
i start buy doing quotient rule
you should prob simplify that
slender mirage
ahh
reef pebble
oh i didn't simplify i just plugged in 2pi/3 since it seemed like stuff would cancel
slender mirage
I see... You've mistaken the derivative of cos x as sin x
It should've been -sin x
reef pebble
ah so it should be
$$f'(x) =\frac{cos(x)*-(cos(2x) * 2 - sin(2x)*sin(x)}{cos^{2}(x)}$$
woven radishBOT
heep
old plank
no
slender mirage
cos times derivative of (sin 2x) - sin(2x) times derivative of (cos x)
reef pebble
im sorry
slender mirage
in numerator
old plank
$$f'(x) =\frac{cos(x)*(cos(2x) * 2 + sin(2x)*sin(x)}{cos^{2}(x)}$$
woven radishBOT
gog IGGa
reef pebble
the last sin in numerator should be negative
slender mirage
yes
reef pebble
$$f'(x) =\frac{cos(x)(cos(2x) * 2 - sin(2x)-sin(x)}{cos^{2}(x)}$$
slender mirage
not the -cos 2x
old plank
what
slender mirage
ehhh
woven radishBOT
heep
reef pebble
i copied and pasted my previous line i forgot to take the mistake out
old plank
no it should all be positive
reef pebble
wdym I think this equation is right cause if i plug in 2pi/3 in all the x
i get 4/(1/4) or -1
which on my guide says is correct
reef pebble
yeah and then the denominator gives me the negative to get -1 so all is well :D
ty for the help tonight
.close
candid sierra
Can someone explain why these are not the same...
devout snowBOT
Can someone explain why these are not the same...
candid sierra
<@&286206848099549185>
main gull
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
candid sierra
mb
leaden aurora
,rotate
woven radishBOT
leaden aurora
Write it as $ax^2+bx^2+c=0$
woven radishBOT
azeem321
leaden aurora
yh
so you can apply the discriminat
Yes
For the $x^2$ terms you can write it as $(1+m^2)x^2$
woven radishBOT
azeem321
slender mirage
which question we doing btw (@_@;)
leaden aurora
if you get imaginary solutions, it means you went wrong in your workings somewhere
last part
woven radishBOT
leaden aurora
,w 100m^4-4(m^2+1)(100m^2-20)=0
woven radishBOT
placid rover
if you get imaginary solutions, it means you went wrong in your workings somewhe...
🤔
slender mirage
Write the line eqn. m = y/(x-10) = -x/y and x^2 + y^2 = 20
placid rover
Nothing.
leaden aurora
oh
slender mirage
,w solve 100m^2 = 20(1+m^2)
woven radishBOT
leaden aurora
yh i got the above too on my calculator
It seems you went wrong somewhere with $x^2+(m(x-10))^2=20$
woven radishBOT
azeem321
slender mirage
for starters, y^2 = -x(x-10) would give away the x coordinates of the tangent anyways.. plug, get y, get m
slender mirage
Write the line eqn. m = y/(x-10) = -x/y and x^2 + y^2 = 20
slow bronze
Hello!
slow bronze
How do I check that a sequence converges or diverges?
supple knot
is this your first calculus class?
twin flint
Thinking about how a sine wave behaves is probably the best first intuition to have
Its y values are bounded between -1 and 1 for all infinity, and the limit as sin goes to infinity is undefined
supple knot
Sorry guys 😦
no worries. it's best to give an answer that suits your background, hence why i ask. not to be condescending
slow bronze
No it's okay
When it comes to learning maths, I have no ego... lol
Can we take a step back and talk about what converge and diverge actually means for a sequence?
supple knot
great question
do you have a definition in your book?
or is it assumed by your instructor you already know it
devout snowBOT
@slow bronze Has your question been resolved?
languid ocean
no help on tests!
the format seems sus
anyways
probably P(k1-k2) then
huh
weird
or maybe they want P as an exponential
in which case the "Use P for P(t)" doesn't make much sense
write "the rate as which the innovation spreads" as dx/dt, and definition of joint proportionality?
what's that even for
i thought you needed dx/dt?
so where's y from?
that's x
x is the variable
dx/dt is the rate
seems right
nah
initially there's 1 person
nah
well
initially, there's one person
initially = at time t=0
so x(0) = what?
is the initial condition related to the derivatives by any chance?
oops misleading question
i mean
x(0) doesn't depend on the derivative of x
it's already given
x(t) = the number of people with the invention at time t
at time t=0, the number of ppl with the invention is 1
so x(0) = what?
yea
glad cypress
What am I doing wrong here?
devout snowBOT
What am I doing wrong here?
glad cypress
is the right side not the inverse??
I just went over the calculations one more time and I don't see an error
leaden aurora
Is this the only method you've been taught to find inverse matrices?
glad cypress
Is this the only method you've been taught to find inverse matrices?
what is the other one? afaik yes
glad cypress
yeah we haven't done that in this section yet :/
leaden aurora
ok
glad cypress
I mean if you think I'm doing it the right way I'm just gonna use some tool to get it done, I just wanna know I can do it on exams, I'm tired
leaden aurora
Multiply this by this. If you don't get $I$, then they are not inverse
woven radishBOT
azeem321
glad cypress
so that means I messed up my calculations
glad cypress
but that doesn't affect the right side
leaden aurora
this is so time consuming
It really is. Have you not been exposed to the determinant method
Does your teacher want you to use the above method?
leaden aurora
For the determinant method, you just swap the a and d, turn the b and c negative and the multiply each element of the matrix by $\frac{1}{ad-bc}$
woven radishBOT
azeem321
glad cypress
but I can't do LU factorization with that can I
leaden aurora
LU factorization?
glad cypress
where you have lower triangular matrix times upper triangular one
I'm just gonna drop this class
glad cypress
no like I'm done
leaden aurora
just learn the content from youtube
glad cypress
I've been working on math for 5 hours, again until midnight
2 math classes at once was a dumb idea
why is this wrong
slender mirage
consider multiplying L and U... you'll get a different value for a_(21) from LU
glad cypress
consider multiplying L and U... you'll get a different value for a_(21) from LU
is my process wrong?
my calculations?
I'm even following a youtube tutorial and getting the same thing
slender mirage
the 1 in L_(21) should be -1
glad cypress
why?
slender mirage
it's probably just a minor miscalculation somewhere
glad cypress
I didn't subtract it
but I added it
or do I write the inverse actions in that matrix?
slender mirage
idk what tutorial you're following (@_@;) I can only point out it should be -1 there, figure how/why
glad cypress
no I figured it out
to get back to my original matrix, I need to use inverse operations
glad cypress
mhm
so how does that help me get x_1 and x_2 then
can't I just solve the system of equations as it was before?
I can
what was the point of this?
slender mirage
calculating inverse of triangular matrices is easier? 
maybe 
x = U^-1( L^-1 ( b ))
devout snowBOT
fervent maple
devout snowBOT
steep sable
devout snowBOT
Available help channel!
jade phoenix
devout snowBOT
pseudo basin
@jade phoenix have you made any progress on this or are you stuck not knowing how to begin?
soft shore
devout snowBOT
@jade phoenix Has your question been resolved?
harsh inlet
oak harness
pseudo basin
@harsh inlet do not give out answers or do people's work for them.
oak harness
Oh, I just assumed it was a help request
Not that someone just actually posted the solution
harsh inlet
Oh Am I not supposed to help them?
harsh inlet
Oh do I just have to give hints?
wicked rover
guide to an answer thru conversation instead of just giving it
wicked rover
see #❓how-to-get-help for rules on receiving/giving help
restive river
devout snowBOT
slender mirage
What's your approach?
Do you have a gist of it? any insight? any simplifications of the problem?
restive river
please just give me the ans @slender mirage i beg u
slender mirage
Sorry, we're not supposed to provide answers.
It's a help channel, as you can see
oak harness
As I like to say, we are not a glorified calculator
leaden aurora
please just give me the ans <@!706934233012371577> i beg u
loooool
slender mirage
As I like to say, we are not a glorified calculator
restive river
devout snowBOT
restive river
Can anyone help pls
devout snowBOT
@restive river Has your question been resolved?
heady coral
Hi, I'm studying analytics geometry. I don't know how to continuous the following proof: "Let A = <a , b> and B = <c , d> vectors on the plane. A and B are linear dependence ⇔ ad - bc = 0" ; so, because it's a bi-conditional, I have proof in both directions, I already proof that "A and B are LD → ad - bc = 0", now, here it's where I don't know, I have to prove that "ad - bc = 0 → A and B are LD", I have both cases when d ≠ 0 and when d = 0, I don't know how to prove when d = 0
devout snowBOT
Hi, I'm studying analytics geometry. I don't know how to continuous the followin...
restive river
<@456226577798135808> Has your question been resolved?
no
devout snowBOT
@heady coral Has your question been resolved?
heady coral
thanks you, I was think it but I don't feel sure about it, thanks you
devout snowBOT
@heady coral Has your question been resolved?
rugged panther
=
devout snowBOT
devout snowBOT
Available help channel!
umbral bolt
I just want to confirm... how would HA be determined here
devout snowBOT
I just want to confirm... how would HA be determined here
umbral bolt
would it just be the LC of the x in the numerator/ LC of x in the denominator
which is 1
and then multiplied by k value (3) and a value (2) and then add 1
to get 7?
vagrant comet
My english is not enough to understand this.do you want to draw a line in coordinate system with this equation or smt else?
umbral bolt
no im trying to determine the horizontal asymptote
which is essentially an imaginary straight horizontal line where the graph will never though that value
okay nvm i got it
.close
golden dirge
devout snowBOT
golden dirge
Not sure how to do these two questions
supple knot
looks like an exam
devout snowBOT
@golden dirge Has your question been resolved?
main gull
Just practice problems
Question 3, apply concept of the discriminant
golden dirge
Thanks
devout snowBOT
Available help channel!
formal pecan
Course: Applied Real Analysis
I'm given this problem (attached).
What I did so far:
I wrote out acos(ct)+bsin(ct)=Acos(ct-p) which is given
I've changed A to sqrt(a^2+b^2) to get acos(ct)+bsin(ct)=sqrt(a^2+b^2)*cos(ct-p)
I then used the hint by changing cos(ct-p) into ((cosctcosp)+(sinctsinp))
The equation I have now is acos(ct)+bsin(ct)=sqrt(a^2+b^2)((cosctcosp)+(sinct*sinp))
What I need help with: I would like to know if I'm on the right track.
magic thicket
"(cosctcosp)+(sinctsinp)" doesn't ring a bell ?
formal pecan
"(cosctcosp)+(sinctsinp)" doesn't ring a bell ?
For clarification, is that a question for me? I have it in the equation. I got it from cos(ct-p).
odd dagger
Hey! Can someone hlpe me solve this problem; f(x) = e^x + tx, solve for x
wicked turtle
Hey! Can someone hlpe me solve this problem; ```f(x) = e^x + tx, solve for x```
In terms of $f(x)$?
woven radishBOT
OurBelovedBungo
slender mirage
In terms of $f(x)$?
(@_@;) Can we do that?
can you share the original question please? writing "x" in terms of f(x) here, is a bit ...
questionable
wicked turtle
(@_@;) Can we do that?
If we interpret the question as $y = e^x + tx$, solve for $x$ as a function of $y$... that's about the only interpretation that seems to make sense.
woven radishBOT
OurBelovedBungo
deft wagon
Go newton method😩
woven radishBOT
wicked turtle
Maybe not with an explicit formula, but $x \mapsto e^x + tx$ is injective (assuming $t \neq 0$), so an inverse function exists on a suitable domain.
odd dagger
slender mirage
yup I saw that 👀
woven radishBOT
OurBelovedBungo
slender mirage
Ah okay, Lambert W function at work here
devout snowBOT
@odd dagger Has your question been resolved?
harsh marlin
i just wanted an explanation on the dotted line, im not sure what it is for
umbral cargo
It is used to help indicate that that is where y=1
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Available help channel!
late rivet
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late rivet
hello i need help with this exercise. this exercise is part of my exam that i had in winter. i have alot of questions and if you need more information just ask
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@late rivet Has your question been resolved?
late rivet
my question has been resolved
plucky stone
if your question is resolved, close the channel with .close
devout snowBOT
@late rivet Has your question been resolved?
wise quartz
hi! how would I got about solving this?
devout snowBOT
hi! how would I got about solving this?
devout snowBOT
wise quartz
.reopen
devout snowBOT
✅
wise quartz
yeah nevermind thought I got it but didn't. they are similar triangle? but don't know where to go from there
would that be right?
restive river
hello guys my profesor (introductory number theory) asks in practice sheet in special question (question for advancend) this:
if 2^n and 3^n are integers, does n have to be an integer?
i dont know how to approach this. any help is appreciate.
thank u in advance for looking at my inquiry
jan sona pona
devout snowBOT
hello guys my profesor (introductory number theory) asks in practice sheet in sp...
placid rover
Hmmm
Let x = 2^n
I will now tell you x = 10.
What do you think ? 🤔 (not sure how else to give hints sry)
placid rover
n^3, wut?
n = log2 10, yes
And isn't an integer.
Does that help answer the question?
OHHHHHHHH
misread
🤦
restive river
my question is if: 2^n, 3^n integers => n integer
placid rover
In any case, I would still consider the same method perhaps
Let a = 2^n
b = 3^n
And assume a and b are integers
If you can find a contradiction you're done
but hmmm
restive river
yes i try this
placid rover
By the way, do you have any sort of idea what answer you will expect?
placid rover
Huh ok 🤔
My intuition says false
I'm not sure how to prove it either though
Contrapositive
no no
For me, I am thinking about hunting for a non-integer n
whch makes both integer
It feels to me you can do it.
Or maybe you can't --- in any case, I think I prefer this approach
Suppose 2^n is an integer. Prove 3^n isn't an integer (or find an example).
restive river
Suppose 2^n is an integer. Prove 3^n isn't an integer (or find an example).
well
2^n and 3^n are integers by definition
placid rover
There are multiple ways you can go about the proof.
If you show 2^n integer => 3^n isn't an integer and 3^n integer => 2^n isn't an integer. That is one way to prove what you want, I think?
lunar crane
let 2^n = 4, then 3^n = 9 and vice versa 🤔
lunar crane
if n is not an integer and 2^n is an integer => 3^n isnt an integer would be one way
restive river
so if a, b are integers, a = 2^n, b = 3^n, we need to maybe make equation for n
$n = log_2(a) = log_3(b)$
woven radishBOT
jan sona pona
placid rover
Is n specified to be real? (think complex might hack this q)
restive river
no, the question ask whether n is always integer
placid rover
2^n = 2^(a + bi) = (2^a)2^(bi) = (2^a)2^(i(b + 2pi))
Or something similar if I might a slight error, lol
I probably need to convert to base e first, and then back
restive river
hm yeah this looks good
placid rover
I feel like n is restricted to be real
restive river
hm its not specified
restive river
yes
restive river
we dont often use complex numbers, yes 😃 (in this course)
woven radishBOT
Ftefan
woven radishBOT
Shuri2060
lunar crane
💀
restive river
🤔
placid rover
a = b = 0, n = -\infty
This is hard 😂
Since this is number theory, something about factorisation/modulo arithmetic ?
Might be the approach
Or induction somehow?????
restive river
ive tried induction but it didnt work
placid rover
How deep is this number theory
Just want to know what tools you have
Rings, fields or no?
restive river
yes we did all that
placid rover
Oh, this proof might go quite deep then
Perhaps you want to consider this statement over the rationals first
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
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Available help channel!
restive river
why is the absolute value of an integral from a to b the area of a fuction from a to b?
devout snowBOT
why is the absolute value of an integral from a to b the area of a fuction from ...
supple knot
why is the absolute value of an integral from a to b the area of a fuction from ...
draw a picture?
are you trying to prove that's true?
restive river
i might said it wrong sorry but im not familiar with integrals
I am trying to find proof of $a->bf(x)dx = F(b) - F(a)
and why if f(x) is continues and f(x)>=0 this is equal to the area of f
restive river
and why if f(x) is continues and f(x)>=0 this is equal to the area of f
this one
supple knot
do you want to prove the fundamental theorem of calculus?
what's the definition of area of $f$ ?
woven radishBOT
riemann
restive river
yes i just dont understand why that is equal to F(b)-F(a)
why does antiderivative and area has connection
devout snowBOT
@restive river Has your question been resolved?
thin rune
Please can someone help me with this paper
devout snowBOT
Please can someone help me with this paper
restive river
Can you post a screenshot?
vagrant comet
Can you send ss
thin rune
I tried 1/2 ab sin c
vagrant comet
You are trying to use trigs for a easy questions think simpler
thin rune
1/2 base * height
thin rune
doesnt 1/2 base * height only work for right angle triangles
thin rune
ok
digital egret
Is the second symbol phi?
devout snowBOT
Is the second symbol phi?
devout snowBOT
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Available help channel!
upper bloom
hey guys so i need help with this work that I am tryna review over for the exams next week. and I need help determining whether my proof is right:
1.) suppose m = even; n = odd
2.) by definition of even, m = 2k; and odd, n = 2k + 1
3.) therefore, m - n = -2k + 2k + 1 = 1
4.) therefore, the difference of any odd and even integers = odd
devout snowBOT
hey guys so i need help with this work that I am tryna review over for the exams...
upper bloom
is my proof correct?
did i like mess up somewhere?
OH HOLD ON.. are the variables for m and n supposed to be different? (the variable k)
spare crypt
yeah they're supposed to be different
upper bloom
yeah they're supposed to be different
gotcha.. 2 and 3 are wrong then yeah?
spare crypt
1.) should probably say "without loss of generality" and 2.) should say that k and whatever other variable you choose there is an integer
upper bloom
1.) should probably say "without loss of generality" and 2.) should say that k a...
gotcha! thanks
need help with another 1 ^^
1.) suppose m = even; n = odd
2.) since m * n = even, therefore m * n = 2r where r is an integer
3.) since m = even, m = 2k
4.) since n = odd, n = 2p + 1
5.) therefore, m * n = 2k * 2p + 1 = 2r, and by definition, m * n is even
spare crypt
2.) shouldn't be there because that's what you're trying to prove
for 5.) you'll have to show that 2k*(2p+1) is a multiple of 2
upper bloom
2.) shouldn't be there because that's what you're trying to prove
ahh makes sense.. what is this issue specifically called? so i can look into it ^^
i overlooked that part
spare crypt
circular reasoning
tacit sorrel
i need help with the christofides algorithm how to use it
devout snowBOT
i need help with the christofides algorithm how to use it
tardy smelt
hello!
tacit sorrel
hi
tacit sorrel
yo mos
mosh
are you familiar with the travellig salesman problem or christofides algorithm?
@spark widget hey
u familiar with christofides algorithm? minimum cost perfect match
copper mango
are you familiar with the travellig salesman problem or christofides algorithm?
don't ping random users, and no I don't
However if your question is "How to use this algorithm?", you can just google that
tacit sorrel
ive watched videos but theres a step i cant understand
devout snowBOT
@tacit sorrel Has your question been resolved?
devout snowBOT
@tacit sorrel Has your question been resolved?
devout snowBOT
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Available help channel!
tacit sorrel
fucking useless
devout snowBOT
fucking useless
placid rover
Well I'm sorry for not knowing that very specific algorithm you were asking about.
main gull
Maybe your question is too complex to be answered?
main gull
@supple knot Noticed you were on, want to close this channel since user apparently left because we're "useless"
placid rover
Need an unhelper role
devout snowBOT
@tacit sorrel Has your question been resolved?
supple knot
<@!261933205387477002> Noticed you were on, want to close this channel since use...
lol wow
.close
delicate quarry
Im trying to find any point that is orthogonal to the coordinate Q=(-1,-2,0) in the three dimensional plane
x-2y+z-3=0.
I know the process of doing so when you have a coordinate and want to calculate where the orthogonal line intersects the plane.
I tried doing the process backwards but that did not work.
I asked previously and got a reply but it turned out it didnt work.
devout snowBOT
Im trying to find any point that is orthogonal to the coordinate Q=(-1,-2,0) in ...
delicate quarry
I have two three-dimensional planes that intersects. on these planes i have marked a coordinate Q=(-1,-2,0) now i need to find any coordinate that is perpendicular to the coordinate Q which lay on the plane x-2y+z-3=0.
I previously got the reply that any coordinate (0,0,z) would work but when i enter that into matlab with any given z it doesnt show the point as being perpendicular.
Might be hard to see but im trying to find a point that is othogonal to the blue dot (Q)
<@&286206848099549185>
copper fossil
charred zodiac
Might be hard to see but im trying to find a point that is othogonal to the blue...
Hello, do you want to find a point P such that PQ is perpendicular to the plane x-2y+z-3=0?
delicate quarry
I wish to find a point P that is perpendicular to Q that lays on the plane x-2y+z-3=0
charred zodiac
A point is not perpendicular to a point. A line, segment, vector etc. can be perpendicular to another one or to a surface
charred zodiac
I wish to find a point P that is perpendicular to Q that lays on the plane x-2y+...
so what exactly do you mean by a point being perpendicular to another point?
delicate quarry
The full problem is. "Calculate a point P so that Q is the orthogonal projection of P on the plane x-2y+z-3=0"
charred zodiac
Ok, now I can see
delicate quarry
Since the point Q is a determined point on a set plane it would be possible to have vertical line running through the point
and any point on that line would answer my problem
charred zodiac
Hello, do you want to find a point P such that PQ is perpendicular to the plane ...
yes, that's what I meant by this
delicate quarry
oh, im sorry
charred zodiac
Well you only need the normal vector of the plane
which you can get with the coefficients of the plane's equation
delicate quarry
the normal vector would be 1 -2 +1 right?
charred zodiac
that vector would be the direction vector of a line that passes through point P
then any point on that line would satisfy what you want
charred zodiac
the normal vector would be 1 -2 +1 right?
yes
delicate quarry
but how do i find a coordinate on that line?
i have the vector (1, -2, 1) and then what
charred zodiac
Do you know how to get the equation of a line using the direction vector and a point?
delicate quarry
ye but i think i tried that already and i plotted the point i got but it was not orthogonal to Q
charred zodiac
mmm it should be, I mean PQ must be orthogonal to the plane because we are using the normal vector
delicate quarry
hold on.
When finding the equation of the line you do the end value minus the start value?
hmm this might be too difficult explaining over text
delicate quarry
let me check my notes real quick
thats what i did and then i set t=1 to get "any" point but when i plotted the point in matlab if didnt look orthogonal
because if i set t=1 i would get the cordinate (0,-4,1)
Here's what it looks like
No matter what i have come much further than before. I am very thankful for the help you gave me @charred zodiac have a nice evening
.close
restive river
