the answer won't give me a sample either, so i have no idea what it'd be
#help-10
sonic bolt
cunning burrow
It could be there is no solution. Are you using a graphing software e.g. desmos
sonic bolt
yeah i am
i think there is no solution but i don't know what to input for the answer
prime didn't work, 0 etc
cunning burrow
If there is no answer then you should figure out how to input your answer. Alternatively there may be mistake with the question
sonic bolt
i've been trying for the past 2 hours or so
cunning burrow
I checked on Desmos. There is no answer
All the best
Perhaps you can give the complex solution?
sonic bolt
it doesn't seem to accept imaginary numbers or anything with text as an answer
seems to be very stubborn about wanting a number but i don't know what to enter
so i'm hoping i get an e-mail back today about the question because i'm genuinely stuck here, and everyone i've asked so far tonight has been the same
and like you said on desmos there is no answer
past solar
if that's the case then it's likely a mistake from the teacher or smth
obtuse pebbleBOT
@sonic bolt Has your question been resolved?
obtuse pebbleBOT
@sonic bolt Has your question been resolved?
rigid plaza
you could try the real part of the solution 0.2
obtuse pebbleBOT
rigid plaza
as an approximate solution @sonic bolt
obtuse pebbleBOT
Available help channel!
hollow plume
AC and AB - tangent to circle. A perpendicular CM drawn from point C to tangent AB intersects the circle at point E.
Find CE if BM=4 and MA=6
obtuse pebbleBOT
AC and AB - tangent to circle. A perpendicular CM drawn from point C to tangent ...
hollow plume
I found that AC=10 and CM = 8
Question from the state exam of Azerbaijan for 11th grade(second attempt)
obtuse pebbleBOT
@hollow plume Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
If X_o is an answer of...
calculate...
I suppose B is X_o
obtuse pebbleBOT
If X_o is an answer of...
calculate...
I suppose B is X_o
timid silo
I have tried different approaches, but I don't know how to solve it yet
Does anyone have any suggestions? In order to start from scratch
gray kiln
what is beta btw?
timid silo
what is beta btw?
I don't know, that's also the problem
I'm just trying to find X_o in hopes that the a's cancel out
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
obtuse pebbleBOT
nocturne bronze
,w (arccos (15/17))*180/pi
warm shaleBOT
obtuse pebbleBOT
Available help channel!
ionic sphinx
4b
ionic sphinx
how to solve when cos 4x = cos 1/2x
obtuse pebbleBOT
@ionic sphinx Has your question been resolved?
ionic sphinx
<@&286206848099549185>
slim cove
how to solve when cos 4x = cos 1/2x
basically there are a couple possibilities, either 4x is 1/2x plus a multiple of 2pi, or negative of that
ionic sphinx
? how so
slim cove
you know how numbers that differ by 2pi represent the same angle?
so like 0 and 2pi are the same angle for example
slim cove
so if 4x and 1/2x are off by 2pi, they will be the same angle
like for example if 4x - 1/2x = 2pi
you can try solving that and seeing if x is in the range of possibilities that they say
slim cove
yeah there could still be other possibilities
like maybe 4x - 1/2x = 4pi
that's another solution
wintry swift
why four pi? btw question also says within 0 and 1 pi
the question says x has to b in [0,pi], thats right. but x/2 and 4x can differ by a multiply of the period of the cos, wihich is 2pi, so try
4x-x/2 = n times 2pi
and its cos (x) = -cos(x), so you have to check this too.
ionic sphinx
how? and why add n?
ionic sphinx
and its cos (x) = -cos(x), so you have to check this too.
the cos isnt squared right?
wintry swift
how? and why add n?
take n = 0, solve 4x-x/2 = 0 times 2 pi.
take n = 1, solve 4x-x/2 = 1 times 2pi ans so on.
ionic sphinx
I got 4pi/7 but i dont think its right
wintry swift
4pi/7 is one solution, thats right.
wintry swift
and its cos (x) = -cos(x), so you have to check this too.
and dotn forget this case, which means 4x+x/2 is a multipy of 2pi.
ionic sphinx
ya but how do we know from beginning that there only 4solutions?
wintry swift
why do we need to knwo "from the beginning" the there only 4 solutions? I would solve it, and count the solutions at the end.
ionic sphinx
shouldnt there only be two since its between 0 and pi?
wintry swift
no.
ionic sphinx
shouldnt there only be two since its between 0 and pi?
and thats like two quadrants?
ionic sphinx
no.
okay, i dont really understand what it means with 0<x<pi
isnt it just the two top quadrants in unit circle?
wintry swift
solve 4x-x/2 = n times 2pi and 4x+x/2 = n times 2pi, and then use 0<=x<=pi.
ionic sphinx
And i still get awnser if n is over 4
wintry swift
And i still get awnser if n is over 4
which one?
wintry swift
is 20/7pi between 0 and pi?
wintry swift
i guess you mix up n and x
ionic sphinx
ya but i get it now, can you help with another
number 6
it has sin and cos
.close
lyric kelp
Hi need help proving, for y and z two variables with values in N that :
|Gz (t) - Gy (t) | <= P(z!=y)
obtuse pebbleBOT
Hi need help proving, for y and z two variables with values in N that :
|Gz (t) ...
lyric kelp
Where Gy and Gz are the generating functions of y and z
obtuse pebbleBOT
@lyric kelp Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
jagged hawk
What’s the remainder of p(x) divided by q(x)
obtuse pebbleBOT
What’s the remainder of p(x) divided by q(x)
old lily
p(x) = q(x)g(x) + (ax + b) for some polynomial g(x) and constants a,b
old lily
What’s the remainder of p(x) divided by q(x)
find the roots of q and plug it in
to find a and b
jagged hawk
find the roots of q and plug it in
There’s no real roots for q
<@&286206848099549185>
slim cove
There’s no real roots for q
you can use the complex roots
jagged hawk
how do I do that
slim cove
do you know how to find the roots of x^2 + x + 1
obtuse pebbleBOT
@jagged hawk Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
weary thicket
how do you do this?
obtuse pebbleBOT
how do you do this?
flint stratus
The tangent and radius are perpendicular.
And the sum of the interior angles of a quadrilateral is 360°.
weary thicket
i know that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
primal oracle
Can anyone help me im confused on what its asking for
obtuse pebbleBOT
Can anyone help me im confused on what its asking for
weary spruce
Can anyone help me im confused on what its asking for
what you learnt sin cos tan?
i assume so
try plugging them int odesmos
and looking for what matches
wait
yeah okay try it
obtuse pebbleBOT
@primal oracle Has your question been resolved?
primal oracle
yeah okay try it
yes i tried it and it worked out to sec
obtuse pebbleBOT
yes i tried it and it worked out to sec
primal oracle
except when i put in sec(x) it says its wrong
so im not sure if its asking for an equation or whaT
weary spruce
yes i tried it and it worked out to sec
your on track
now pay attention to the y values
how do you adjust the equation to fit it?
also probadly reopen the channel for now
primal oracle
okay
primal oracle
how do you adjust the equation to fit it?
I think move it to the right right so subtract a value
weary spruce
yep
nise
now x value is adjusted
what about the y value?
you know transformations right?
primal oracle
what about the y value?
I think it stays at 1 right cause usually sec starts at 1
primal oracle
x equation
would it be +1.5
primal oracle
Ohhh ok
primal oracle
okay cool
weary spruce
pay attention to the y values
primal oracle
sec(x-1.5) +1
weary spruce
?
primal oracle
pay attention to the y values
okay
weary spruce
why +1
primal oracle
would it move one up cause of the y value
weary spruce
do you want it to?
primal oracle
wait so it wouldnt
primal oracle
Ohhh
weary spruce
this is what a +1 graph looks like
primal oracle
yes
primal oracle
ist 2
primal oracle
ohhh -1
weary spruce
you want it to go upwards twice as fast
what do you do
to make it go upwards twice as fast
weary spruce
hm
primal oracle
like stretch it
primal oracle
sloep
primal oracle
yea
primal oracle
double it on the blue too
primal oracle
x=y
weary spruce
what
primal oracle
bro im lost 😭
weary spruce
what does inverting it do;-;
primal oracle
flip it o
weary spruce
also y=x inverted is still the exact same
primal oracle
yeah
primal oracle
ohh
primal oracle
broo
weary spruce
until it does come out
weary spruce
yeah just dw about inverting
primal oracle
ohh ok
primal oracle
yes
weary spruce
so equation 1 is y = 1x
primal oracle
yea
primal oracle
2x
weary spruce
how do you transform y=x (blue graph) into the green graph
so whats green graph here?
primal oracle
2x
weary spruce
yesss
weary spruce
this is sinx
primal oracle
yeah
weary spruce
how do you transform it into this
primal oracle
You stretch it
primal oracle
yeh
weary spruce
stretch it where?
primal oracle
at the start of the equation
weary spruce
what does that mean
okay when i say stretch dont tihnk about it that like
complicated
your confusing yourself
primal oracle
Oh
weary spruce
stretch horizontally or vertically
primal oracle
ohh yeahj
weary spruce
now how do you stretch it vertically
original equation is y=sinx
peak of first graph is y=1
primal oracle
2sinx
weary spruce
2nd is y=4
primal oracle
yeah
primal oracle
Man idek
weary spruce
original is sinx
primal oracle
sin(2x)
weary spruce
it stretches by 4 times vertically
primal oracle
4sin(x)
weary spruce
good
how did you even get sec(x-1.5)
thats like the hardest part
of this topic
stretching should be easiest
primal oracle
bro thats the only thing i remember
primal oracle
yea lol
weary spruce
now back to the question
primal oracle
2sec(x)-1
primal oracle
yeahg
weary spruce
YESS
primal oracle
OHHH
weary spruce
good job
primal oracle
yup yup
weary spruce
just tihnk about it normally
dont use like uhh adjust the base equation
or whatever u were yappin ga bout
primal oracle
ohhh alr bruh 💀
primal oracle
okay got it
primal oracle
so now is it 2sec(x-1.5)-1
weary spruce
yessir
weary spruce
wait
oh the uh
stretch horizon
multiply top and bottom by denomitaor
wait
why is it wrong
primal oracle
why is it wrong
i dont even know bro
i put in sec(x) as well and it says its wrong
weary spruce
2sec(x-1.5)-1
primal oracle
it asked "of what function" and that would mean sec(x) too and thats wrong to
weary spruce
try 1/sin
primal oracle
Nope it dont
primal oracle
fax bruh
weary spruce
fax bruh
any luck?
try asking your teacher honestly
and just send full answer
can you send whole question for context?
we might be able to guess and check solution
primal oracle
we might be able to guess and check solution
yeah tahts true
it said its supposed to be an expression
weary spruce
like words?
primal oracle
primal oracle
yup
weary spruce
without y=
primal oracle
Yeah
primal oracle
primal oracle
lmaoo your all good bro i really appreciate your help
primal oracle
ask your teacher
yea thats my last resort
weary spruce
you learnt the concept so goal was accomplished
primal oracle
ima ask chat gpt
primal oracle
you learnt the concept so goal was accomplished
yup exactly
primal oracle
Ik bruhhh
weary spruce
did you try using sin?
primal oracle
gpt wont help with this
Yeahhh
primal oracle
I just tried it didnt
weary spruce
its over
primal oracle
is ur teacher even awake
idek its an online class
weary spruce
oh its in 15 minutes
primal oracle
Nahh im PST
primal oracle
so its still 9;40 rn
weary spruce
yo wouldn't it be like the amplitude midline period stuff
the hell that mean
physics?
primal oracle
wait you dont know that
weary spruce
thats physics
primal oracle
Like the midline, amplitude, period, phase shift
weary spruce
i know amplitude and stuff
primal oracle
it has Pi in it
primal oracle
yeahj
primal oracle
Nope bruh it didnt work
weary spruce
yeah just wait
primal oracle
these are trig functions
I think its something like this
except i just need to figure out what to move it for the x axis
obtuse pebbleBOT
@primal oracle Has your question been resolved?
primal oracle
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
thin cedar
obtuse pebbleBOT
weary spruce
what do you not get
static furnace
the question wants you to find the intersection point of the two functions and explain the meaning
obtuse pebbleBOT
@thin cedar Has your question been resolved?
thin cedar
the question wants you to find the intersection point of the two functions and e...
can u help me do that
static furnace
to find the intersection point, all you need to do is equate the two functions
so 5^x=-x+6
find the x-value that makes this equation true, and insert that x-coordinate into one of the two original functions to get your y-coordinate
thin cedar
ok
obtuse pebbleBOT
<@1177922913605795882>
rare flicker
I don't understand this.
wintry stump
In a cartesian system plot these equations
rare flicker
In a cartesian system plot these equations
yeah still dont understand it
how do we get the answer
wintry stump
So first you have to draw your x and y axis
rare flicker
wintry stump
Yes
All these are lines parallel to the x and y axis
for example x=1 is straight line parallel to the y axis that passes through 1 in the x axis
wintry stump
Could you show it?
rare flicker
Could you show it?
wintry stump
Yes! That is x=1
rare flicker
Yes! That is x=1
wintry stump
Yes!
wintry stump
Sure
wintry stump
Yes, you got it!
rare flicker
OOO
wintry stump
Yes
obtuse pebbleBOT
@rare flicker Has your question been resolved?
wintry stump
Yes, all correct
obtuse pebbleBOT
@rare flicker Has your question been resolved?
rare flicker
Alright, I got a few more questions for next unit
rare flicker
@wintry stump Please let me know once you are able to help me again
wintry stump
Ok, I am back
rare flicker
Ok, I am back
Alright.
this graph is 3-x
for that, its -6, -5, -4, -3, -2, 1, 0
for x-2 its
-5
-4
-3
-2
-1
0
1
so, -3 and -5 does. cause look
does this count in 5th square
@wintry stump
safe haven
so, -3 and -5 does. cause look
you're solving for a coordinate no?
so whats your conclusion
rare flicker
you're solving for a coordinate no?
for coordinate
I need those to go on the red line
-2, -4
-3,-5
-1,-3
safe haven
negative or positive?
rare flicker
Those all go on the line right?
rare flicker
negative or positive?
That red one
rare flicker
rare flicker
but are you sure the y coordinate for x = -3 is -5?
yeah think
safe haven
where are negative y values located?
rare flicker
English?
safe haven
?
rare flicker
where are negative y values located?
Don't know it just that
you tell me if its right
safe haven
no its not right
rare flicker
show me how.
safe haven
look at the x axis
and find where -2 is
then look at the line where it crosses x = -2
whats the y coordinate of it
rare flicker
Hold on hold on, I don't understand you.
cinder kestrel
do you know what a function is?
rare flicker
The negative is where R is located, (Q3)
rare flicker
do you know what a function is?
Uh, no.
rare flicker
yep
safe haven
it asks
the coordinate of point with x = -2 that lies on the line y = 3-x
to write the coordinate, you need to have its x and y
yes?
safe haven
what do you think
rare flicker
what do you think
nah im dumb is it -6 or 0
safe haven
neither
rare flicker
so its 6.
safe haven
yes
rare flicker
da hell
safe haven
two negatives makes a positive
cinder kestrel
well because
3 - 3 = 0
3 - 2 = 1
3 - 1 = 2
3 - 0 = 3
3 - (-1) = ?
Should be 4 if you want the pattern to continue
rare flicker
man I forgot. I thought the 2 was a negative
@safe haven @cinder kestrel
so 6-5 is
rare flicker
the hardest question ever 💀
rare flicker
two negatives makes a positive
shio
rare flicker
?
#help-10 message this is just 2 right?
safe haven
the hardest question ever 💀
this?
safe haven
draw 2 lines in 1 graph
safe haven
yep
i mean y = 2 contains all possible coordinates where its y coordinate is 2
so (6, 2) does indeed lie on the line y = 2
obtuse pebbleBOT
@rare flicker Has your question been resolved?
obtuse pebbleBOT
@rare flicker Has your question been resolved?
ebon sand
obtuse pebbleBOT
ebon sand
How do I do this 4ii?
I tried to make it ln(1-tanx)- ln (1+tanx)
and then sub in the bounds for x
thats wrong tho for reasons I don't know
weary reef
The derivative of $ln(1 - tan x)$ is not $\frac{1}{1 - tan x}$
warm shaleBOT
StrangeQuarkAL
weary reef
Notice the hence in the question
high lily
why don't use consider the "hence" and use the result from i)
high lily
no
weary reef
Oh I see what you're doing
high lily
you could if you wanted, but you may or may not be skipping ahead / doing what we're recommending
ebon sand
yeah I did the last question fine
the first part
I use tan2x in what way tho i dont get
weary reef
Go from here actually
weary reef
I use tan2x in what way tho i dont get
That expression inside the integral is equal to tan(2x)
ebon sand
yeah im trying to
but idk which expansion to use
like in what form I should have it in
high lily
do you know how to integrate tan(x)
weary reef
Consider the derivative of ln(f(x))
ebon sand
yeah so 1/f(x)
so
yeah shouldnt it be ln cosx as part of it
I googled and it said sec tho
or -ln cos x
cause it differentiates to 1/cos x -sinx
oh appar thats the same thing
as the sec thing
ebon sand
yo
weary reef
yeah so 1/f(x)
No, it's f'(x)/f(x)
safe ravine
Integration of tan2x is
weary reef
Using that knowledge and the relationship between sin(2x) and cos(2x), can you figure it out
No answer
safe ravine
Wait what I integrated it
weary reef
Pardon me, I meant you're not supposed to give out the answer( immediately at least)
weary reef
No no, keep on going
ebon sand
forgot what deravative of cos 2x is xD
ebon sand
lncos2x multiplied by the deravative of cos 2x
ln cos2x times -4sinxcosx
safe ravine
Yes correct
dusky arrow
obtuse pebbleBOT
dusky arrow
how did we get this by substitution
dark stirrup
Log rules
hexed topaz
Hello
dusky arrow
can u give a step by step simplification?
safe ravine
@hexed topaz occupy new
wooden cipher
omg i loved this one
move all constants to one side then use simons favorite factoring trick
dusky arrow
Product rule is what you want
can u just give the steps?
dark stirrup
can u just give the steps?
I gave you the tools
wooden cipher
you have to use simons favorite factoring trick
dusky arrow
I gave you the tools
i know that i am expected to solve it by myself but can u give a step by step solution only this time?
dusky arrow
you have to use simons favorite factoring trick
i think there are other ways aswell
wooden cipher
this is the easiest way to do it
dark stirrup
i know that i am expected to solve it by myself but can u give a step by step so...
!noans
obtuse pebbleBOT
i know that i am expected to solve it by myself but can u give a step by step so...
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
dark stirrup
Use product rule for $\log_{10}2000xy$
warm shaleBOT
SWR
dusky arrow
Use product rule for $\log_{10}2000xy$
im not getting 2 as the argument
im getting log_10 2000 +a+b-ab=4
wooden cipher
2000 = 2*1000
dark stirrup
how did we get this by substitution
It's this gpt?
dusky arrow
log_10 2 + b +c-b(c)=1
dark stirrup
im getting log_10 2000 +a+b-ab=4
This is good. Now simplify it
dusky arrow
This is good. Now simplify it
how should i proceed
dark stirrup
2000 = 2*1000
You got a hint here @dusky arrow
dusky arrow
You got a hint here <@1156620428777902190>
log_10 2 + 3 +a+b-ab=4
i dont understand how is it useful tho
wooden cipher
i love the part where you use simons favorite factoring trick
dusky arrow
i love the part where you use simons favorite factoring trick
ill take a bit of time to learn sfft
wooden cipher
its pretty simple
dusky arrow
i have to sleep in like 5 minutes
wooden cipher
ok try it after you wake up then
dusky arrow
its pretty simple
i wanna understnad how to solve it with the normal method b4 i sleep
wooden cipher
you can learn sfft in a few minutes, but the problem is gonna take longer
dark stirrup
i wanna understnad how to solve it with the normal method b4 i sleep
$\log_{10}2000=\log_{10}(2\times1000)$ use product rule.
warm shaleBOT
SWR
obtuse pebbleBOT
@dusky arrow Has your question been resolved?
inner drum
Hi i have a question about the discussion of this limit:
obtuse pebbleBOT
Hi i have a question about the discussion of this limit:
inner drum
$$a(x,y) = \arctan\left( x^2 + y^2 \right) \cdot \frac{y}{(x^2 + y^2)^k}$$
warm shaleBOT
nicocl94
inner drum
Suppose im evaluating the limit when (x,y) - (0,0), for k real
Is it correct to say that arctan(x2+y2) is equivalent to (x2+y2) ??
Because if i switch to polar coordinates I get different values for k to discuss, so i assume the previous procedure is wrong
short spire
are you asking if arctan(x) = x + O(x^2) ?
here x is just a dummy variable
put differently, are you asking if arctan(x)/x goes to 1 as x goes to 0?
as saying "arctan(x2+y2) is equivalent to (x2+y2)" is not quite right
inner drum
Wait
inner drum
put differently, are you asking if arctan(x)/x goes to 1 as x goes to 0?
I know that, but if i say z=(x^2+y^2) then arctan(z)/z tends to 1
short spire
yup
inner drum
However if i do polar coordinates i have to discuss other values of k
short spire
let me ask you do this instead
what does arctan(x)/x^2 tend to?
as x approches 0
or any k infact bigger than 1?
inner drum
It's not bounded if k bigger than 1/2
Im taking into account that y/sqrt(x¨2 + y¨2) is bounded
Doesnt have a limit, but its deff bounded
short spire
So uh why are you saying its unbounded if k is bigger than 1/2?
Does that fall out if you use polar coords or something?
inner drum
Does that fall out if you use polar coords or something?
Yeah i have to discuss for greater or lower than 1/2 after using polar, but if i bound y with sqrt of the denominator i have to discuss for k=3/2
Geogebra dies when plotting the graph, idk why
short spire
this seems really tedious, im not sure what youre even doing; could you show your work?
short spire
Hm, so youve shown theres a limit when k < 3/2?
but you dont know about when k=3/2?
Or whats the trouble rn?
inner drum
When k=3/2 it's a product of bounded things that do not have a limit
inner drum
Or whats the trouble rn?
My brain cannot process that i got k=1/2 with polars and 3/2 without them
Im stupid..
short spire
Oh i see, so you want to see why that happened?
inner drum
Yes!
short spire
Ok let me scan trhough ur work again
inner drum
Sorry that it's not even in english, and the notation is rubbish
short spire
You could if you want just write down the steps here in the mean time, i would appreciate it
it doesnt hurt, as you might spot the mistake(?) that way too
inner drum
I'll go through it again to check for mistakes
short spire
also im not sure what happens in the second image, but i woulnd write that arctan(z) = z etc..
in a limit
as you may miss something with the error terms
always best to write that arctan(z) = z + O(z^2) or something simliar
to have control over the error terms, and as this is an actual equality compared to the other
Oh nvm, its a product of limits
Well you should be careful there too
you can only do this when you know that both factors have a limit
inner drum
you can only do this when you know that *both* factors have a limit
So it's incorrect to proceed as i did in the paper?
Look at this tho..
short spire
Well its correct up to whatever happens with either factor, in your case its pretty wrong to do so, since youre in one case starting to argue that one factor indeed blows up when k is bigger than a certain number
inner drum
short spire
Well its correct up to whatever happens with either factor, in your case its pre...
then product of limits dont apply anymore
short spire
Look at this tho..
yeah thats just pure luck tbh since you werent aware that product of limits doesnt work there
inner drum
So it worked but it's incorrect
I see now, this is interesting, i'll be careful from now on
inner drum
Thanks for the insight
short spire
but this was just for the second image, i havent acutally looked at the one you were asking about lmao
let me look at the polar one
inner drum
Okay.. i surely made a mistake over there too
I found the mistake i believe, the one with polars
short spire
okay so, so look at 2 lambda -1
inner drum
I saw it
short spire
nice
inner drum
Thanks for your time!
short spire
however we need to be careful with product of limits here too
np!
nice that you spotted it too
inner drum
And ur comments are super helpful, i'll be careful from now on. Ive been doing this since calc1 and i've been lucky i see
But the method that i use is wrong
Thanks for pointing it out
short spire
yeah no worries, im glad you say that
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hidden mauve
give A, a 3x3 matrix, what is the maximum value of det(A) such that each cell can either be 0 or 1?
obtuse pebbleBOT
give A, a 3x3 matrix, what is the maximum value of det(A) such that each cell ca...
hidden mauve
so is there supposed to be a trick for this other than just trying possible values and seeing?
fossil crag
this has no trivial resolution but with 3x3 you can at least find what the maximum value can't be
write down the det 3*3 formula
hidden mauve
done that
fossil crag
and will all coefficients being either 0 or 1 you have an idea of how far the det can go
hidden mauve
right but like what do i just try and see if i get to the max?
fossil crag
first, what did you get for max det with just looking at coeff
say this
what's the MAX max the det can be
hidden mauve
well it cant be bigger than 3
hidden mauve
well no
yeah if the first 3 are 1s then the last 3 have to be 1s
so ig i can try to make it 2
hidden mauve
yeah
fossil crag
so try to make such a matrix, see if it works
hidden mauve
only dhc are 0
right yeah thanks
what about if the possible values are 1 and -1 instead of 1 and 0?
fossil crag
good question
hidden mauve
oh actually
fossil crag
answer says 4
hidden mauve
its the same as the old one
hidden mauve
answer says 4
not 5?
fossil crag
nope, 5 is too much as well
fossil crag
so 6 is impossible
hidden mauve
yes
fossil crag
notice
that the determinant is always even
because every term is either 1 or -1
so mod 2
it's just 1 + 1 + 1 + 1 + 1 +1
so 0 mod 2
the determinant is odd
hidden mauve
where did the mod 2 come from
hidden mauve
right
fossil crag
say this
and every term in the determinant
is a product of -1 and 1
so either 1 or -1
hidden mauve
right
hidden mauve
yeah yeah
warm shaleBOT
rafilou2003
fossil crag
well multiple matrices are gonna work
brittle swan
give A, a 3x3 matrix, what is the maximum value of det(A) such that each cell ca...
It's much more helpful to think of det(A) as a volume here
hidden mauve
whats a volume
fossil crag
whats a volume
you know, what you measure in m^3
hidden mauve
well multiple matrices are gonna work
yeah but i didnt think it would work with only 2 terms equal to -1
hidden mauve
you know, what you measure in m^3
what?
hidden mauve
how can i think of a matrix like a 3d shape
fossil crag
how can i think of a matrix like a 3d shape
a parallelepiped
side 1 is given by the vector
a1 a2 a3
hidden mauve
a parallelepiped
whats that
fossil crag
whats that
think cube, elongated and distorted
hidden mauve
oh
fossil crag
side one is given by the vector a1 a2 a3 (say it's the length)
side two given by b1 b2 b3 (width)
side three given by c1 c2 c3 (height)
a regular cube of length 1 is gonna be given by identity matrix
hidden mauve
how would the side 1, -1, 1 look like
fossil crag
how would the side 1, -1, 1 look like
well, 1 meter in the x direction, -1 meter in the y direction, 1 meter in the z direction
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hasty gazelle
stuck on this integral
obtuse pebbleBOT
stuck on this integral
hasty gazelle
i just do u sub with u = arctanx right?
so now im here
should i not factor the bottom?
thin pawn
you can't have an integral of both x and u
shut lagoon
should i not factor the bottom?
You should be able to get a (1+x^2) out of the denominator. Group the terms 1 and 3 and the terms 2 and 4.
obtuse pebbleBOT
@hasty gazelle Has your question been resolved?
hasty gazelle
You should be able to get a (1+x^2) out of the denominator. Group the terms 1 an...
oh i see
hasty gazelle
you can't have an integral of both x and u
yea so thats why i need to cancel the x's out no?
this doesn't seem right?
shut lagoon
You can rewrite x in terms of u from your substitution, I think the resulting integral is doable.
sage sleet
hi guys
sage sleet
basically
a friend gived me a question and if i answer correctly i get a reward
(i'm not smart)
the question is : Mario had a great pie factory, but he sells his pies in dozens. Today, after 3 days of no profits, he sold his 44th dozen of pie, he had such a great selling! All his earnings were equivalent to the number of that dozen!! He added all of the digits of his profits
any helps can be useful btw
btw just to help
the answer is a sentence
<@&286206848099549185>
nocturne bronze
The answer should be 8
As his earnings are equal to the number of that dozen (44)
Then he added all the digits 4 + 4 = 8
obtuse pebbleBOT
@sage sleet Has your question been resolved?
fallen inlet
I don’t think I set this up correctly lol can anyone help me out?
15/x+2 = 20/x+2-14
obtuse pebbleBOT
I don’t think I set this up correctly lol can anyone help me out?
15/x+2 = 20/...
high lily
missing () to clearly indicate denominator of fractions
also you didn't get the correct expression for the unmarked segment
why did you do
x+2 -14
obtuse pebbleBOT
@fallen inlet Has your question been resolved?
obtuse pebbleBOT
@fallen inlet Has your question been resolved?
fallen inlet
you'd subtract the whole expression
14 - (x+2)
OHHHH
So it would become 14 -x -2
Uh
-x+12
?
high lily
yes
fallen inlet
Okay Tysm
lone harbor
