Yea u got it
#help-27
tacit wedge
mystic bloom
tacit wedge
I think so
barren garden
devout snowBOT
barren garden
devout snowBOT
@barren garden Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
jaunty gazelle
Could someone help me with this F?
devout snowBOT
Could someone help me with this F?
@jaunty gazelle Has your question been resolved?
jaunty gazelle
<@&286206848099549185>
devout snowBOT
@jaunty gazelle Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
blazing latch
Given a rectangle ABCD where |AB| : |BC| = 2 : 1.
On its sides AB, BC, CD, DA are given by
K, L, M, N so that KLMN is a rectangle,
in which |KL| : |LM| = 3 : 1. Calculate the ratio
of the areas of the rectangles ABCD and KLMN.
My process:
AB = 2x, CD = x, MN = 3y, KN = y
AKN is similar to DNM, k = 3 (hypotenuse of DNM is 3y and hypotenuse of AKN is y)
DN = 3AK, DM = 3AN
hence 3AN + AK = 2x and AN + 3AK = x
so x = 8AK, AN = 5AK
S(ABCD) = x * 2x = 8AK * 16AK = 128AK²
NK² = AN² + AK² = 25AK² + AK² = 26AK²
S(KLMN) = 3 * NK² = 78AK²
S(ABCD) : S(KLMN) = 128:78 = 64:39
devout snowBOT
Given a rectangle ABCD where |AB| : |BC| = 2 : 1.
On its sides AB, BC, CD, DA ar...
devout snowBOT
@blazing latch Has your question been resolved?
devout snowBOT
@blazing latch Has your question been resolved?
blazing latch
<@&286206848099549185>
summer dome
hello
devout snowBOT
@blazing latch Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
turbid forge
following from this message, I am unable to find any ordered pairs satisfying the condition. #help-32 message
devout snowBOT
following from this message, I am unable to find any ordered pairs satisfying th...
solid osprey
assume when you press a button, a 60% chance that a number from 1,2,3 randomly chosen will show up, if a number shows up then that number and the numbers below it will never show up, what is the average ammount of presses needed until 3 shows up?
devout snowBOT
assume when you press a button, a 60% chance that a number from 1,2,3 randomly c...
solid osprey
so say you get a 2 in the first press, your not getting a 1 or a 2 after that
dunno how to start
like i would assume you would say that you can get 1, 2, 3 in the first "show up" and the 2 will show a 3, the 1 will either show a 2 or 3 and if its a 2 it would be 3 next
if you average ir all out you will get (3+2+(2×2)+(1×2))/6 which is
1.8333333...
but thats the number if it showing, do you actually just divide it by 60%?
devout snowBOT
@solid osprey Has your question been resolved?
devout snowBOT
@solid osprey Has your question been resolved?
stuck prairie
5 times?
The chances of you getting a 3 is 60% times 1/3 or 20%
Meaning on avg, it should take 5 presses
restive river
I have a Differential equation: dy/dx=(x-4y+2)^2 I dont know wich method to use but i do know the answer.
devout snowBOT
I have a Differential equation: dy/dx=(x-4y+2)^2 I dont know wich method to use ...
cold bough
$dy/dx=(x-4y+2)^2$
woven radishBOT
everg
restive river
i know the answer is (2x-8y+3)/(2x-8y+5)=C*e^-4x
devout snowBOT
@restive river Has your question been resolved?
supple knot
I have a Differential equation: dy/dx=(x-4y+2)^2 I dont know wich method to use ...
You want to get rid of the x on the right side since y is a linear shift of x. Set u = x-4y and solve the differential equation in u(x)
Should get a separable equation in terms of u and x
restive river
Im not sure to understand
supple knot
Im not sure to understand
Which part
restive river
U=x-4y
restive river
Yes sorry i just didn’t made the association
Im just not sure how the substitution will lead me to the answer
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
supple knot
Im just not sure how the substitution will lead me to the answer
Did you try it
Substitution is a common technique
And if you don't try it yourself you won't understand why it works
restive river
do you mean seperation of variables?
supple knot
Substitution is a common technique
.
restive river
i dont know what is the substitution technique. I only know direct integration, bernoulli, linear first order, homogeonous first order, seperation of variables and exacts (with or withoutn integration factor)
supple knot
That's a substitution
This is exactly the same as substitution from integral calculus
Even if you haven't seen it, plugging u = x-4y is a straightforward substitution with no chain rule
supple knot
You want to get rid of the x on the right side since y is a linear shift of x. S...
Which I described here
supple knot
Should get a separable equation in terms of u and x
And here
restive river
but where do you want me to plug u=x-4y?
supple knot
but where do you want me to plug u=x-4y?
Into the differential equation
woven radishBOT
riemann
restive river
@restive river do you still need help?
restive river
Your very first line is wrong
Yes omg
restive river
<@456226577798135808> do you still need help?
If can give me any hints ill be pleased
restive river
If can give me any hints ill be pleased
did you try redoing the problem
fixing the first line?
Not yet im on my lunch break
vapid nest
,tex .freshman
woven radishBOT
nosqldb
supple knot
i cannot tell if it's right or wrong or incomplete
Plug your y back into the original differential equation to check
arctic crystal
devout snowBOT
arctic crystal
how did they get x0 as 1
supple knot
how did they get x0 as 1
That's just a given initial condition
devout snowBOT
@arctic crystal Has your question been resolved?
formal venture
devout snowBOT
formal venture
How is this not right?
supple knot
How is this not right?
!show
devout snowBOT
How is this not right?
Show your work, and if possible, explain where you are stuck.
modest inlet
devout snowBOT
modest inlet
is my answer correct??
devout snowBOT
@modest inlet Has your question been resolved?
barren frigate
Can someone help me confirm?
devout snowBOT
Can someone help me confirm?
barren frigate
That b) has one solution
because not accute and a__>__b is true since 8 is bigger than 7
and that c) is one solution as well because a__>__b
right?
Since:
devout snowBOT
@barren frigate Has your question been resolved?
barren frigate
<@&286206848099549185>
barren frigate
Can someone help me confirm?
.
barren frigate
.close
restive river
Find all functions R to R
F(x+y) + f(x-y) = 2f(x) + 2f(y)
devout snowBOT
Find all functions R to R
F(x+y) + f(x-y) = 2f(x) + 2f(y)
mild comet
Find all functions R to R
F(x+y) + f(x-y) = 2f(x) + 2f(y)
this is for all x and y?
restive river
Yes
mild comet
try the usual tricks with functional equations: substitute in x = 0, y = 0, x = 1, y = 1, or x = y
and then you’ll have some relations you can use to find values for f(0) and f(1), hopefully
mild comet
I got smth like
F(2x) = 4f(x)
how did you get that
mild comet
try substituting x = 0
mild comet
so the function is even
restive river
Thats the answer?
mild comet
No, the question says to find all functions from R to R
and we’ve only gotten one or two constraints
restive river
Oh
mild comet
how about y = 2x and y = ax
mild comet
I got f(3x) = 5f(x)
can you show your steps for that one
restive river
f(y) = f(-y)doesnt apply for x right?
mild comet
f(y) = f(-y)doesnt apply for x right?
No, it applies for all real numbers
x and y are just dummy variables
they could be s or t or u or v or w
restive river
So f(3x) + f(-x) = 2f(x) + 2f(2x)
F(3x) = 4f(x)
F(3x) + f(x) = 2(fx) +8f(x)
So, f(3x)= 9f(x)
mild comet
Idk how I got this, I suck at functionals
I thought about this for a while more and I realized that
x^2 satisfies the functional equation
and
if a function g satisfies the equation, then any constant multiple of it does as well
devout snowBOT
I thought about this for a while more and I realized that
> x^2 satisfies the fu...
mild comet
So f(3x) + f(-x) = 2f(x) + 2f(2x)
F(3x) = 4f(x)
F(3x) + f(x) = 2(fx) +8f(x)
So, ...
see if you can get f(ax) = a^2 f(x) if a is a positive integer, maybe using induction
restive river
Nice
mild comet
.close
kindred kayak
could someone help me with this? i have no idea how to even start
weak cove
Do you know what the principle of inclusion exclusion is
kindred kayak
no
weak cove
Well I assume this is for a class
And it was covered in a lecture , or a textbook you have access too
Have you tried either of those?
kindred kayak
i have slides
weak cove
I doubt that someone here can explain better than whatever materials were provided to you (or can be found online)
As far as just learning the topic that is.
The problem itself we can help once you are familiar just a bit with inclusion exclusion
Could you point to a specific piece of the slides that you don’t understand?
weak cove
Okay try that and then if parts of it confuse you, ask about them here
kindred kayak
Okay try that and then if parts of it confuse you, ask about them here
is it possible to go over one of the questions first
weak cove
It wouldn’t make sense to do that if you don’t know what inclusion exclusion is
Right
So it’s best we don’t
kindred kayak
i can get like an idea on how to solve the problem
weak cove
The idea involves using the inclusion exclusion principle almost exactly 😭
kindred kayak
i have to create a venn diagram?
weak cove
Please just watch the entire video
The question is testing your knowledge of the inclusion exclusion principle
So it requires that you know what that is and how it works
Which requires you watch the video atleast once
devout snowBOT
@kindred kayak Has your question been resolved?
kindred kayak
Please just watch the entire video
ive finished the video
<@&286206848099549185>
.close
grizzled crest
A 200-W motor operates a Carnot refrigerator between -2 to 15 C.
(a) What is the amount of heat per second extracted from the inside of the refrigerator? (b) How much heat is exhausted to the outside air per second? c) Suppose a Carnot engine can be operated between two reservoirs as either a heat engine or a refrigerator. How is the coefficient of performance of the refrigerator related to the efficiency of the heat engine?
devout snowBOT
A 200-W motor operates a Carnot refrigerator between -2 to 15 C.
(a) What is the...
grizzled crest
ask chatgpt
i showed work
earnest kite
ok ask chatgpt
devout snowBOT
devout snowBOT
Available help channel!
stuck ether
devout snowBOT
pallid lava
idk
dense jay
semi-annually, twice a year
stuck ether
how do I solved for the payment if the future value and present value is missing??
and vise versa
stuck ether
there should be a way
because our teacher did not say that the problem is unsolvable
dense jay
unless theres some information you havent shown, then as far as i can tell, no
stuck ether
thats all that there is
I already tried deviating but nothing
hmm, do I give the value for the payment???
<@&286206848099549185>
devout snowBOT
@stuck ether Has your question been resolved?
sly shadow
okay
dense jay
hmm, what do I do solved this??
i really dont think theres much you can do, you could add a value of your own and go from there i suppose
stuck ether
i really dont think theres much you can do, you could add a value of your own an...
I suppose thats all I can do
devout snowBOT
bro woke up and chose violence
sly shadow
bro woke up and chose violence
YE
dim dune
does this bot help with math questions using excel forms?
sly shadow
no need to apologise to them, just ignore them
u gay?
mild comet
does this bot help with math questions using excel forms?
What bot?
devout snowBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
mild comet
this bot?
devout snowBOT
@dim dune Has your question been resolved?
viscid shadow
The theoretical probability of the following
devout snowBOT
The theoretical probability of the following
viscid shadow
I believe my calculations are correct, but I just wanted to get a second opinion on the first two lines. Did I interpret the question correct?
devout snowBOT
@viscid shadow Has your question been resolved?
viscid shadow
<@&286206848099549185>
devout snowBOT
@viscid shadow Has your question been resolved?
cerulean crater
devout snowBOT
cerulean crater
I know how to find the derivative but the given point is giving me trouble
And the “four second partial derivatives” part is confusing too, do the want the next 4 derivatives or what?
quaint citrus
f_xx,f_yy_f_xy,f_yx
quaint citrus
I know how to find the derivative but the given point is giving me trouble
Plug in
cerulean crater
f_xx,f_yy_f_xy,f_yx
Do I need the double derivative in x direction and double derivative in y direction ?
quaint citrus
Ok ur first image is correct
cerulean crater
In the second one I found the equation for the tangent plane, with the points plugged in
quaint citrus
How come
cerulean crater
I was thinking I can use that to look for the x direction and y direction slopes at the point
It was also the equation professor taught us last (which isn’t a good reason 😅 )
quaint citrus
lol
Well idk what functional notation is
But to find slope of a surface at a given point
Just plug ur point into ur calculated partials
cerulean crater
Okay I’ll do that now, but what about the z value in the coordinates?
quaint citrus
So it’d be f_x(2,1) = ? And f_y(2,1) = ?
quaint citrus
Okay I’ll do that now, but what about the z value in the coordinates?
Well we don’t have to worry about that because our function isn’t implicit + it’s just asking for x and y directions
cerulean crater
So it’d be f_x(2,1) = ? And f_y(2,1) = ?
I got 5 and 6
quaint citrus
Good
cerulean crater
Well we don’t have to worry about that because our function isn’t implicit + it’...
So was I just overthinking it?
quaint citrus
I think so
cerulean crater
It’s just 5 and 6, that makes sense according to the other equation of the tangent plane
quaint citrus
Yea
quaint citrus
For part B use clairauts for mixed partials
cerulean crater
For part B use clairauts for mixed partials
What’s clairauts
quaint citrus
cerulean crater
Oh yes, we learned that one last lecture too, I just didn’t recognize the name
cerulean crater
So the question is asking for fxy and fyx which are equal
quaint citrus
Yes
quaint citrus
f_xx,f_yy_f_xy,f_yx
.
cerulean crater
f_xx,f_yy_f_xy,f_yx
This makes a ton more sense now, the wording was very confusing for me
Thanks man, you saved me!
quaint citrus
Np
quaint citrus
finite briar
Hello
so, I was 3b1b's video on the Fourier series
devout snowBOT
Hello
so, I was 3b1b's video on the Fourier series
finite briar
Now that I am done watching
I want to apply it
consider the following graph
generated by this code
wait actually
I should try this first 
lemme try this
hmm okay so the problem is integrating a piecewise function involving modular arithmetic
something like this
wait no this isnt the graph of what I plotted
devout snowBOT
@finite briar Has your question been resolved?
short island
devout snowBOT
short island
Could i have help with this question
safe knoll
Could i have help with this question
if u are asking about 3
the blank would be <1 is congruent to <6
cuz if <1 is congruent to <3 (givent) and <3 is congruent to <6 then <1 is congruent to <6
short island
.reopen
devout snowBOT
✅
safe knoll
is there any diagram given?
short island
Could you help with 4 and 5 also @safe knoll
short island
is there any diagram given?
Yes one moment
safe knoll
it would be simpler with a diagram
wintry jasper
i was wondering if there was a diagram
safe knoll
oh i thought they were triangle 
pseudo basin
angles 3 and 6 are not congruent due to "defn of congruence"
safe knoll
<1 and <4 are congruent due to vertical angles
wintry jasper
its because they are opposite angles
safe knoll
vertical angles are always equal
pseudo basin
its because they are opposite angles
vertical angles
wintry jasper
huh thats what they're called?
A pair of angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles or vertically opposite angles. They are abbreviated as vert. opp. ∠s.
all the names are valid ig but thats besides the point
@short island you can find which angles are equal using the vertical angle theorem
message here once you're done with that much?
devout snowBOT
Available help channel!
lusty swift
Regarding the product to sum identities for Trig: Do I need both sinAcosB and cosAsinB?
devout snowBOT
Regarding the product to sum identities for Trig: Do I need both `sinAcosB` and ...
wooden veldt
not really just remember one of them and switch the sin and cos if you get it in the other order
restive river
devout snowBOT
restive river
Please help
devout snowBOT
@restive river Has your question been resolved?
charred frigate
Hello, can you please check my mathematic calculations. i am cross-referencing my friends and I am not getting the values like my friend.
devout snowBOT
Hello, can you please check my mathematic calculations. i am cross-referencing m...
charred frigate
So this is my data.
This is her data
our density of ice (method 2) does not match up
i used this equation
we got the first one (that's the same) but the other values we got different
This is how i approached it in excel...
i even crossed check my second data with symbolab.. same answer
here is the equation
.close
marsh isle
tan^2(theta)-1 = 0
devout snowBOT
tan^2(theta)-1 = 0
marsh isle
I am not sure where to start
pseudo basin
gentle reminder that simply not saying anything is always an option
pseudo basin
I am not sure where to start
do you know how to solve equations that look like tan(x) = (number)?
marsh isle
i believe I have to use algebra in some way, but math isnt my strong suit lol
did a message just get deleted
willow helm
It did
marsh isle
okay i thought i was going insane
frozen aurora
yes, whoops
pseudo basin
i believe I have to use algebra in some way, but math isnt my strong suit lol
answer my yes/no question please
pseudo basin
do you know the unit circle...?
marsh isle
yes i do
pseudo basin
like, whatever you do, you'll end up reducing tan^2(x) - 1 = 0 to tan(x) = ±1
so you need to know which angles have tan equal to 1 or to -1
willow helm
If that's not understandable, try introducing a new variable for tan(θ), solve that and then substitute back
devout snowBOT
devout snowBOT
Available help channel!
cerulean rover
If I'm given a transformation such as f(x/5), how should I approach it? How would it affect a coordinate on a graph? And because it's horizontal, am I supposed to make it the opposite of itself 
Links to resources that I could use would also work! I can't find anything explaining a transformation using division anywhere online
devout snowBOT
If I'm given a transformation such as f(x/5), how should I approach it? How woul...
frozen aurora
If I'm given a transformation such as f(x/5), how should I approach it? How woul...
what would you do if instead of f(x/5) you had f(2x)?
what kind of transform is that?
cerulean rover
dilation right?
cerulean rover
Isn't that a type of dilation?
frozen aurora
maybe my english isn't the best
cerulean rover
oh np
frozen aurora
wdym by dilation, then?
cerulean rover
it would compress by 1/2
frozen aurora
oh i looked it up. yes, dilation
frozen aurora
it would compress by 1/2
great
so now, instead of (2)*x, we have (1/5)*x
it would compress by __?
just follow from how you got 1/2
cerulean rover
ohh so just x divided by 5?
frozen aurora
yes
it would compress by 5
aka stretch/dilate/whatever
open up desmos and put some sample functions and play around. i've never had any issues with function transformations simply because i gained my intuition from just tampering with parameters
cerulean rover
that's actually really good advice 
thank you so much!
frozen aurora
you can also think of the stretch in terms of "time" if travelled from right to left
if instead of f(x) you had f(x/5), it would take x 5 times as much "time" to get to the same value as before
it doesn't matter what kind of intuition you pick as long as it works for you lol
cerulean rover
Ohhh that makes a lot of sense
haha yes
and since it's horizontal, am I supposed to divide by 5 inside of 1/5?
cerulean rover
and since it's horizontal, am I supposed to divide by 5 inside of 1/5?
oh wait that's the same thing
frozen aurora
or divide by 1/5 ig
this is more general, use it
cerulean rover
pfft
cerulean rover
multiply by 5
oh okay! so it's the same thing as multiplication?
frozen aurora
i think dividing is better
if you have $f(ax)$, $a \in \mathbb{R}$, then the coordinate will now be at $\frac{1}{a}$
woven radishBOT
artemetra
cerulean rover
OH
frozen aurora
makes sense right?
cerulean rover
yes!! Thank you
frozen aurora
no problem
cerulean rover
using desmos is the best idea ever
frozen aurora
if instead of f(x) you had f(x/5), it would take x 5 times as much "time" to get...
btw, same goes for horizontal shifts
cerulean rover
Thank you so much for that too
frozen aurora
using desmos is the best idea ever
ikr!!! it's amazing
cerulean rover
btw, same goes for horizontal shifts
ohh right :0 it's a good way to think about it
thanks again!!!!
.close
finite stream
would the next x value be 0.5 or 1?
devout snowBOT
would the next x value be 0.5 or 1?
finite stream
,rotate
woven radishBOT
devout snowBOT
@finite stream Has your question been resolved?
finite stream
<@&286206848099549185>
devout snowBOT
@finite stream Has your question been resolved?
mild bronze
Why when sometimes I calculate it shows 1. as an answer? What does the dot mean?
mild bronze
worthy arch
The answer is 1 lol
spare hawk
Just to be clear this is what your calculator reads the way you have typed it $\frac{6}{2(2+1)}$
woven radishBOT
Winus
mild bronze
Why kid
mild bronze
Why did you harass me in DMs?
devout snowBOT
@mild bronze Has your question been resolved?
rapid lotus
what is he yappin about?
rapid lotus
dont open channels for practically no reason, someone might have an important question
supple knot
Why kid
You were given the answer, it's just formatting. What question do you still have
devout snowBOT
@mild bronze Has your question been resolved?
hidden hinge
devout snowBOT
hidden hinge
How is the second bound obtained?
plucky silo
-17/x + 6 is you top border and its a monotonically non-increasing function
that means that your highest point x = 0
y(0) = -17*0/2 + 6 = 6
lowest is x = 12/17
y(12/17) = -17/2 * 12/17 + 6 = 0
then you just write your top border as x(y)
just draw it to make it easier to understand
devout snowBOT
@hidden hinge Has your question been resolved?
midnight terrace
devout snowBOT
midnight terrace
no clue how to do this
radiant anvil
midnight terrace
alr ty
dense jay
that doesnt even have a vertex, again
should just say complete the square
unless it wants to make a function from it, but meh
midnight terrace
agh too bad i cant ask my teacher
dense jay
sure
dense jay
add to both sides (b/2)^2
what do you have at this stage
midnight terrace
c on the other side of =
dense jay
i mean, give me the whole equation at that stage after doing that
midnight terrace
mb
dense jay
nw
midnight terrace
x^2-8x=-12
dense jay
i guess, but thats not helpful
dense jay
actually
midnight terrace
(x-4)^2=4
dense jay
the left side of this is fine for immediate factorisation if youre gonna do it like this
midnight terrace
(x-4)^2-4=0?
dense jay
that would be all
open scaffold
not sure how to even go about this
devout snowBOT
not sure how to even go about this
brittle burrow
for a), you need some trig ratio that relates x and y
restive river
not sure how to even go about this
whats the problem
vernal lion
I am confused on how to factor this trinomial, I tried to solve using the Pythagorean theorem but it didnt help. Im not sure which numbers to mulply or add to start factoring
devout snowBOT
I am confused on how to factor this trinomial, I tried to solve using the Pythag...
smoky nimbus
Why Pythagorean theorem?
vernal lion
idk I was just spit balling
smoky nimbus
Do you know how to factor in general?
vernal lion
yea, you have to find a common factor
brazen pollen
idk I was just spit balling
I recommend trying to use the X-factor if you know it, if you don't I can give you a visual.
smoky nimbus
yea, you have to find a common factor
Not quite
vernal lion
I recommend trying to use the X-factor if you know it, if you don't I can give y...
yea idk what that is
smoky nimbus
This is one method https://www.youtube.com/watch?v=f0GqRY1ORbQ&ab_channel=BrianMcLogan
brazen pollen
This is one method https://www.youtube.com/watch?v=f0GqRY1ORbQ&ab_channel=BrianM...
This video helps, it'll show you the x-factor method
vernal lion
yes the video clears alot of thins up
for thr trinomial I cant seem to find any two numbers that when multiplied equal 18 but when added equal -17
smoky nimbus
It can be in any possible combination
But don't forget, it's A * C, and A = 6 and C = -3
So that's -18
smoky nimbus
So now you find the combinations of pairs that multiply to -18 but add to -17
vernal lion
(x−3)(6x+1) ok here is what I got as a final answer
alright yea it was correct thxs for the help
.close
flat marlin
devout snowBOT
flat marlin
I was getting some help earlier on this
Where I left off was that I needed to make this in terms of sin
I know csc is 1/sin
so 1/sin(5x) = =2sqrt(3)/3 is as far as I've gotten
this seems familiar to me but I can't exactly remember the means to solving it
brittle burrow
flip both sides to get sin5x=-3/(2sqrt3)
flat marlin
Wait I can flip both sides
Thats insen
Okay so sin(5x) is -3/(2sqrt(3))
So now I assume the next step is to somehow solve for (maybe an angle of) 5x?
flat marlin
yes try getting rid of the square root on the denom
Rationalize or do you mean get rid of it get rid of it
brittle burrow
eviscerate it by rationalising
flat marlin
Okay
I havent rationalized in a hot minute
Would that be multiplied by just sqrt3/sqrt3 or does the 2 come along for the ride as well
brittle burrow
just the square root
flat marlin
Okay so sin(5x) = -3sqrt(3)/12
brittle burrow
not 12
flat marlin
ahhhhh
now I recognize this more
So its a 60 degree triangle I believe
in the 4th quadrant
?
brittle burrow
which would be -60, but that's not the only possible answer
it is a property of sine that sin(180-x)=sinx
and sin(x+k360)=sinx for any multiple of k
flat marlin
So its -60, 240, 300
also does the 3rd quadrant work too
I was just thinking about that
brittle burrow
yes if you subtract 360 from 240
but also keep in mind the domain asked, from 0 to 360
the current answers you have are for 5x, so you're going to need more repeated solutions to find all of the solutions in that domain
flat marlin
Not sure what you mean by that
brittle burrow
and sin(x+k360)=sinx for any multiple of k
gives repeated solutions, like -60, 300, 660, etc. are all answers, but they are the same position on the unit circle
brittle burrow
and then about the 5x: to find values for just x, you will divide by 5
so 300 turns into just 60, for example
so you need to add more multiples of 360 to get all the answers for x:[0,360)
brittle burrow
and the same for 240
flat marlin
1740/5 is 348
brittle burrow
yes
brittle burrow
we'll start from $\sin(5x)=\frac{-\sqrt3}2$
woven radishBOT
chlamydia
brittle burrow
which gives $5x=-60, 300, 660, ...,$ and $240, 600, 960, ...$ by adding multiples of 360
woven radishBOT
chlamydia
flat marlin
so -60, 300, 660, 1020, 1380, 1740, 2100
this
for 300
wait
-60 to 240 is 300
and then 240 to 600 is 360
and 360
I'm not sure I get this
brittle burrow
-60 to 240 is 300
you first got that -60 was a solution, and then because it is a property of sine that sin(180-x)=sinx,
180-(-60)=240
those are two separate sets of repeated solutions
flat marlin
ohhh
okay okay I see
so 240 is the seperate set
and I need to add 360 to that set
so 240, 600, 960, 1320
1680
and that should be it
so -60, 300, 660, 1020, 1380, 1740, 2100, 240, 600, 960, 1320, 1680
All of those are the solutions?
brittle burrow
for 5x, yes
but not -60 because the domain is from 0 to 360
no negative solutions
flat marlin
AH
yeah that's right
So
I'm assuming this probably needs to be in radians
or nah
brittle burrow
the question is in radians, so yes
flat marlin
Okay so
5pi/3 , 11pi/3, 17pi/3 , 23pi / 3, 29pi/3, 35pi/3, 4pi/3, 10pi/3, 16pi/3, 22pi/3, and 28pi/3
devout snowBOT
@flat marlin Has your question been resolved?
devout snowBOT
@flat marlin Has your question been resolved?
devout snowBOT
@flat marlin Has your question been resolved?
devout snowBOT
@flat marlin Has your question been resolved?
restive river
Solve for $x$ in: [
5^{\map \ln x} + x^{\map \ln x} + 5^{1 + \map \ln x} = 35
]
devout snowBOT
Solve for $x$ in: \[
5^{\map \ln x} + x^{\map \ln x} + 5^{1 + \map \ln x} = 35
\...
woven radishBOT
restive river
so uh
i can see some obvious factoring and mingling to do in there
but nothing that makes this easier to solve
echo lagoon
combine those 5s so its nicer on the eye
restive river
yeah
echo lagoon
6*5^lnx
rich summit
,w 5^ln(x) + x^ln(x) + 5^(1 + ln(x)) = 35
woven radishBOT
rich summit
I don't think there is a nice solution
restive river
no there is
its a multiple choice question to a university entrance exam lmao
oh wait
rich summit
you mistyped
arctic field
restive river
.close
vestal hornet
ok so I just wanna make sure I'm getting this problem right
devout snowBOT
ok so I just wanna make sure I'm getting this problem right
vestal hornet
Use the Newton-Raphson method to figure estimate the 0-points with with an error that is smaller than $10^-5$
The functions have 0-points in the given interval
$$f(x) = x\sin x - \cos x \qquad x \in [0, \frac{\pi}{2}]$$
woven radishBOT
Feevo
vestal hornet
I didn't really get how to choose the first number, so I threw a shot in the dark and chose pi/4
so
$$f'(x) = x\cos x + 2\sin x$$
$$x_0 = \frac{\pi}{4}$$
$$x_1 = \frac{\pi}{4} \times \frac{\frac{\pi}{4} \times \sin (\frac{\pi}{4}) -\cos(\frac{\pi}{4})}{\frac{\pi}{4} \cos (\frac{\pi}{4}) + 2 \sin (\frac{\pi}{4})}
$$
woven radishBOT
Feevo
vestal hornet
and then solve that fraction, equate that to x_2, and go on until the error margin is smaller than 10^-5 ?
or am I missing something here?
devout snowBOT
@vestal hornet Has your question been resolved?
restive river
for $\m gx = \m {f^{-1}} x$: [
\m fx = \f1x -12\m gx
]
devout snowBOT
for $\m gx = \m {f^{-1}} x$: \[
\m fx = \f1x -12\m gx
\]
woven radishBOT
restive river
I'm trying to find the solution to this functional equation
i never did functional equations with inverses
what's the technique for these situations 
finite briar
Ig isolate g(x)?
u could also try calculate the inverse function using the second equation in terms of g(x)
but its possible that might involve g^-1 (x)
restive river
but its possible that might involve g^-1 (x)
i managed to conclude until [
x = \m f{\m{f^{-1}}x} = \m f{\f1{12}\p{\f1x -1}\m fx}
]
woven radishBOT
restive river
although dont know how to proceed
finite briar
wait I have dealt with functional equations of the form f(af(x)) = something before
but i dont remember 😭
paper latch
u can get $f(f(x)) \times f(x) = 1 - 12xf(x)$ by subbing in f(x) into x. might be useful idk
woven radishBOT
Frog_Man
finite briar
well f(f(0))=1
finite briar
**Frog\_Man**
f(f(1))*f(1) +12(f(1))=1
f(1)(f(f(1)) + 12) = 1
(I am subbing x=1 to find something)
okay no doesnt help
let $\frac{f(x)}{12x} - \frac{f(x)}{12} = z$ @restive river can you try substitue for x, f(x) from this equation?
woven radishBOT
ItzKraken
restive river
substitute for x?
finite briar
substitute for x?
Like isolate x from the equation I typed and substitute in the functional equation u found (dont sub for f(x))
restive river
[
x = \f{\m fx}{\m fx + 12z}, \q \m fx \ne -12z, ; x\ne 0
]
woven radishBOT
finite briar
okay that did not become what I was thinking..but if we substitute from here, \
$\frac{f(x)}{f(x) + 12z} = f(z)$
woven radishBOT
ItzKraken
finite briar
then $f(x) = f(z) \cdot (f(x) + 12z)$
woven radishBOT
ItzKraken
finite briar
then subbing for f(x), $f(x) = \frac{12zx}{1-x}$
woven radishBOT
ItzKraken
finite briar
$\frac{12zx}{1-x} = f(z) \cdot ( \frac{12zx}{1-x} + 12z)$
woven radishBOT
ItzKraken
finite briar
$\frac{12zx}{1-x} = f(z) \cdot ( \frac{12zx+12z-12zx}{1-x})$
woven radishBOT
ItzKraken
finite briar
$\frac{12zx}{1-x} = f(z) \cdot ( \frac{12z}{1-x})$
woven radishBOT
ItzKraken
finite briar
wait this becomes f(z) = x
wait this is the same functional equation we started with 
restive river
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
woven radishBOT
bathroom mug
tidal mulch
well f(f(0))=1
0 cant be in the domain can it?
finite briar
0 cant be in the domain can it?
no, not rlly
tidal mulch
I was checking if that was possible
1/x can be in your functional equation for f(x) and f(0) can still be defined
Or wait is it possible
tidal mulch
for $\m gx = \m {f^{-1}} x$: \[
\m fx = \f1x -12\m gx
\]
Where did you find this?
I mean you can try guessing solutions
Definitely won't have polynomial solutions
f(x)=1/13x works
calm frigate
Where did you find this?
is it solving for f(x) or for z in terms of f(x)?
calm frigate
oh ok ok
tidal mulch
f(x)=1/13x works
You get this by putting f(x)=kx^r
restive river
Where did you find this?
I found it in a set of challenging problems
arctic field
@restive river 
tidal mulch
I found it in a set of challenging problems
Well i can only find 1/(13x)
tidal mulch
Are there any other?
restive river
I'm unsure yet
tidal mulch
Do you have the solutions
restive river
nope
tidal mulch
If there are other this is pretty scary
Its pretty scary even if this is the only one
tidal mulch
1/13x is the only polynomial solution
Not a polynomial
I mean any solution thats a combination of powers of x
restive river
so rational?
tidal mulch
Yeah I was trying to find that word
You need degree 0 by degree 1 or else the degrees of both sides dont match up
arctic field
I found it in a set of challenging problems
and you're sure you didnt typo
like you did with that other question
restive river
this time definitely not no
oh wait
💀
💀 💀 💀
this is so embarrassing
please just like
tidal mulch
Dude
restive river
kick me out forever
tidal mulch
No way
tidal mulch
Lmao
arctic field
tidal mulch
I'm actually happy I found a solution to an incorrect fe
restive river
for $\m gx = \m {f^{-1}} x$: [
\m fx = \f1x \m fx -12\m gx
]
woven radishBOT
calm frigate
ig i m wrong but isnt it f(x)=12z/(1-x) @tidal mulch
restive river
THATS DEFINITELY IT
tidal mulch
Usually if you fuck up an Fe its just unsolvable
arctic field
its time for you to be exiled
tidal mulch
ig i m wrong but isnt it f(x)=12z/(1-x) <@961947864941068321>
No because you need f(x) purely in terms of x
calm frigate
No because you need f(x) purely in terms of x
ohh
restive river
They should make a !lex factoid which is "Please make sure u latex'd your question correctly"
tidal mulch
That too a solution like 1/13x
restive river
goddamn it why do i fuck it up everytime 
ill say @tidal mulch
f(x) has a fixed point at 1/13
arctic field
well you see
restive river
like with this
arctic field
your original question
tidal mulch
Yeah
arctic field
restive river
snow pls call me out everytime i post sus latex q's
thank u very much
actually
let me reopen with a consistent question
because like
this channel is a fucking mess
.close
gilded coyote
Not sure if more general math questions are allowed here. If not, just let me know and I can delete it.
I've heard of Euclidean Geometry and I've also heard of Non-Euclidean Geometry.
I don't exactly know what studying them looks like.
Is there a specific subject I'd look into if I was interested in non-euclidean geometry? Are there actual courses on this in undergrad? What level is it (meaning, what are the prereqs)? Does this have anything to do with differential geometry?
I'm very interested in looking at non-euclidean geometry because it just sounds so fun.
devout snowBOT
Not sure if more general math questions are allowed here. If not, just let me kn...
spare zealot
Non-euclidian geometry is any sort of geometry that isn't done on the typical n-dimensional plane (usually 2- or 3-dimnsional)
Common forms are hyperbolic and spherical geometry
If you want to look into it to see some of the differences, try playing around with spherical geometry (It'll be pretty easy to follow along because a lot of good examples are based on the Earth being an approximate sphere)
gilded coyote
Okay, thanks! I appreciate it 🙂
fallow sparrow
how do I express XOR using only NOT and AND?
devout snowBOT
how do I express XOR using only NOT and AND?
frozen aurora
try looking at the truth table
fallow sparrow
exclusive or
fallow sparrow
only true when both inputs are different
frozen aurora
good, we are getting closer
what does it mean for inputs (let's say x and y) to be different?
frozen aurora
yep
fallow sparrow
XOR = (X AND NOT X) OR (Y AND NOT Y)
fallow sparrow
false u mean?
frozen aurora
not yet
fallow sparrow
it also needs to be true when X is FALSE and Y is TRUE
fallow sparrow
X AND NOT Y OR Y AND NOT X?
frozen aurora
need a hint?
fallow sparrow
yes pls
fallow sparrow
why not put NOT NOT (everything we have)?
so do I get NOT(NOT(X AND NOT Y) AND NOT (Y AND NOT X))
frozen aurora
let me check
frozen aurora
so do I get NOT(NOT(X AND NOT Y) AND NOT (Y AND NOT X))
correct
sorry for late reply, my internet completely stopped working for a moment
flat pawn
can someone help me with my homework?
devout snowBOT
@fallow sparrow Has your question been resolved?
alpine forge
I did this, but with 0,0
i got fxx = 0 fyy = 0 (fxy)^2 = 0
so D = 0
which is inconclusive, how does (0,0) give the absolute minimum
alpine forge
It is a saddle point as I see here
lusty sapphire
It is a saddle point as I see here
You consider the local extremes AND the boundary of the domain
alpine forge
the domain is a circle
but since >= 0 we have a semi circle
lol
so hm
it's going down though?
lusty sapphire
but since >= 0 we have a semi circle
Quarter circle
alpine forge
right
alright let me check what that looks like
you're right
sadde point is the lowest
man how am i supposed to visualise that
lusty sapphire
I don't
alpine forge
uh
lusty sapphire
Just find the extreme points, evaluate those, then parametrize f along the boundaries of the domain and find those extreme points
It's a tedious process
devout snowBOT
lusty sapphire
devout snowBOT
Available help channel!
true ether
devout snowBOT
true ether
I don't even know where to start
pseudo basin
,rccw
woven radishBOT
pseudo basin
If $\log_9(5) = x$ and $\log_{27}(2) = y$, express $\log_3(100)$ in terms of $x$ and $y$.
woven radishBOT
AnnGhost
pseudo basin
(transcribing the problem for my own convenience.)
pseudo basin
I don't even know where to start
do you know log laws
devout snowBOT
@true ether Has your question been resolved?
runic hemlock
d
runic hemlock
If I want to calculate the growth of an account for investment, should I use the formula A=p(1+r/n)^nt?
woven radishBOT
Villiam
woven radishBOT
Villiam
devout snowBOT
@runic hemlock Has your question been resolved?
runic hemlock
.close
winter steppe
devout snowBOT
pseudo basin
did you write those values on purpose?
winter steppe
No
At first I wrote 7.365 and 7.375
And I tried to remove the 0.005s’ still incorrect
pseudo basin
At first I wrote 7.365 and 7.375
that would round to 7.37
you want to round to 7.36 instead
so shift that down by 0.01 lol
devout snowBOT
@winter steppe Has your question been resolved?