So what can I do?
#help-10
honest forum
brave bramble
I'm not sure! At this point, I want to try examples.
I'm looking at 41 = 16 + 25
Double that is 82, which is 9² + 1²
A way to go from 5² + 4² to 9² + 1²...
I mean 5-4 = 1 so your subtraction method seems lit. 5+4 = 9 too
honest forum
I looked at 13, which is 3^2 + 2^2, and 26, which is 5^2 + 1^2
Which gives the same pattern
However, if you start with 10, which is 3^2 + 1^2, you get that 20 = 4^2 + 2^2, which breaks any ideas of a pattern
brave bramble
3+1 = 4, 3-1 = 2
brave bramble
I'm about ready to check out
(n - k)² + (n + k)²
honest forum
ohhhhhhhhhhhhhhhhhhhhhhhhhhhh
thats crazy
So any ideas for 5q?
Taking similar examples, we get 65, which is 5(3^2 + 2^2)
Which is 8^2 + 1^2
brave bramble
I don't know off-hand, but again I think we can determine a pattern here
honest forum
Taking 145, which is 5(5^2 + 2^2), we get 12^2 + 1^2
hmmmm
seems to be some pattern
So WLOG, assume that $n \ge k$
warm shaleBOT
Dork9399
honest forum
Can we prove that 5(n^2 + k^2) = 2*n^2 + k^2 + 1?
so 5n^2 + 5k^2 = 2n^2 + k^2 + 1
3n^2 + 4k^2 = 1
wait waht
oh whoops
it should be that 5(n^2 + k^2) = (2n+k)^2 + 1
5n^2 + 5k^2 = 4n^2 + 4nk + k^2 + 1
n^2 + 4k^2 - 4nk = 1
or only when $n - 2k = \pm 1$
warm shaleBOT
Dork9399
obtuse pebbleBOT
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Available help channel!
dry tulip
Okay this question is really screwing me over
obtuse pebbleBOT
Okay this question is really screwing me over
dry tulip
I dont understand how I got this wrong
Ive reviewed my work so many times
can someone tell me where I made the mistake, because I cant see it
<@&286206848099549185>
obtuse pebbleBOT
@dry tulip Has your question been resolved?
obtuse pebbleBOT
@dry tulip Has your question been resolved?
glacial wasp
do you need help
dry tulip
do you need help
yes please
I literally
got no idea why my answer is wrong
I have my work up if you have any questions
glacial wasp
what is the question you are working on?
dry tulip
its this
My answer is 8040 but for some reason, its still incorrect
heres my work to show for it
glacial wasp
Is this financial math?
dry tulip
yes
glacial wasp
algebra based or business calculus based?
glacial wasp
Is there a formula?
glacial wasp
I have no idea, you might try someone else who is better in finite math.
so ping again.
obtuse pebbleBOT
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red trench
does $f'(x^2)$ mean you plug in $x^2$ into $f'(x)$ or is it $(f(x^2))'$?
warm shaleBOT
lunchbox
twilit fable
f'(x) @red trench
red trench
so plug in $x^2$ into $f'(x)$ right?
warm shaleBOT
lunchbox
twilit fable
yes
obtuse pebbleBOT
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Available help channel!
graceful marten
obtuse pebbleBOT
graceful marten
Now you can get,
3a + lna - ln2a -> 3a + ln (a/2a)
Or
3a - (ln2a + lna)
a is positive
which one do I use
Or can i still use both
fickle turret
What's a/(2a)?
graceful marten
3a - (ln2a + lna)
Isnt this also correct
3a - ln (2a^2)
no?
but a has to be positive, so there will be a + and - answer for a via 2nd method?
fickle turret
Where does the a^2 come from?
zenith raft
fickle turret
But the two ln got different signs here?
graceful marten
But the two ln got different signs here?
-[ ln (2a^2) ]
fickle turret
Yes, and if you move a - out it becomes -(ln 2a - ln a)
fickle turret
Happens 👍
graceful marten
-ln2a/a = - ln 2
3a - ln2 =
zenith raft
when do we get an error_5507
fickle turret
-ln2a/a = - ln 2
3a - ln2 =
And then you can use the inverse rule for log
fickle turret
okokokokokkoko
If you are talking to sharp always react with 😂. She likes this
ill try it out
solar meadow
Could anyone sort them out please. It make take a while but I am doing it too.
Elementary Algebra
Abstract Algebra
Linear Algebra
Universal Algebra
Advanced Algebra
Classical Algebra
Structural Algebra
Commutative Algebra
Pre – Algebra
Boolean Algebra
Algebra 1
Algebra 2
College Algebra
Algebraic …
Associative Algebra
Unital Algebra
Zero Algebra
Non - Associative Algebra
Monoid theory
Group theory
Ring theory
Module Theory
Galois Theory
Field Theory
Category theory
Topos theory
Quaternions and Quadratic Forms
Lattice Theory
L-group Theory
Group theory
Representation theory
Homological Algebra
Number theory
Ring Theory
Advanced linear algebra
Field and Galois Theory
Category Theory.
Lie Algebra
Clifford Algebras
Tensor Calculus
Trigonometry
Calculus I
Calculus II
Calculus III
obtuse pebbleBOT
Could anyone sort them out please. It make take a while but I am doing it too.
...
graceful marten
Have you tried chat gpt
kind hawk
wdym, "sort them out"
graceful marten
Alphabetically
brisk matrix
i would seriously ask chatgpt to sort that
a lot of those are branches too which dont really compare like that
and a lot are intertwined as well
solar meadow
i would seriously ask chatgpt to sort that
Does it even have enough knowledge?
solar meadow
chatgpt is able to describe and interpret the names of those fields
Ok.
#close
.close
obtuse pebbleBOT
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viral robin
obtuse pebbleBOT
viral robin
for cosx in the last part i dont get how cos -1 get pi /6
how do u convert the degrees into pi
i forgot it was somethin g to do with radians
woeful lintel
multiply the angle in degrees with pi/180
u get radian equivalent
for eg
60 degrees
is
60*pi/180
=pi/3
ok'?
zenith raft
If you are talking to sharp always react with 😂. She likes this
wtf 
viral robin
pi/6
viral robin
how do u get the 11 pi/6
viral robin
i need to add some sort of degrees or something
brisk matrix
how do u get the 11 pi/6
arccos, or cos^-1, only gives you values between 0 and pi
but there are more angles on the unit circle which have cos(x) = sqrt(3)/2
the other one is 11pi/6
viral robin
how do i find the other valie 11pi /6
ik its between 0 and 360 degrees on the unit circle
i need to add 180 deggres
brisk matrix
viral robin
or something like that
brisk matrix
i need to add 180 deggres
you either do 360 - the other angle in degrees
and convert that to radians
or 2pi - the other angle in radians
viral robin
oh yea
woeful lintel
which grade u guys in?
viral robin
9
viral robin
idk what that is
i live in aus
so 2pi -pi/6 i get 5.759...
how does this lead to 11pi/6
viral robin
delicious
woeful lintel
☠️
viral robin
Its great the sausages are great if u ever come down u should try some
woeful lintel
fathom flicker
i would seriously ask chatgpt to sort that
.
whole halo
Hi, I need help with Question 14
obtuse pebbleBOT
Hi, I need help with Question 14
whole halo
mb
cyan oxide
I havent the fucking slightest what you just sent, looks like an 18th century thesis about isaac newton
whole halo
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obtuse pebbleBOT
obtuse pebbleBOT
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spare spruce
Hey i need help with a question
obtuse pebbleBOT
Hey i need help with a question
spare spruce
Can i send it here?
zenith raft
yes
spare spruce
also forgot to ask, will you be sending the answers as an image?
are you working out questions?
obtuse pebbleBOT
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young sonnet
@spare spruce for a
obtuse pebbleBOT
young sonnet
D < 330
inland matrix
It's closed
young sonnet
ight
obtuse pebbleBOT
Available help channel!
flat lance
general steps to solve a double sigma problem ?
∑∑ij types ?
obtuse pebbleBOT
general steps to solve a double sigma problem ?
∑∑ij types ?
slender kraken
such as?
this is p vague as theres plenty of problems you could come up with that involve double sums
obtuse pebbleBOT
@flat lance Has your question been resolved?
swift stream
Yeah, too vague
That being said double summations are just like any other summation
There is no need of anything that new. Other than switch the order of summation if it is more convenient, there are not that many tricks when it comes to double sums
worn gazelle
How would i do this
obtuse pebbleBOT
How would i do this
obtuse pebbleBOT
@worn gazelle Has your question been resolved?
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@worn gazelle Has your question been resolved?
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@worn gazelle Has your question been resolved?
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Available help channel!
dull pilot
Any hint
dull pilot
How to Solve That inequality ?
in place with heart i feel like i have problems
with right
estimaton
i wanted to get
to use
but i feel lke it aint work
full cloud
I am pretty sure you can directly use AM-GM
full cloud
@dull pilot hope that made sense
dull pilot
Thanks i will try using soon
digital badger
obtuse pebbleBOT
digital badger
Is this right?
reef topaz
What is the problem about?
inland hill
reef topaz
Is it given that the base is a regular hexagon?\
digital badger
Yup
reef topaz
Right, so a regular hexagon is made out of 6 equilateral traingles
You can use this information to find the base area
obtuse pebbleBOT
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obtuse pebbleBOT
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Available help channel!
brisk sedge
This is the work of a friend. Not sure if the answers are correct but I need someone to explain how to do them.
obtuse pebbleBOT
This is the work of a friend. Not sure if the answers are correct but I need som...
serene crane
brisk sedge
All of them
obtuse pebbleBOT
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tropic locust
Of the circled part, where did the right side of the equation come from?
obtuse pebbleBOT
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fluid gulch
How do i do b
obtuse pebbleBOT
How do i do b
fluid gulch
tired shell
one way would be to subtract from (a) all the arrangements with BB next to each other yea
to help with that count how many ways you can place BB amongst the other 4 circles and count how many ways you can arrange ARER
fluid gulch
What would the together equation be
fluid gulch
one way would be to subtract from (a) all the arrangements with BB next to each ...
Is it 5! X 2!
Would the final answer be 60
tired shell
ummm I can check but it should look like 180-something for most ways of doing it
I get 120 doing 180-(ways to place the BB)(ways to arrange ARER)
fluid gulch
I get 120 doing 180-(ways to place the BB)(ways to arrange ARER)
Huh
Isnt total 6! /2!x2!
And together 5!
So you subtract it then it would be 60
tired shell
oh by together you mean consider BB as one item? that's cool
you'd do 5!/2 because of the double R's still
fluid gulch
Oh ok
fluid gulch
oh by together you mean consider BB as one item? that's cool
Can you help me with this question
I dont understand
tired shell
there's an idea called the pigeonhole principle that deals with this sort of guaranteeing something has at least n things
if n = km + 1 objects are distributed among m sets, the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects.
fluid gulch
Is it?
tired shell
nah you could do 7+7+7+4 like evenly distribute them
steep pivot
Oh, 'guarantee'
tired shell
you can really just think of the worst case scenario and add 1
steep pivot
Guarantee requires worst case, which is even distribution
tired shell
like if I hand out 1000 seeds some pigeon is going to have a lot
tired shell
steep pivot
Worst case is even distribution, which would be 6+7+6+6 for 25
tired shell
it's asking about when there's no choice but for one bucket to have 25
steep pivot
Because of the word 'guarantee'
fluid gulch
So is the answer 6?
steep pivot
Why would the answer be 6?
fluid gulch
it's asking about when there's no choice but for one bucket to have 25
And what abt it?
steep pivot
Maybe think less random, and more if some jerk was purposefully distributing your seeds so that none of the pigeons would be full
steep pivot
no?
tired shell
tired shell
the answer is close to 100 because that's when it's around 25 seeds per pigeon
fluid gulch
Ohhhhh
steep pivot
24+24+24+25
steep pivot
(n-1)*(bins-1)+n
obtuse pebbleBOT
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obsidian oar
what equation represents the construction cost of a square based box with no top (open lid), where the cost to construct the base is double the cost to build the 4 sides
obtuse pebbleBOT
what equation represents the construction cost of a square based box with no top...
latent walrus
you tell me
obsidian oar
is it 4a + 2a...
latent walrus
technically sure, it probably wants it in terms of the box's dimensions though
obsidian oar
yeah my brain isnt working i cant figure it out.
ive labeled box height = y, length and width both = x
since square base
.close
obtuse pebbleBOT
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Available help channel!
sudden frost
Alright let's hope I get the formatting right this time
obtuse pebbleBOT
Alright let's hope I get the formatting right this time
sudden frost
Hey! I have an exact different equation here that I'm trying to solve but I'm getting stuck when it comes to integration constants (...yes, really.)
I need to find a solution for this:
$2 \frac{x}{y} dx + \left(1 - \frac{x^2}{y^2}\right) dy = 0$
Where x and y are non-zero. My step by step got me this far:
$2 \frac{x}{y} dx = - \left(1 - \frac{x^2}{y^2}\right) dy$
warm shaleBOT
Lucas
sudden frost
$\text{Find } \phi(x, y) \text{ s.t. } \frac{\partial \phi}{\partial x} = \phi_x = 2\frac{x}{y}, \ \frac{\partial \phi}{\partial y} = \phi_y = 1 - \frac{x^2}{y^2}$
warm shaleBOT
Lucas
sudden frost
$\phi = \int \phi_x dx = \int 2 \frac{x}{y} dx = \int \phi_y dy = \int 1 - \frac{x^2}{y^2} dy$
warm shaleBOT
Lucas
sudden frost
$\phi = \frac{x^2}{y} + g(y) = y + \frac{x^2}{y} + h(x)$
warm shaleBOT
Lucas
sudden frost
$g(y) = y + h(x)$
warm shaleBOT
Lucas
sudden frost
And then I got stuck. The expected answer is $\phi(x, y) = y + \frac{x^2}{y} + K$ where K is a constant. What I don't understand, however, is how on earth g(y) and h(x) became K. Can anyone enlighten me please?
From my understanding, both g(y) and h(x) are functions, not necessarily constants
sudden frost
last message is actually the first message. sorry for that, \\ doesnt seem to break latex into different lines and I had to fix the first msg.
ah, i figured it out!
well, since phi of (x, y) can be found by integrating either partial derivative, we can stick to a single one
.close
proven cape
7 and 8 please
obtuse pebbleBOT
7 and 8 please
proven cape
I tried 100=something
proven cape
oh 6 and 7, sorry
wary badger
7 and 8 please
so solve the differential equation first
using the initial condition after you integrate
to find an equation for y
the amount of grams
then t=1 hour
proven cape
y=Ce^(-0.6t)
C=100, t=1
so 7
V=Ce^([-1/40]t)?
ok so V=(1/10)Y sub 0
it is 9/10 sorry
ok it is done
.close
obtuse pebbleBOT
proven cape
Thanks @wary badger for help with 7
obtuse pebbleBOT
Available help channel!
empty mantle
Determine the value(s) of the local extrema you identified in the previous step. Write DNE for all extrema that do not exist. Separate multiple answers with a comma, if necessary.
obtuse pebbleBOT
Determine the value(s) of the local extrema you identified in the previous step....
empty mantle
i dont even know what the hell this is
the asnwer box is "local minimum values" and "local maximum values"
civic socket
empty mantle
ive done that, like the x value that they are at and it said they were wrong
high lily
for the min/max values they want the y value
empty mantle
so thats what it means by the value
just the y
okay that was correct
thanks
.close
obtuse pebbleBOT
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ember frost
Given a regular cyclic polygon with 20 sides. Calculate how many trapezoids (US) can be constructed whose vertices are of the cyclic polygon.
obtuse pebbleBOT
Given a regular cyclic polygon with 20 sides. Calculate how many trapezoids (US)...
ember frost
if it were asking how many trapeziums (US), its easy, there would be 20C4 trapeziums (US)
but im stumped on how to eliminate non-trapezoids (US)
obtuse pebbleBOT
@ember frost Has your question been resolved?
ember frost
<@&286206848099549185>
versed stratus
Given a regular cyclic polygon with 20 sides. Calculate how many trapezoids (US)...
US?
ember frost
trapezoid has different definition in the US and the UK
so i added that to avoid ambiguity
trapezoid US is trapezium UK, and trapezium US is trapezoid UK
versed stratus
hmm, so a quad with one pair of sides parallel?
ember frost
yea
versed stratus
hmm
find the set of points parallel to each otehr I guess
each pair of two points will have one anothe pair parallel to it
ember frost
each pair of two points will have one anothe pair parallel to it
yeah thats my goal, but i dont know the method to do so
versed stratus
hmm
for any two points you join, there will exist a side parallel to it
so they are c(20,2) such shapes
,w c(20,4)-c(20,2)
warm shaleBOT
versed stratus
yeah thats my goal, but i dont know the method to do so
does that make any sense
ember frost
does that make any sense
hm
obtuse pebbleBOT
@ember frost Has your question been resolved?
next slate
Hi there I am having trouble with this question, could I please get some help on it? Cheers!
obtuse pebbleBOT
Hi there I am having trouble with this question, could I please get some help on...
next slate
I tried equating the left and right of -1, getting 1/2 as an answer but that was not correct
fierce elbow
I tried equating the left and right of -1, getting 1/2 as an answer but that was...
what did u equate exactly
fierce elbow
for the function to be continuous
THe left hand limit should be equal to the right hand limit
not the functions itself
LHL = RHL
next slate
ahh okay let me have a look
Just wanted to ask one thing since were on the topic.
For this one I equated x^3+7/x^2+1 = bcos 3(x-2) and got it right
All I did was substitute 2
next slate
So I thought it would be the same here for this qn?
next slate
a=3, b=3
obtuse pebbleBOT
@next slate Has your question been resolved?
ember frost
THe left hand limit should be equal to the right hand limit
no
left hand limit = right hand limit = function value at that point
fierce elbow
left hand limit = right hand limit **= function value at that point**
yeah
oh I didnt mention the function value
mb
tawdry pewter
obtuse pebbleBOT
green epoch
product rule
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obtuse pebbleBOT
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Available help channel!
untold mirage
$$\frac{\left(\left(x\cos\left(R_{97}\right)-y\sin\left(R_{97}\right)\right)-c_{97}\right)^{2}}{z_{97}}+\frac{\left(\left(x\sin\left(R_{97}\right)-y\cos\left(R_{97}\right)\right)-d_{97}\right)^{2}}{z_{97}}=r_{97}^{2}$$
obtuse pebbleBOT
$$\frac{\left(\left(x\cos\left(R_{97}\right)-y\sin\left(R_{97}\right)\right)-c_{...
warm shaleBOT
Ayayon
untold mirage
Hi, im using this equation to create a circle and to be able to move it around
i am also able to dialate it to make a ellipse
but im not sure how i can rotate the ellipse (preferebly at its centre point)
obtuse pebbleBOT
@untold mirage Has your question been resolved?
untold mirage
this is in desmos btw
untold mirage
<@&286206848099549185>
obtuse pebbleBOT
@untold mirage Has your question been resolved?
untold mirage
<@&286206848099549185>
obtuse pebbleBOT
@untold mirage Has your question been resolved?
untold mirage
<@&286206848099549185>
cinder basalt
rotate towards what direction
brazen viper
@untold mirage https://math.stackexchange.com/a/434482/25445
untold mirage
rotate towards what direction
?
untold mirage
how abbout translating it then?
brazen viper
<@690847627239096410> https://math.stackexchange.com/a/434482/25445
@untold mirage this link contains the general form
untold mirage
cant seem to copy it properly?
brazen viper
Because it's typeset with mathml, just retype it
cinder basalt
untold mirage
https://www.desmos.com/calculator/urgd5ulglg
this loks like itll work ty
cinder basalt
okay maybe not
I don't know why it rotates counterclockwise
my bad
i mean
counterclockwise
fkwaokfo
clockwise*
nevermind
its ok
positive t --> clockwise
negative t --> counterclockwise
just change this bounds
untold mirage
okay
cinder basalt
ok to be honest i dont know why it rotates clockwise
obtuse pebbleBOT
Available help channel!
timid silo
Hello
paper dome
timid silo
I have some math questions I need help with. I just got into a uni and I'm lost,can I send photos here?
I'll send It here, wait a seconr
If 10^2x = 25, then 10^-x is equal to:
Simplify the expression
Simplify the expression
I'd like help in these three questions
Someone there? 😭
hexed gull
I'd like help in these three questions
you only need two operations to achieve 10^-x
you can start modifying the exponent
eg. by taking (...)^(1/2) on both sides
timid silo
I dont get It...
timid silo
The teacher gave these questions to us study potentiation
hexed gull
hexed gull
But 10^2=100
?
timid silo
They are
So
So It is basically a association? It doesnt mean that the value is literally that?
hexed gull
So It is basically a association? It doesnt mean that the value is literally tha...
but it is
10^2x = 25
x is a variable
so we don't know its value yet
hexed gull
ofc 10² = 100, x changes the value
10^(2x), if x = 2 for example, then it's 10^(2*2) = 10^4 = 10000
timid silo
Oh, i finally got it
Só I need to find the value of 10^-x using 10^2x?
But How do I do It?
And why do i use 1/2
obtuse pebbleBOT
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ruby elm
obtuse pebbleBOT
ruby elm
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obtuse pebbleBOT
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cerulean sapphire
The information given here is that the distance between AC is the same as the circles radius. We're supposed to decide what the angle v is. I have been stuck on this issue since I am not quite sure how to proceed with the problem.
obtuse pebbleBOT
The information given here is that the distance between AC is the same as the ci...
wispy wadi
https://en.wikipedia.org/wiki/Inscribed_angle
You can use this
They give AC = radius so you know what kind of triangle MAC is
cerulean sapphire
.close
obtuse pebbleBOT
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forest coyote
how can i prove this series is convergent?
obtuse pebbleBOT
how can i prove this series is convergent?
forest coyote
[\sum \frac{(n+1)!n!}{4^n}]
warm shaleBOT
diiegorgueez
worn yoke
ratio test is a good place to start
obtuse pebbleBOT
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ionic shore
hey
ionic shore
when we use newtons method
ionic shore
if I could have understand from that
why would then I ask on discord
whats newtons method for you
what or how can you describe it
civic socket
whats newtons method for you
I normal get it in coding way
using py
it's already on wikipedia https://en.wikipedia.org/wiki/Newton's_method
ionic shore
wait a second
you got and solve newtons method using programming
that so amazing
how you do that
civic socket
if you are good at py, you can get used to it
ionic shore
i know py
civic socket
ok then you should be fine
ionic shore
been making games using it
(lmodule -pygame)
civic socket
ill provide you an example, hold on
ionic shore
ill provide you an example, hold on
ok
subtle sinew
dude
i got newtons matheod but for what reason should i use
You can use it to find solutions to equations, that are complex to do by hand, to a good accuracy
civic socket
ok
def f(x):
return x**3 - 5 # f(x) = x^3 - 5
def f_prime(x):
return 3*x**2 # f'(x) = 3x^2
# define the newtons method here
def newtons_method(x0, f, f_prime, tolerance=1e-6, max_iterations=100):
for _ in range(max_iterations):
y = f(x0)
yprime = f_prime(x0)
if abs(yprime) < tolerance:
break
x1 = x0 - y / yprime
if abs(x1 - x0) <= tolerance:
return x1
x0 = x1
return None
# here's an example
initial_guess = 2
root = newtons_method(initial_guess, f, f_prime)
print("Approximate root:", root)
@ionic shore Has your question been resolved?
ionic shore
```py
def f(x):
return x**3 - 5 # f(x) = x^3 - 5
def f_prime(x...
What you mean by abs
civic socket
What you mean by abs
absolute value of a number
civic socket
yep
obtuse pebbleBOT
obtuse pebbleBOT
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summer pond
obtuse pebbleBOT
summer pond
Can I get any help to get started? Im not sure what it is asking 🥲
safe haven
,rccw
warm shaleBOT
smoky hound
Can I get any help to get started? Im not sure what it is asking 🥲
typically with these problems you want to start off analyzing the units of rates
obtuse pebbleBOT
@summer pond Has your question been resolved?
smoky hound
they give u really nice numbers to work with here. i would try making fractions with units and see where u get from there
obtuse pebbleBOT
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formal turtle
Could I walk through part a with a helper?
obtuse pebbleBOT
Could I walk through part a with a helper?
@formal turtle Has your question been resolved?
wispy canyon
How does one find the decimal answers to 6cos(x)+9=7 in the interval of [0,2pi)
wispy canyon
I got to cos(x) = -2/6 but that’s where I’m stuck
brisk matrix
have you heard of arccos
brisk matrix
what do you mean
brisk matrix
well the idea is x = arccos(-2/6) and x = 2pi - arccos(-2/6)
those are the only two possible answers between 0 and 2pi
wispy canyon
You lost me
brisk matrix
can you tell me what arccos(0) is
wispy canyon
Arccos of 0 is 1 right?
wispy canyon
Then I’m not sure
brisk matrix
do you know what arccos(0) means
wispy canyon
Wait is the 0 a reference to the range?
brisk matrix
it should return an angle on the unit circle where cos(that angle) = 0
can you look at the unit circle and give me an angle that does that
wispy canyon
And angle that gives 0 would be pi/2 then
brisk matrix
yes, but there is also another
wispy canyon
Ok
brisk matrix
the idea now is that arccos gives you an angle specifically between 0 and pi
so out of all the options
arccos(0) = pi/2
wispy canyon
Ok ok
brisk matrix
but if we want to find every solution to cos(x) = 0 between 0 and 2pi
we need to also include 3pi/2
wispy canyon
Right
brisk matrix
the way to do this is to count
arccos(0) = pi/2, and 2pi - arccos(0) = 3pi/2
wispy canyon
Ah ok
brisk matrix
in general you'd do arccos(whatever) and 2pi-arccos(whatever)
wispy canyon
Ok
brisk matrix
and that will give you all the solutions between [0,2pi]
wispy canyon
Ok
I got that
Im just not understanding the problem I guess
Because I tried what you explained to me and I still haven’t gotten the right answer
At least I don’t think I did
obtuse pebbleBOT
@wispy canyon Has your question been resolved?
wispy canyon
How does one find the decimal answers to 6cos(x)+9=7 in the interval of [0,2pi)
.close
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Available help channel!
vague isle
why dr/dt = dr/ds ds/dt ?
obtuse pebbleBOT
why dr/dt = dr/ds ds/dt ?
vague isle
it's the chain rule, but applied to what?
is r a function of s ?
civic socket
does dt represents time, dr represents velocity and ds the speed?
also they've used the chain rule
without seeing the full question whatsoever asking I think they wanted derivative of speed which is ds/dt
vague isle
dt time
dr is the position of the point along a curve
ds is the length of the displacement along the curve
my question is
why dr/dt = dr/ds ds/dt ?
civic socket
chain rule
obtuse pebbleBOT
@vague isle Has your question been resolved?
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@vague isle Has your question been resolved?
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Available help channel!
random quiver
how do I solve this: (x+3)/(x^2sqrt(2x+3))
obtuse pebbleBOT
how do I solve this: (x+3)/(x^2sqrt(2x+3))
fallow cove
how do I solve this: (x+3)/(x^2sqrt(2x+3))
What does this function equal to?
cuz we can't solve that if we don't have a = sign
random quiver
srry i meant integrate it
fallow cove
ahh
teal turret
$\int \frac {x+3}{x^2\sqrt {2x+3}}$
warm shaleBOT
Stephen
teal turret
$\int \frac {0.5 (\frac {u-3}{2} + 3)}{\sqrt{u} \cdot (\frac {u-3}{2})^2}$
fallow cove
srry i meant integrate it
so how did you do this ques?tion
warm shaleBOT
Stephen
teal turret
maybe that doesnt help
teal turret
oh yea perhaps
fallow cove
oh yea perhaps
So how did it went?
I don't have a pen and pencil rn
And also @random quiver here's a tip
If you are integrating something that has a square root, there is a high percentage that u-sub is needed and you u-sub the square root
random quiver
yeah i did that and then i could split the integral and the first part was easy but im stuck on the second part
$\int \frac {dt}{{(t^2 -3)}^2}$
warm shaleBOT
ouwedouwe
random quiver
this
fallow cove
Huh so you got this?
random quiver
12 times that and also another integral I already solved
granite dragon
**Stephen**
Try putting it into integral calculator they use u= square root 2x+3
The working out is SUPER long
fallow cove
12 times that and also another integral I already solved
So are you good now?
random quiver
So are you good now?
no i still dont know the other integral
random quiver
**ouwedouwe**
this one
random quiver
yeah im doing that now
I did sub with u and v and now I have 2 integrals and for the second one i have to do partial fractions
fallow cove
Cool
summer cliff
can someone tell me the answer
obtuse pebbleBOT
can someone tell me the answer
minor belfry
try first
high lily
can you show your work
high lily
you're misapplying the relationship between radicals and exponents
$\cbrt{x} = x^{\frac13} \redneq (\sqrt{x})^{\frac13}$
warm shaleBOT
ℝαμΩℕωⅤ
teal turret
yea
fleet stag
obtuse pebbleBOT
fleet stag
I don’t know how to do 10 b
I subbed in got an equation and don’t know what to do from there
obtuse pebbleBOT
@fleet stag Has your question been resolved?
violet compass
what software is best for drawing figures for a dissertation paper?
obtuse pebbleBOT
what software is best for drawing figures for a dissertation paper?
kind hawk
well depends on the figures
but shouldnt really matter too much. use software that you can use
obtuse pebbleBOT
fossil crag
just saw this <@&268886789983436800> jic they're not banned yet
last pilot
just saw this <@&268886789983436800> jic they're not banned yet
they arent
been going on for like 20 mins
they opened two separate channels; pinged mods in both. no response
warm canopy
Only blues are online rn so we can't ban
They're muted but we have to hunt down the links
And I'm on mobile 
fossil crag
If there's not enough mods I could be one but sometimes not that active
slim cove
just saw this <@&268886789983436800> jic they're not banned yet
they're dead now
warm canopy
Ty eric
fossil crag
they're dead now
thank you
last pilot
*ty
obtuse pebbleBOT
Available help channel!
cerulean maple
obtuse pebbleBOT
cerulean maple
I think
balmy cosmos
im gonna tell you how
so first you need to bring down the problem to 2 separate rectangles, and it will be easier if you draw them one next to the other
in the same position
one rectangle, the biggger one is 10x4
10 on base, 4 tall
right?
cerulean maple
Yep
balmy cosmos
no
i want you to extract it
i know that in the image is 4 tall
but i want you to extract it, and imagine it or draw it with base 4, meaning, rotate it
cerulean maple
Got it
balmy cosmos
so its EQUIVALENT to the other one. This way its easier for you to see it
okay, when 2 rectangles are equivalent
usually, they are not the same size
but there are certain RATIOS
that hold between them
cerulean maple
Like the scale factor
balmy cosmos
in this case
the scale will be the same
meaning that 10/4 will be equal to 4/x
the RATIOS
hold
now there you have it
10/4 = 4/x
balmy cosmos
keep it upo
obtuse pebbleBOT
@cerulean maple Has your question been resolved?
urban kiln
obtuse pebbleBOT
urban kiln
here's my attempt^
i did get m=c=0 and a=b but im unable to find what a or b is equal to
<@&286206848099549185>
bruh
torpid pasture
try sin²x=(1-cos(2x))/2
wintry swift
you need to find a and b such that $\lim_{x\rightarrow 0^{-}}(\frac{a-b \cdot cos(2x)}{x^2})=2$
warm shaleBOT
ThM
torpid pasture
Since you got a=b, this means (a-bcos(2x))/x² is actually a 0/0 form which is supposed to equal to 2 on the right hand side
wintry swift
Since you got a=b, this means (a-bcos(2x))/x² is actually a 0/0 form which is su...
youre arguing for a = b does not work, as you use x = 0, so you cant multipy by x^2 before
torpid pasture
true its circular logic
rotund kite
In a simple random sample of 70 automobiles registered in a certain state, 24.00 of them were found to have emission levels that exceed a state standard.
Find a 95% confidence interval for the proportion of automobiles in the state whose emission levels exceed the standard. (Round the final answers to three decimal places.)
The 95% confidence interval is ( , ).
obtuse pebbleBOT
In a simple random sample of 70 automobiles registered in a certain state, 24.00...
rotund kite
I got 0.232 and 0.454, and I do not understand why it is wrong, I also tried a few other answers I got including 0.2335, 0.4660. Still not right. I can't seem to get any of these confidence intervals right no matter what I do, including through chegg, calculators, or ai lol.
my calculations being
p= 24/70
n=70
z=1.96 (for 95%)
SE = 0.0567
ME= 0.111132
So then applying the Margin Of Error to my sample proportion it is 24/70 ± 0.111132 = 0.231657 (Rounded to 0.232), 0.454057 (Rounded to 0.454)
obtuse pebbleBOT
@rotund kite Has your question been resolved?
rotund kite
I also checked with my friend who's done engineering stats before and they with a calculator got the same exact answer so idk
obtuse pebbleBOT
@rotund kite Has your question been resolved?
obtuse pebbleBOT
rotund kite
.reopen
obtuse pebbleBOT
✅
twin sandal
I also checked with my friend who's done engineering stats before and they with ...
I just got the same with my calculator, that's correct
rotund kite
I just got the same with my calculator, that's correct
gonna kms cuz the system we use has marked every single answer I’ve gotten as wrong. I got a test due today n I’m not gonna take it bc I’ll just fail since it marks them all wrong 🤷♂️
I emailed him basically what I put here n hopes he looks at it lol
obtuse pebbleBOT
@rotund kite Has your question been resolved?
timid silo
.reopen
obtuse pebbleBOT
were you trynna reopen mine to talk ab it or smthn?
@rotund kite Has your question been resolved?
Available help channel!
steep cloak
So I need help with this task
obtuse pebbleBOT
So I need help with this task
steep cloak
So I know about the binomial coefficient but I have tried many times and didn't get the correct result.
(I have an answer sheet but unfortunately it has no calculation method) The answer for 1) should be ||7.4%|| and for 2) it should be ||30.02%||
Thank you in advance!
<@&286206848099549185>
<@&286206848099549185> 
tired shell
for 1) what's the probability for the first digit being a letter? multiply that by itself 8 times
for 2) you need to add to 1) the chance of exactly 1 digit for that you can do:
(ways to place the single digit in 8 slots)*(chance of digit)*(chance of letter)^7
obtuse pebbleBOT
@steep cloak Has your question been resolved?
steep cloak
for 1) what's the probability for the first digit being a letter? multiply that ...
Ooh so it is like either no digit at all (26/36) or (+) P(X=1) the probability of exactly one digit in there, so 8 (there are 8 ways to place 1 single digit) * 10/36 (probability of one digit) * 26/36 ^7 (^7, all the other are letters)
tired shell
👍 correct
obtuse pebbleBOT
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Available help channel!
hardy pike
obtuse pebbleBOT
hardy pike
i have this, i dont know how to do with a ordered pair. I end with the same.
warm shaleBOT
dqvidutzul
hardy pike
you have to replace all Xs in f(x) with $\sqrt{x}$
i dont get it, i mean the question say f: R -> R x R, so its ( x + 5 , 3x) or (x + 5,3x).
the question say whenever its possible, how can i compose the codomain R x R with N?
obtuse pebbleBOT
@hardy pike Has your question been resolved?
obtuse pebbleBOT
@hardy pike Has your question been resolved?
obtuse pebbleBOT
@hardy pike Has your question been resolved?
obtuse pebbleBOT
@hardy pike Has your question been resolved?
limber anvil
the question say whenever its possible, how can i compose the codomain R x R wit...
You can't
hollow island
Consider a digit sequence, an infinite list of digits between 0-9. The 'sequence product' is calculated by multiplying the corresponding entries of each sequence and adding them up. For example, if you had a_i=1234500000...... and b_i=678900000......, then the sequence product would be a_i*b_i which will be 1 x 6 + 2 x 7 + 3 x 8 +4 x 9 + 5 x 0 + 0 x 0 + 0 x 0 +.... = 6+14+24+36=80. If the sequence product of two digit sequences is 2024, is there anything that we can say about either of them?
obtuse pebbleBOT
Consider a digit sequence, an infinite list of digits between 0-9. The 'sequence...
tired shell
question is wayyyy too vague but here's something related https://en.wikipedia.org/wiki/Chebyshev's_sum_inequality
drifting wraith
we can say there's 25+ non zeroes
hollow island
question is wayyyy too vague but here's something related <https://en.wikipedia....
i understand that it is very vague lol. i just dont know how to a way to approach this question because of how vague it is. i was thinking we do smaller cases for the sequence product and find a pattern idk
hollow island
we can say there's 25+ non zeroes
yes, but thats obvious
obtuse pebbleBOT
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@hollow island Has your question been resolved?
obtuse pebbleBOT
@hollow island Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
covert palm
Hello i have a trigonometry question
obtuse pebbleBOT
Hello i have a trigonometry question
