Got it?
#help-19
winter cradle
wary notch
rigid dragon
It would be easier to write it as 2 and 8/12 or in decimal form
Just remember it’s not 2.8
odd edgeBOT
@wary notch Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
light zodiac
What does a fraction to a negative power look like written out
mystic saffron
[
\f1a = a^{-1}
]
clever fjordBOT
rotund hawk
Wat are fraction powers like
a^(1/b) is the bth root of a
hybrid carbon
I would think n≥2
why?
hybrid carbon
The but s(1) is defined, right?
light zodiac
Yes
hybrid carbon
So if n=1, then s(1) can be found without using the expression s(n-1)/2
light zodiac
Soo is it C
hybrid carbon
I think so
The notation in this problem is a little funky
I can see why you got confused
light zodiac
Meow
hybrid carbon
...ok
light zodiac
Omg we got it right
hybrid carbon
it should be written like s(n) = brackets
with a case for n=1 and a case for the other formula
hybrid carbon
ah, just a sec
$
s(n)=
\begin{dcases}
24,& \text{if } n=1\
s(n-1)/2, & \text{otherwise}
\end{dcases}
$
clever fjordBOT
Xenophon
hybrid carbon
something like this
but instead of otherwise, you might have a blank
And the question should ask you to fill in the blank
with the answer being c
odd edgeBOT
hybrid carbon
np
odd edgeBOT
Available help channel!
fringe flame
odd edgeBOT
neon musk
oh man
fringe flame
oh rip
soz bro
i put it in the form e^z = e^a(cos(b) + isin(b)) = -2022 but i have no clue where to go from here
fringe flame
yep
so from there what do i need to do
do i convert them to complex
e^a(cos(b) + isin(b)) = -2022
like this or is there something else?
little tulip
exp(πi) = -1
e^z = -2022
e^z = 2022e^(πi)
e^(z-πi) = 2022
solution to the exp(z) = 1 are i(2πn)
little tulip
hence here it would be...
heady badger
odd edgeBOT
heady badger
does anybody know what z is here
odd edgeBOT
@heady badger Has your question been resolved?
fervent hound
does anybody know what z is here
you need to find out the value of phi (argument of Z) using trig formulas
and |Z| using the Pythagorean theorem
merry marsh
this is the function, I already differentiated it and found the critical numbers but how do I tell if its increasing or decreasing
winter cradle
Well what does the derivative tell you about a function?
merry marsh
this is the derivative, and the critical numbers are -2,0,4
and I just don't understand how to tell when its decreasing vs increasing off of the critical numbers
winter cradle
Yeah i got that
Again do you know what it means to take the derivative of a function
winter cradle
The derivative tells you how much a function changes or what the slope is at each point
When the derivative is negative the function decreases and when the derivatice is positive it increases
merry marsh
so if I set the derivative = 0 and solve with the critical number -2 and it comes out negative for example then its decreasing on that point?
merry marsh
I can't use the graph unfortunately, I can only use the function
winter cradle
It's so you can see what I mean
in this part the function is increasing
Also after
merry marsh
-2,0 and from 0,4
merry marsh
Ok I understand that, how do I figure that out without the graph
winter cradle
take a the derivative again
merry marsh
so the second derivative?
merry marsh
ok I got -20x^3+30x^2+80x for f''(x)
merry marsh
so set the function = 0? and factor out a 10x
winter cradle
Yes thats a good idea
Is there something about the function you can tell me already?
After factoring out the 10x
winter cradle
How did you get to that answer?
merry marsh
well I factored out a -10x instead so the 2x^2 could be positive
so I have -10x(2x^2-3x-8)
winter cradle
Do you know the Quadratic formula?
merry marsh
yes
winter cradle
Try using that I don't think there is a pretty way of factoring this one out
merry marsh
3/4?
winter cradle
What do you mean by that?
We are looking for the points at which the function is zero
merry marsh
x-3/4
winter cradle
What do you mean? Is that a solution ?
winter cradle
They should be three points at which f''(x) is 0
merry marsh
0,3/4, idk
merry marsh
hm? what is it then
merry marsh
odd edgeBOT
@merry marsh Has your question been resolved?
merry marsh
I actually need help
bronze canyon
ok I got -20x^3+30x^2+80x for f''(x)
you should find when f''(0)>0 and f''(0)<0 instead
when f''(0)>0, the function is increasing and when f''(0)<0, the function is decreasing
bronze canyon
you typed +8 instead of -8
try -8 instead, then we need -10x=0 because we divded -10x, which we know cannot be 0 because we cannot divide 0, so we need to consider this case seperately
then you can follow through with your properties of inequalities and find where f is increasing/decreasing
odd edgeBOT
@merry marsh Has your question been resolved?
odd edgeBOT
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Available help channel!
still stag
odd edgeBOT
still stag
i have no idea how to solve this
boreal juniper
okay
so we need an expression for the area of OMNP
we need the length and breadth right
you there?
still stag
yes
still stag
yes
boreal juniper
so the length OM is x
we need the breadth now
which is MN
now
MN is a vertical line
can we say that the x coordinate is same? For M and N
still stag
yep
boreal juniper
okay
so the coords of N are (x, something)
N lies on f(x) right
can we find the y coordinate?
boreal juniper
N lies on f(x) right
use this
still stag
okay
still stag
oh M doesnt lies on f(x) sorry i thought it was N
boreal juniper
im sorry
its N
N lies on f(x)
so the y coordinate of N will be f( its x coordinate)
right?
still stag
yes
boreal juniper
so it is sqrt(9-2x)
since the x coord of N is x only
as MN is a vertical line and the x coords of M and N are same
still stag
yes
boreal juniper
we get M as (x,sqrt(9-2x))
now we need breadth which is length of MN
M (x , 0) and N (x , sqrt(9-2x))
do you know distance formula
still stag
no
boreal juniper
hmm
the length of MN will be sqrt(9-2x)
you dont know the formula for distance between two points?
well this complicates things-
still stag
oh yes i know nvm
boreal juniper
okay
so M is (x , 0) and N is (x , sqrt(9-2x))
distance is sqrt( (x-x)^2 + (0 - sqrt(9-2x)^2 )
still stag
yes
still stag
yes
still stag
okay
still stag
i see
still stag
i get it now thank you !
boreal juniper
okay 🙂
still stag
.close
boreal juniper
odd edgeBOT
boreal juniper
I tried to write the individual terms but without knowing the value of n, it seems impossible
wooden python
do the {} refer to fractional part or are they just brackets?
boreal juniper
just brackets
wooden python
ok
boreal juniper
doesnt seem to be a geometric series
wooden python
if $L := \lim_{n \to \infty} f(n)$ exists, then $L = \frac{1}{2} \paren{L + \frac{9}{L}}$.
clever fjordBOT
AnnGhost
wooden python
doesnt seem to be a geometric series
nor does it need to be.
wooden python
we don't... neglect it as such.
boreal juniper
Then?
wooden python
rather we state $\lim_{n \to \infty} f(n) = \lim_{n \to \infty} f(n+1)$
clever fjordBOT
AnnGhost
wooden python
and we use the recurrence relation that defines f to turn this into an equation in L
naive bobcat
hi how do u differentiate
odd edgeBOT
hi how do u differentiate
wooden python
product and chain rules, or expand in full with binomial thm.
btw what are your pronouns? @naive bobcat
naive bobcat
anything
wooden python
we have an "any pronouns" role
naive bobcat
everytije i do chain rule i get soemthing weird
naive bobcat
boreal juniper
You have to use the product rule too
naive bobcat
do i do product rule first
wooden python
,rccw
clever fjordBOT
naive bobcat
wooden python
also your handwriting could be better
naive bobcat
like that
wooden python
so far so good, keep going.
boreal juniper
If the product rule seems complicated you can just simplify the expression?
wooden python
,rccw
clever fjordBOT
wooden python
but the answer from my calcukator is differebt
do you mean "it looks different" or "i can tell for sure it ISN'T equal to mine"
also your fives have started to suck again
naive bobcat
boreal juniper
you gotta simplify that
wooden python
so the former
yeah, some simplification is in order for yours
can factor out 5(1-x)^2
odd edgeBOT
odd edgeBOT
Available help channel!
clear tree
Cab the following be solved using geometric series
odd edgeBOT
Cab the following be solved using geometric series
clear tree
Or divergence test only?
wooden python
i mean you can view this series as the sum of a convergent geometric series and 1+1+1+1+1+....
and i think it is fairly obvious what happens to the series of infinitely many 1's even to those uninitiated in the topic
odd edgeBOT
@clear tree Has your question been resolved?
lucid stirrup
odd edgeBOT
lucid stirrup
How can I develop this i cant find a way
odd edgeBOT
@lucid stirrup Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
plain sun
for question e
odd edgeBOT
for question e
plain sun
how did they get the second answer
I know the first one just by doing the cos inverse and subtracting pi/6 on both sides, then the periodicity of cos is 2npi
but idk how to get the second answer
something something cos is a symmetrical function I think
thin kelp
I know the first one just by doing the cos inverse and subtracting pi/6 on both ...
cos is positive is quadrant 1 and 4
plain sun
right
plain sun
cos is positive is quadrant 1 and 4
but 7pi/12 is in the second quadrant
so is the other answer in the third
quadrant
thin kelp
ah ur right, yeah that means our answer is negative
and cos is negative in those 2 quadrants
plain sun
aight
so for the second quadrant cos is 7pi/12
wouldn't that mean 255 degrees (17pi/12) would be the third quadrant equivalent
plain sun
mm
but 255 - 360 is just -105
which is -7pi/12
so im curious how they got the -11pi/12
thin kelp
oh sorry i was eating
plain sun
np
thin kelp
so 7pi/12 is in quadrant 2 right that means our second answer would be 13pi/12, to which we can subtract 2pi or 24pi/24 to get -11pi/12
plain sun
so 7pi/12 is in quadrant 2 right that means our second answer would be 13pi/12, ...
but if pi - 5pi/12 is for the second quadrant, wouldn't pi + 5pi/12 be the third quadrant answer
like how sin 30 is equal to sin 150
.close
scenic raft
prove that: (A Δ B) = (A n B) implies A=B=∅
I am pretty sure we are gonna use the absurd method
I just need a clue on how to start
what exactly should I suppose
A not empty?
wooden python
suppose one of A and B wasn't empty
thin kelp
.close
mb sorry ill explain it in full, so we have x= cos^-1(-root2/2)-pi/6 right, ignore the pi/6 and note that our first angle is 135 right, and cos is negative in also the third quadrant, that means as pi-45=135 that means for our third quadrant we have pi+45 which is 225, so now we can subtract pi/6 and get our answers x= 105 (7pi/12) and 195 (13pi/12), now we know that 13pi/12 is outside the range so we subtract 2pi or 24pi/24 to get -11pi/12
plain sun
mb sorry ill explain it in full, so we have x= cos^-1(-root2/2)-pi/6 right, igno...
oh ok
thanks
odd edgeBOT
@scenic raft Has your question been resolved?
scenic raft
suppose one of A and B wasn't empty
what do I do from there
a not empty means there exists an x
in A
wooden python
without loss of generality let x ∈ A
does it belong to B or not? consider both cases.
scenic raft
hmm soo
wooden python
,rccw
clever fjordBOT
wooden python
and i already told you: consider both cases: one where x ∈ B and the other when x ∉ B
scenic raft
im sorry but like im struggling to understand
let’s say x belongs to B what do I do then
odd edgeBOT
scenic raft
what does it then belong to
.reopen
odd edgeBOT
✅
scenic raft
it belongs to A n B
I kinda did smth
which means it belongs to A delta B
implies x belongs to (A u B) n (B barre U A barre)
implies x belongs to (B barre U A barre)
wooden python
you overthought this
scenic raft
hmm
scenic raft
implies x belongs to (B barre U A barre)
which is the absurdity
wooden python
if x ∈ B then x belongs to A ∩ B but NOT to A Δ B
if x ∉ B then it's the other way around
either way we have contradicted the equality of those two sets
scenic raft
if x ∈ B then x belongs to A ∩ B but NOT to A Δ B
if x ∉ B then it's the other w...
that's what im struggling to understand I saw it somewhere but I don't get it
scenic raft
why do we say that
wooden python
https://discord.com/channels/268882317391429632/1168153444083847178
!noadvert
odd edgeBOT
https://discord.com/channels/268882317391429632/1168153444083847178
Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, and no one person can be prioritized over other people, so please patiently wait. Anyone who chooses to help you is a volunteer who is doing so out of their own kindness.
wooden python
that's what im struggling to understand I saw it somewhere but I don't get it
do you understand that finding an element which belongs to S but not to T, or vice versa, contradicts S=T
scenic raft
do you understand that finding an element which belongs to S but not to T, or vi...
I understand that
scenic raft
if x ∈ B then x belongs to A ∩ B but NOT to A Δ B
if x ∉ B then it's the other w...
but how did we implement it here
wooden python
you must be topper lol
"topper"?
wooden python
but how did we implement it here
in the very next line
either way we have contradicted the equality of those two sets
i.e.
either way we have contradicted the equality of A Δ B and A n B
scenic raft
can I ask for a favor ?
if you have the time and ability to write the solution down for me so I can understand it please
scenic raft
cuz I rly do not understand
I am so sorry
I mean I do but shouldn't we demonstrate it ?
the fact that if x belongs to AnB it doesn't belong to AdeltaB
it's obvious in the venn diagram
.close
strange mural
Let $d$ be a metric on $X$. Show that $\mathcal{B}_d={B_d(\varepsilon,x):x\in X,\ \varepsilon>0}$ forms a basis for a topology.
clever fjordBOT
jsidind810
strange mural
We check both properties of a basis:
This one is clear:
For each $\mathbf{x}\in X$, is there at least one ball $B=B_d(\mathbf{x},\varepsilon)$ in the basis with $\mathbf{x}\in B$? Yes -- for any $\mathbf{x}\in X$ and any $\varepsilon>0$, the ball $B_d(\mathbf{x},\varepsilon)\ni\mathbf{x}$ is in the basis.
clever fjordBOT
jsidind810
strange mural
But this one:
If $\mathbf{x}$ is in the intersection of two basis balls $B$ and $C$, is there another basis ball $D$ with $\mathbf{x}\in D$ and $D\subset B\cap C$?
clever fjordBOT
jsidind810
odd edgeBOT
@strange mural Has your question been resolved?
strange mural
<@&286206848099549185>
solid rune
**jsidind810**
Yes
odd edgeBOT
@strange mural Has your question been resolved?
woeful rivet
hi
woeful rivet
for this graph
for this do i say 15km/hr constant speed for 2 hours and then stop at 0km/hr for 1 hr and then 60km/hr constant speed for 30 minutes and then 46km/hr constant speed back to start
woeful rivet
wait
can u help me i dont get it
cus i did
60km/1.30hr
and then divided it by 1.30
60 by 1.30
to get just 1 hour
woeful rivet
its 40km/hr
hello sir
odd edgeBOT
odd edgeBOT
Available help channel!
untold jay
Let $H = \set{(x, y): x < y} \subset \bR^2$. How do I show H is connected?
clever fjordBOT
untold jay
It looks connected because it looks like a triangle
I tried contradiction, saying suppose it is disconnected
And then I instantly got stuck
My first idea was path connectedness
But I'm not allowed to use it
How would I do this without the notion of path connectedness
tough brook
There are a couple good ways to show things are connected
One of them is, assume it's disconnected and find a point that's in the closure of both disconnecting sets
untold jay
another idea was to produce a continuous map from some connected space onto this space
tough brook
Another one is, use the fact that a continuous function sends connected sets to connected sets
If you know that
Yeah
Another nice one is, prove that any continuous function to {0, 1} is constant
I like that one
untold jay
I really quite like the path connectedness method but egh
tough brook
I really quite like the path connectedness method but egh
It's really similar to the thing I mentioned about closures
Just a little more hands on
untold jay
hmmmm
yeah that might be a decent idea
the boundary of H is just the line given by (x, x)
tough brook
yeah the fact that H is open and not closed makes it hard to do the continuous function thing
odd edgeBOT
@untold jay Has your question been resolved?
trim venture
@untold jay can you use the fact that the product of connected spaces is connected?
untold jay
how would you write that space as a connected space
odd edgeBOT
odd edgeBOT
Available help channel!
crisp flume
could you please check if my solution is correct.
odd edgeBOT
could you please check if my solution is correct.
crisp flume
we were asked to determine whether transformation f from R^3 to R^2 is one-to-one, onto or bijection. and we were supposed to find kernel of transformation and its image
this is my solution
stiff shard
we were asked to determine whether transformation f from R^3 to R^2 is one-to-on...
sure, go ahead
stiff shard
yes I can
meanwhile I think you've written your transformation matrix incorrectly
it's $$\begin{bmatrix}2 & -1 & 1\
-4 & 2 & 1\end{bmatrix}$$
clever fjordBOT
_Kookie
stiff shard
the reason why it's like this is because of matrix multiplication
and also you generally want to write both inputs and outputs in column vector form
now I'll let you go ahead and give the problem another crack
crisp flume
But should I ignore transposition of matrix then?
That is why I wrote it in that form because I first swapped columns and rows
odd edgeBOT
@crisp flume Has your question been resolved?
odd edgeBOT
crisp flume
.reopen
odd edgeBOT
✅
odd edgeBOT
@crisp flume Has your question been resolved?
lapis turret
Is ab * ac = 2a + bc? or is it 2a * bc?
odd edgeBOT
Is ab * ac = 2a + bc? or is it 2a * bc?
stone cipher
twin urchin
i have a question regarding partial differentiation
twin urchin
i understand that the basis of this concept regardings holding one variable(s) constant to see the change of z in terms of another variable(s)
but
when actually computing the value numerically
why would I ever consider putting in the other variable
like
if I had f(x,y) = x^2 + y^2
and i wanna find the derivative in terms of y
and I get x^2 + 2y
why do I keep the x^2
I thought the 2y was the only valuable component
since thats what actually tells me how quickly my function is changing in terms of y
odd edgeBOT
@sullen kindle Has your question been resolved?
upper path
odd edgeBOT
upper path
I cannot figure out how to solve this 😭
fair prism
the entire 2y+2 is under the cube root, so naturally the entire expression should be raised to (1/3), not just the +2
odd edgeBOT
upper path
.reopen
odd edgeBOT
✅
upper path
This is confusing me
frail thistle
I think the just want the exponent and root on c
since any exponents or roots on 1 is just 1
upper path
So just root 5, c^4
upper path
For the C?
frail thistle
cause idk if they want the 1/ or just a -
upper path
frail thistle
With your first answer, the numerator will simplify to just 1
but the denominator (c) still needs the root and the exponent
frail thistle
ok so when you have a negative exponent, it is the same as putting it in the denominator and then taking that exponent
upper path
No negative exponents allowed
frail thistle
for example: x^-2. = 1/x^2
frail thistle
That's not right
upper path
A^1/11*1/11
frail thistle
a^m× a^n = a^(m+n)
upper path
Oh so is it a^11+11
upper path
Square root of 11?
frail thistle
if x^11th root what is it as a fraction?
frail thistle
yes that's right
upper path
Oh okay
upper path
Add
frail thistle
right
frail thistle
yup
upper path
For some reason it says it wrong
frail thistle
A^1/11+1/11
.
frail thistle
yup
upper path
TYY
frail thistle
no problem
upper path
.close
grand kindle
Cant figure out why my solution is wrong
odd edgeBOT
Cant figure out why my solution is wrong
grand kindle
I wrote the formula for a right hand cone
Then I subbed in h/2 instead of r because we know h = d
Then I just went along like normal
took out pi/12 cause its a constant multiple and that should be allowed
Cant see a reason this answer should be wrong
nvm
.close
tall iris
is $(S^{-1})' (10)$ the same as $[S^{-1}(10)]'$
odd edgeBOT
is $(S^{-1})' (10)$ the same as $[S^{-1}(10)]'$
tall iris
is $(S^{-1})' (10)$ the same as $[S^{-1}(10)]'$
south plume
what's S?
wary pawn
is $(S^{-1})' (10)$ the same as $[S^{-1}(10)]'$
' in this case is derivative?
tall iris
yes
wary pawn
By linearity yes
south plume
f'(10) = (f(10))'
south plume
it's more of a notational thing
tall iris
so its the same?
south plume
or am i interpreting this wrong
wary pawn
Yeah, S sounds like frame of reference
wary pawn
so its the same?
Yes
south plume
so its the same?
yep
wary pawn
It's because S' is usually used for a different referece frame
south plume
state-of-art AI is not particularly best at math
especially in such a case where notation is different
south plume
f'(10) = (f(10))'
but this applies if you take f(x) to be S^-1(x)
wary pawn
Euler notation on top 
wary pawn
Dxf
south plume
huh
wary pawn
$D_x f$
clever fjordBOT
Jane
wary pawn
i've seen it like twice in my life lol
It's nice for differential equations
tall iris
im trying to solve this question
one sec
\begin{mdframed}
Suppose that sand is stored in a large bag, but at time $t = 0$ the bag develops a leak. The amount of sand $S$ (measured in kilograms) in the bag at time $t$ (measured in minutes) can be modeled by the following function:
$$S(t) = K(1 - \frac{t^2}{\mu})^3$$
where $K$ is a positive constant and $\mu$ is a positive constant called the coarseness constant of the sand. The domain of $S$ is $[0, T]$ where $T$ is the time when the bag becomes empty
\end{mdframed}
\vspace{12pt}
\textbf{3. $S$ is an invertible function. You do not need to prove that. For this question, suppose that $K = 80$ and $\mu = 8$. Find $(S^{-1})'(10)$ using any method. (You do not need to provide units here unless you want to.)
}
clever fjordBOT
aaaaaaaa
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tall iris
$$S'(t) -\frac{6Kt}{\mu}\left(1 - \frac{t^2}{\mu}\right)^2$$
clever fjordBOT
aaaaaaaa
wary pawn
That should be easy enough, take out the 10, use chain rule, take that out then contants go to zero
Let K and mu be constant
tall iris
$$S'(t) -10t›\left(1 - \frac{t^2}{8}\right)^2$$
clever fjordBOT
aaaaaaaa
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
tall iris
when i sub in the values
tall iris
for the original equation i dont make it = 10?
wary pawn
Hold on
tall iris
$S(t) = K\left(1 - \frac{t^2}{\mu}\right)^3$
$S(t) = 80\left(1 - \frac{t^2}{8}\right)^3$
$80\left(1 - \frac{t^2}{8}\right)^3 = 10$
you get
$t=2,t=-2$
clever fjordBOT
aaaaaaaa
iron bear
is $(S^{-1})' (10)$ the same as $[S^{-1}(10)]'$
no
iron bear
f'(10) = (f(10))'
no
tall iris
whaat
south plume
huh?
iron bear
most people would read (f(10))' as the derivative of f(10), which is just 0
south plume
oh
iron bear
this is completely different from f'(10), which is f' evaluated at 10
south plume
why not?
iron bear
f(x) is a constant
south plume
well f(x) clearly depends on x
iron bear
yeah, and when you evaluate it, it becomes a constant
f(x) is a number
f is the function
south plume
i see
hm
so is it wrong to write something like (3x*e^x)' when finding derivatives
i've been doing this forever and my teacher was fine with it lol
iron bear
thats notational abuse which is done in highschool
south plume
so is it wrong to write something like (3x*e^x)' when finding derivatives
so how should this be written
or just.. not written at all
iron bear
well, i think in that context its clear enough
changing the notation would make it worse
south plume
what about $\frac{d}{dx}(3x\cdot e^x)$
clever fjordBOT
artemetra
iron bear
sure
south plume
okay
iron bear
anyway, (f(10))' is definitely not okay
south plume
got it
iron bear
thats all i wanted to say
south plume
TIL
clever fjordBOT
Jane
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
mystic saffron
**Jane**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
$S^{-1\prime}$
clever fjordBOT
mystic saffron
fwiw
fast ivy
odd edgeBOT
cold sage
ln is log base e, yeah
fast ivy
oh ok
odd edgeBOT
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odd edgeBOT
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mystic saffron
[(p ^ r) V q] -> (~q V r) need to find CFN and AFN from that formula
tall veldt
i worked out ag its 16.18
!occupied
odd edgeBOT
i worked out ag its 16.18
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
agile meadow
my bad
raven hinge
[(p ^ r) V q] -> (~q V r) need to find CFN and AFN from that formula
it might help if you clearify what mathematics genre this is and rather than writing acronyms actually write them out since there are alot of different cultures here. makes it easier for us to help (tho this might be above myhead tho)
mystic saffron
it might help if you clearify what mathematics genre this is and rather than wri...
ohh sorry thats from subject called logic and set theory
odd edgeBOT
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.close
lethal willow
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cold sage
...........
cold sage
void yew
lean willow
Where's peoblem 6,7,8,9 and so on?
lethal willow
its only 5
cold sage
i dont really agree with the way youre writing this
it is not by the inductive hypothesis that
1+2+4+8+...+2^k+2^(k+1)=2^(k+2)
its by the inductive hypothesis that
1+2+4+8+...+2^k+2^(k+1)=2^(k+1)-1+2^(k+1) which then =2^(k+2)-1
feels dodgy to write it in the order you did
void yew
you're actually checking all of these mad respect 🫡
lethal willow
i did like kinda what my teacher showed in class
to substitute a part of the IS using the IH then simplify
cold sage
yeah thats fine, its just you should only have equalities getting to the conclusion rather than having the conclusion there the whole time
and the adding one to each side also felt quite meh
cold sage
this is how it should be structured
lethal willow
alr
pls let me know if any of the other ones need any corrections, ill be back in a while, ty
odd edgeBOT
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lethal willow
.reopen
odd edgeBOT
✅
lethal willow
<@&286206848099549185> , pls let me know if 2-5 need anything to be changed
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lethal willow
.close
fresh token
Hello I need help in making my solution and the formula. really need help with my homework, thank you in advanced! ^^
fresh token
Im trying to find the measure of the angle of the two intersecting bike trails and the length of the pathway to the bridge
<@&286206848099549185>
.close
little mountain
I need help showing my work on how i found the multiplicative inverse of a 2x2 matrix from an x + y equation
fluid moth
surreal bluff
need help
clever fjordBOT
crisp wadi
Try perhaps 11^(x^3 - 8) * 3x^2ln(11)
odd edgeBOT
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hushed island
hushed island
can anyone help me wrap my head around this problem
I don't know where to start like at all
odd edgeBOT
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simple marten
The maximum is when every 2 lines intersects
And there is no intersection of 3 or more lines
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glacial terrace
Hello, can somebody explain to me how to solve this question. I have attached the solution along with the question.
glacial terrace
I tried to rewrite the inequality to that of an ellipse but couldn't get a proper answer
odd edgeBOT
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.close
finite scaffold
I have a set of numbers that repeat every 15th number. If I know all 15 numbers, I can calculate the phase and magnitude of the 15hz cosine wave, where 1hz covers all 15 numbers. Is the a way to calculate the phase of the 15hz cosine wave, without using all 15 numbers?
finite scaffold
I might have explained it wrong so I'll give an example. A list of numbers is:
2,35,20,21,37,12,38,34,40,7,29,13,32,25,42
Repeating over and over. I calculated the phase by summing
e^(2pii*index/15) over all 15 numbers, with the number 2 being 0 indexed, and taking the atan2(imaginary,real). The phase calculated to be about 149.888 degrees. Can I get the same answer with less numbers from the set?
odd edgeBOT
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teal folio
can someone help me
odd edgeBOT
can someone help me
void loom
so when you mirror a graph along the x axis it is just multiplied by -1
so y' = -y
y' being the reflected graph
teal folio
so when you mirror a graph along the x axis it is just multiplied by -1
my bad sir
im right here
can you walk me through this immensly complex situation
clever fjordBOT
Aino
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keen delta
ordinary differential equation
quasi sparrow
ordinary differential equation
!show
odd edgeBOT
ordinary differential equation
Show your work, and if possible, explain where you are stuck.
Available help channel!
night rapids
incomplete proof
odd edgeBOT
incomplete proof
night rapids
but idk how to finish it
Show that the subspace in F= is spanned by the polynomials of degrees at most p1, p2, and p3 together, constituting the subspace P_2 {p(x) = ax^2 + bx + c | a, b, c are real numbers}.
I did by using basis we can
say
where M is given to be convertible since it is not 0
And here it is shown
odd edgeBOT
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viscid kite
im confused how to do this question,
Kurtis is creating a game for a math fair. They attach n circles, each with radius 1 metre, onto a square wall with side length n metres, where n is a positive integer, so that none of the circles overlap. Participants will throw a dart at the wall and if the dart lands on a circle, they win a prize. Kurtis wants the probability of winning the game to be at least
If they assume that each dart hits the wall at a single random point, then what is the largest possible value of n?
wooden python
Kurtis wants the probability of winning the game to be at least
at least what?
dont delete your msg now!
wooden python
wdym won't allow it
wooden python
you could have just... written 1/2
viscid kite
oh i can?
wooden python
yes
wooden python
k
ok so we're assuming the probability of landing in any region is proportional to its area, yes?
viscid kite
yeah
wooden python
ok
then youll need to find the winning area and the board area, both in terms of n, and divide one by the other
and then write down the inequality (that) ≥ 1/2
viscid kite
thing is im not sure how to determine the winning area of the board area
wooden python
do you know how to find the area of a circle?
viscid kite
do you know how to find the area of a circle?
ya i just forgot the formula 😭
its area = pi • 1 (radius) right?
wooden python
it's pi r**^2**.
viscid kite
whys that?
wooden python
well, you know how area is measured in square meters, right
so it would make no sense for the formula to be A = πr -- on the left you would have an area and on the right you would have a length...
wooden python
in any case your circles have radius 1 each.
so what's the total area of the winning region, which consists of n such circles that don't overlap?
viscid kite
6.28 meters?
wooden python
are meters a unit of area or a unit of length?
viscid kite
unit of length
viscid kite
im pretty sure yes
wooden python
you are wrong, they cannot.
m (length) and m^2 (area) are units that are related to each other, but at no point should you EVER confuse yourself into thinking they are the same thing.
also, let me remind you that the area of a circle is given by A = πr^2.
so i ask you again:
what is the area of ONE circle with radius 1?
with units, please.
viscid kite
3.14^2?
clever fjordBOT
Ann
wooden python
also i did not ask you to approximate pi with 3.14, just leave it as pi.
also units.
@viscid kite
wooden python
wdym "get"
it is not like i did some formal manipulation that caused them to appear
i was only pointing out a misconception you had about what the exponent applies to in the expression $\pi r^2$. it applies only to the $r$, and not to the $\pi$ as well. the parentheses' purpose is to make that transparent.
clever fjordBOT
Ann
wooden python
if you really, really insist: i "got" them from my knowledge of the order of operations.
viscid kite
ok so is it just pi^2
wooden python
NO!!!
viscid kite
do i calculate the power?
viscid kite
well yes and no it depends if im going to approximate pi with 3.14
wooden python
❌❌❌❌
extremely loud incorrect buzzer
reading comprehension failed
no, the ^2 does NOT apply to the pi, and no it does NOT depend on whether or not you choose to replace pi with 3.14 (which you should not, anyway).
viscid kite
okay
wooden python
asking for the third time:
what is the area of ONE circle with radius 1 meter?
with units, please.
and leave pi as pi.
wooden python
viscid kite
what is 1^2?
its um 1 and the unit is 2 meaning squared right?
wooden python
no
fuck
the unit i wanted from you is square meters
the reason i asked is because you kept trying to say ordinary meters could be used as area units (which they can't)
viscid kite
so its 1m^2?
viscid kite
🥲
wooden python
it is pi m^2.