So prob the acceleration is wrong?
#help-42
unreal flame
jolly pilot
yeah
calm coralBOT
calm coralBOT
Available help channel!
blissful carbon
excuse me how would i do 14a
calm coralBOT
excuse me how would i do 14a
mossy gulch
brazen elbow
<#488120190538743810> I need Help in Differenciation and integration
you should open another channel
blissful carbon
when i do dot product of this do i just expand it normally
like how i would like (r+p)(r-p)?
.close
modern canyon
Can anyone guide me how to approach this problem?
calm coralBOT
Can anyone guide me how to approach this problem?
@modern canyon Has your question been resolved?
modern canyon
$C(A)$
potent lotusBOT
Pato
modern canyon
This is what I've tried: I must prove that C(AA^t) is a subset of C(A), and that C(A) is a subset of C(AA^t)
I define these sets:
\begin{align}
R(A) = \left{
\begin{aligned}
x_r \in \mathbb{R}^{k}
\end{aligned}
\ \middle|
\begin{aligned}
A^ty = x_r, y \in \mathbb{R}^{m}
\end{aligned}
\right}
\end{align}
\begin{align}
R(AA^t) = \left{
\begin{aligned}
y_r \in \mathbb{R}^{m}
\end{aligned}
\ \middle|
\begin{aligned}
(AA^t)^tz = y_r, z \in \mathbb{R}^{m}
\end{aligned}
\right}
\end{align}
\begin{align}
C(A) = \left{
\begin{aligned}
b \in \mathbb{R}^{m}
\end{aligned}
\ \middle|
\begin{aligned}
Ax = b, x \in \mathbb{R}^{k}
\end{aligned}
\right}
\end{align}
\begin{align}
C(AA^t) = \left{
\begin{aligned}
c \in \mathbb{R}^{m}
\end{aligned}
\ \middle|
\begin{aligned}
AA^ty = c, y \in \mathbb{R}^{m}
\end{aligned}
\right}
\end{align}
Then I assume a $v \in R^{m}$ that must satisfy:$\exists v \in \mathbb{R}^{m}$: $v \in C(AA^t) \implies v \in C(A).$
potent lotusBOT
Pato
modern canyon
i) $C(AA^t) \subseteq C(A)$: \begin{align}
\forall x \in \mathbb{R}^{k}: x = x_r + x_n \implies v = AA^ty = Ax_r = Ax_r + Ax_n = A(x_r + x_n) = Ax = b \in C(A)
\end{align}
potent lotusBOT
Pato
modern canyon
ii) $C(A) \subseteq C(AA^t)$: now, I asume a $w \in R^{m}$ that must satisfy: $w \in C(A) \implies w \in C(AA^t).$ $
potent lotusBOT
Pato
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
modern canyon
\begin{align}
w = Ax = A(x_r + x_n) = Ax_r + Ax_n = Ax_r = AA^ty = c \in C(AA^t)
\end{align}
potent lotusBOT
Pato
modern canyon
So, because $C(AA^t) \subseteq C(A)$ and $C(A) \subseteq C(AA^t)$, $C(AA^t) = C(A)$
calm coralBOT
@modern canyon Has your question been resolved?
calm coralBOT
@modern canyon Has your question been resolved?
heady thistle
How do I prove that if ab|ac then b|c
calm coralBOT
How do I prove that if ab|ac then b|c
heady thistle
Where a, b, c are integers
torn gorge
divide by "a" the following equality ac=abd
torn gorge
That’s not proving it
are you sure ?
calm coralBOT
@heady thistle Has your question been resolved?
carmine sorrel
How do I prove that if ab|ac then b|c
write out the definition of what it means for ab | ac
calm coralBOT
@heady thistle Has your question been resolved?
heady thistle
write out the definition of what it means for ab | ac
I don’t get wym
ac = abm ??
Like
calm coralBOT
@heady thistle Has your question been resolved?
heady thistle
.close
calm coralBOT
unique ore
4/612/9+(-3/8)(-12/9
gloomy ibex
4/612/9+(-3/8)(-12/9
calm coralBOT
Available help channel!
viral kiln
um hello?
I would like some help with an algorithm.
#Trying to create a converting with minimal ifs/thens/else's and without the usage of any mappings
#a purely mathematical solution:
def number_to_symbol(num):
# Convert to ASCII value
ascii_val = ord(num)
# Apply a mathematical transformation
new_ascii_val = (ascii_val - 22) % 10 + 33 if ascii_val >= 49 else 41 - (ascii_val // 48) * 7
# Convert back to character
return chr(new_ascii_val)
# Example usage:
print(''.join([number_to_symbol(str(i)) for i in range(10)])) # Output: !@#$%^&*() I get an output of "()*!"#$%& instead.
@viral kiln Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
mellow pond
Am I going about solving this the correct way? I don't think im getting the correct answer.
calm coralBOT
Am I going about solving this the correct way? I don't think im getting the corr...
@mellow pond Has your question been resolved?
cloud token
hey this isn’t too math related but is someone available to call and help me study for the psat
quasi seal
just take the practice test bluebook has
cloud token
where
cloud token
uhhh
quasi seal
whens the psat?
cloud token
whens the psat?
tmr 💀
quasi seal
pffff
quasi seal
What’s on the psat
reading, grammer, "writing" (really just more grammer", and math
fudge off female dog
mossy furnace
<@&268886789983436800>
cloud token
what concepts
quasi seal
what kind of math
i think its mostly basica algebra
quasi seal
when u took urs
lol sorry i got banned for a second
cloud token
it’s alr
quasi seal
anyways i think when i first took it I got a 1540?
calm coralBOT
@cloud token Has your question been resolved?
livid hound
If 0<a<b and r is any positive rational number
then prove a^r<b^r
I know how to prove it for integers but not any positive rational numbers
ancient thistle
If 0<a<b and r is any positive rational number
then prove a^r<b^r
I know how to ...
are you able to prove that a^n < b^n if and only if a < b (assuming everything is positive and n is integer)
livid hound
yes
ancient thistle
okay so write r as a fraction and try to use this fact to deal with the denominator
viral kiln
.reopen
viral kiln
what math exactly do you need help with
the formula i'd just posted?
calm coralBOT
calm coralBOT
Available help channel!
hollow sphinx
calm coralBOT
calm coralBOT
@hollow sphinx Has your question been resolved?
hollow sphinx
<@&286206848099549185>
remote mural
i think rhis is a Cauchy-Euler differential equation, so try the substitution $y=x^r$ , which transforms the differential equation into an algebraic one to solve for $r$
potent lotusBOT
JustYourAverageDude
calm coralBOT
@hollow sphinx Has your question been resolved?
hollow sphinx
i think rhis is a Cauchy-Euler differential equation, so try the substitution $y...
It is, but why is the method of undetermined coefficients not working here?
i've tried it on other cauchy eulers and it works
calm coralBOT
@hollow sphinx Has your question been resolved?
calm coralBOT
@hollow sphinx Has your question been resolved?
calm coralBOT
@hollow sphinx Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
remote mural
I have a small doubt
I have this question and I solved for 2θ which lies between (0,π/2) however in wolframalpha alpha the range is given as [0,π)
remote mural
,w range of arccos((1-x²)/(1+x²))
potent lotusBOT
calm coralBOT
@remote mural Has your question been resolved?
bright sentinel
hey I need help with this integral.
So the integral of sin(x) is -cos x + c, but what do I need to do if there is a 3x?
bright sentinel
u = 3x
du = 3dx
dx = du/3
rocky knot
unless you're one of those "reverse chain rule" weirdos
i was about to say that, but i agree with you saying that u-sub will be cleaner
bright sentinel
$\frac{1}{3} \int -cos(x)$
potent lotusBOT
Frank
bright sentinel
is this the answer
hasty fiber
drop the int and add +c
bright sentinel
$\frac{1}{3} -cos(x) + c$
potent lotusBOT
Frank
bright sentinel
wow I walays forget this C
hasty fiber
still no, you didn't properly un-sub
bright sentinel
still no, you didn't properly un-sub
what do you mean
hasty fiber
after taking the antiderivative you have -1/3cos(u) +c
potent lotusBOT
Frank
hasty fiber
$\cos(3x)$
potent lotusBOT
Steakanator
hasty fiber
let's make our tex look a little nicer 😌
bright sentinel
$\ -\frac{1}{3} cos(3x) + c$
potent lotusBOT
Frank
bright sentinel
how did you do that
hasty fiber
\cos
bright sentinel
$-\frac{1}{3} \cos(3x) + c$
potent lotusBOT
Frank
bright sentinel
$-\frac{1}{3} \cos(3x) + c$
potent lotusBOT
Frank
hasty fiber
now we're talking
bright sentinel
so this is the answer
lets goo
What is the reverse chain rule or do I not ned to know that @hasty fiber
hasty fiber
it's a shortcut that basically just does u-sub without explicitly doing u-sub
bright sentinel
it's a shortcut that basically just does u-sub without explicitly doing u-sub
is it recommened to use it?
or is u-sub good enoguh
enough
tight isle
U essentially just remember to divide by the number in front of x
hasty fiber
u-sub is more explicit and thus better for exams and such
tight isle
Debatable
In som textbooks it shows u to just divide and it's all simpler, a one liner solution
bright sentinel
probably just gonna stick with the u sub
have a test next week but need to practice more
thanks for the answers!
.close
calm coralBOT
calm coralBOT
Available help channel!
dusky verge
im not sure if this is a mathematical question but what is mean radius?
dusky verge
dusky verge
thhank you
do you have any advice on how to potenitally answer the question
do you know what the mean radius will be for a cylinder
calm coralBOT
@dusky verge Has your question been resolved?
dusky verge
i found the answer online but i was wondering if you guys can possibly explain to me on how they got the answer
like the whole integrals , why 0 to 2 pi, 0 to 1/4 pi and 0 to 2 pi again, and 3/4
and h/cos theta and a/sin theta
idk where it comes form
from
leaden thunder
find the definition of mean radius in your book
should be given in terms of an integral
or double integral
leaden thunder
yea so it just looks like they solved for r in both y = r cos(theta) and x = r sin(theta). not quite sure why pi/4 is taken to be the separating angle though.
dusky verge
this was there explaination in where i found the answer but tbh it was confusing me... it was a while since i touched calc so
could you possibly try to explain that
by ny chance do you know where 2h/cos theta is coming from and a/sinthata is coming from. like
why is one 2h / and the other is a /
calm coralBOT
@dusky verge Has your question been resolved?
calm coralBOT
@dusky verge Has your question been resolved?
untold compass
by ny chance do you know where 2h/cos theta is coming from and a/sinthata is com...
radius is from the middle to the outer surface, and for a cylinder it's either the round side or the 2 flat sides
since a is horizontal and h is vertical you use different trig functions for them
dusky verge
Oh i see!
That makes so much sence
sense
but now my question are the integrals. i know 0 to 2 pi is simply talking about the whole cylindr
where im confused is 0 to 1/4 pi and 1/4 pi to 3/4 pi
why is that the case.. yk
and your explaination makes sense why its h/2 cos theta and a sin theta
but what about the 2 before all of the integrals?
calm coralBOT
@dusky verge Has your question been resolved?
calm coralBOT
@dusky verge Has your question been resolved?
calm coralBOT
@dusky verge Has your question been resolved?
fleet cairn
I need help on this question about integration by parts
calm coralBOT
I need help on this question about integration by parts
fleet cairn
Lemme rewrite on paper actually
I gotta make left side equal right side and I tried by parts but I get stuck
Pls someone
I tried doing it by plugging in a number for n such as 2 or 3 but like then I can just sub in double angle formula for cosine
So idk how to use by parts for this
I’m getting 3 terms
Am I using the by parts formula wrong
<@&286206848099549185>
lapis sundial
,rotate
potent lotusBOT
lapis sundial
,rotate
potent lotusBOT
lapis sundial
wtf
frozen talon
try something like sin(x) sin^(n-1) (x)
not
sin^n (x) and 1
since
u get the term of
x
and x sin^power ( x) stuff is really hard to integrate
frozen talon
yep
lapis sundial
frozen talon
since he has it for 0 to pi/2 u can just use the beta function
frozen talon
So what would be my u in this case is it just sinx
try thinking which one will be more beneficial for u
the choice might be obvious after that
lapis sundial
orelse apply king queen
frozen talon
no
lapis sundial
you know that?
frozen talon
yeah i do
lapis sundial
damnn
fleet cairn
try thinking which one will be more beneficial for u
I’m trying using sinx as dv
fleet cairn
Ooohh wait
frozen talon
go on
lapis sundial
@fleet cairn whats the answer
lapis sundial
did u put limits?
fleet cairn
Oh shoot wait
Imma just do this again on another page this is too messy
Gimme a second
Now what do I do
<@&286206848099549185>
calm coralBOT
@fleet cairn Has your question been resolved?
calm coralBOT
@fleet cairn Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
@rigid hollow Has your question been resolved?
Available help channel!
coral moss
calm coralBOT
potent lotusBOT
k
nimble harbor
so
potent lotusBOT
k
nimble harbor
apply l'hopital and u'll realize the limit is 1
coral moss
it timed out
potent lotusBOT
k
fleet cairn
it timed out
U think u such a big shot huh bud
nimble harbor
u got it, ya?
calm coralBOT
calm coralBOT
Available help channel!
wind trail
i was sleepy as hell copying this off the board how do i find the divisor😭
wind trail
ik its (x-1) and (x-2) but idk from where
pure kayak
looks like theyre using the rational root theorem if you want to look that up
wind trail
is that different from rational zero theorem
pure kayak
nope, same thing
pure kayak
once they find a root, eg if they find that 1 is a root then (x-1) must be a factor of the polynomial
so thats our divisor
wind trail
whats the criteria for it to be the divisor? because in {-6, -1/2, 1} and {-1, 2} 1 and 2 were the divisor as u can see
just non negative?
pure kayak
im not sure what you mean
all that they do is, use the rational zero theorem to try find a zero, x=a
then (x-a) is a factor of the polynomial
so divide the polynomial by (x-a)
then factorise the left over to find the other roots
calm coralBOT
calm coralBOT
Available help channel!
honest kite
Hello! If anyone is into physics could you lend me a small hand in this exercise. I figured out the radius, the gravitational force and the centripetal force, but I dont have a clue where to continue with this exercise.
untold leaf
First step of general mechanics is to always draw your forces on the diagram!
honest kite
I have something like this
honest kite
First step of general mechanics is to always draw your forces on the diagram!
Im confused on what to do after this
untold leaf
Might be a bit more useful mentally to imagine your centripetal to be centrifugal so that it opposes Tension
but theyre the same force
Next step of general mechanics is to balance your forces!
The key here is to isolate it into vertical/horizontal forces (or force components)
honest kite
hmm.. and I already have those values of sin and cos because of this
untold leaf
yeah thats right, sorry im not too used to having values
honest kite
theyre symmetrical, plus Im not sure how would I even find the separate tensions
untold leaf
They are symmetrical but unless angular momentum is suffeciently high the top string has to oppose gravity
To find each tension seperately
you know that the horizontal tensions add together to Fc
and you can find what Fc is
untold leaf
same with mg
honest kite
same with mg
same
untold leaf
The reason we cant assume T1 = T2 is T1y is opposing mg and T2y is not, so vertically they are imbalanced, which affects T1
untold leaf
Nope, horizontally they are equally opposed by Fc
honest kite
from where did you get sixty?
untold leaf
theyre symmetrical, plus Im not sure how would I even find the separate tensions
assuming equilateral triangle (fair assumption in this case by how the labeled left side) then 60 degrees is the theta for the top left corner
the y component would be T1 * cos(60) in that case
untold leaf
That works, but make sure your trig functions are correct
that should be all, I gotta head to a solid state mechanics lab now
You got this
untold leaf
oh and last thing @honest kite, in future if you go down the list of
-Label force diagram
-if force is not axial, write out its direction components in terms of the force and trig
-write out the equations for each force
-equalize your forces
Then you'll never need help solving a mechanics question again, only checking your answer ;)
calm coralBOT
calm coralBOT
Available help channel!
west ermine
can anyone help me with this
calm coralBOT
can anyone help me with this
calm coralBOT
calm coralBOT
Available help channel!
rancid totem
ignore 39,41,43, i forgot how to rewrite natural log to exponential form pls i need the formula 
rancid totem
oh and ignore 37
calm coralBOT
@rancid totem Has your question been resolved?
amber yacht
calm coralBOT
@rancid totem Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
sturdy sequoia
hey i don't get how we can cross out the 5*y^6/6
calm coralBOT
hey i don't get how we can cross out the 5*y^6/6
pure kayak
because its even
it has the same value when 4 and -4 are subbed in
so they will cancel out in the evaluation step
calm coralBOT
calm coralBOT
Available help channel!
midnight torrent
can anyone help?
calm coralBOT
can anyone help?
midnight torrent
I just want to know if i did it correctly
its for intermediate microeconomics
But i am not sure if i derived correctly or calculated MRS correctly or got the marginal utilities right
calm coralBOT
@midnight torrent Has your question been resolved?
glad sinew
calm coralBOT
glad sinew
how did they divide the term multiplied by y''
is it just matrix multiplication with its inverse?
wait a minute
but the solution doesnt divide the term multiplied by y''
prime yacht
Wdym divide
glad sinew
cause its y'' multiplied by some term
mortal orbit
mortal orbit
(here it's row expansion instead of column)
mortal orbit
but its not in form y''+p(x)y'+q(x)y=0
It is if you remember what W is
glad sinew
wronskian says if the determinant != 0 then its two terms on the first row are linearly independent solutions
glad sinew
here in the question it says y1 and y2 are linearly independent
mortal orbit
here in the question it says y1 and y2 are linearly independent
I don't doubt that
I'm asking
what W is
what it's equal to
glad sinew
its the wronskian of ohhhh y1, y2
glad sinew
oh so this is already y''
mortal orbit
yes
mortal orbit
no worries
glad sinew
thank you thank you
calm coralBOT
@glad sinew Has your question been resolved?
glad sinew
imma stay here
calm coralBOT
@glad sinew Has your question been resolved?
calm coralBOT
@glad sinew Has your question been resolved?
glad sinew
Im not really sure whats happening here... so isnt gen sol supposed to be y=c1e^(r1x)+c2e^(r2x)?
and so y' would also be different
like this
mortal orbit
Im not really sure whats happening here... so isnt gen sol supposed to be y=c1e^...
it is, typo
glad sinew
oh ok
Im getting diff c1 values tho..?
currently doing another q, I'll take a look at this in a bit again
glad sinew
gon take a break, will be back
calm coralBOT
@glad sinew Has your question been resolved?
tired comet
i know this is a bit basic but i cant exactly figure it out: suppose BC is a chord of circle A, and that chord EF is perpendicular to BC at D. how do you show precisely that ED is maximized when EF is a diameter?
boreal rose
i know this is a bit basic but i cant exactly figure it out: suppose BC is a cho...
are there any ways u want to do this
like preferred topic
u can employ AM-GM inequality to show this i think
tired comet
u can employ AM-GM inequality to show this i think
can u show me how?
tired comet
like preferred topic
not rlly
calm coralBOT
@tired comet Has your question been resolved?
calm coralBOT
@tired comet Has your question been resolved?
tired comet
@boreal rose
calm coralBOT
@tired comet Has your question been resolved?
calm coralBOT
@tired comet Has your question been resolved?
calm coralBOT
@blissful zephyr Has your question been resolved?
calm coralBOT
@blissful zephyr Has your question been resolved?
steel depot
What is the sum of the first five prime factors of $2024^{2024} - 1$?
potent lotusBOT
m13
calm coralBOT
@steel depot Has your question been resolved?
gentle stream
What is the sum of the first five prime factors of $2024^{2024} - 1$?
keep doing difference of 2 squares until stuff happens
calm coralBOT
@steel depot Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
devout scaffold
Hi guys, I am struggling with this exercise. The reason I am struggling is because I am not sure what is meant by the line where it says "use |x| = {x >= 0, x < 0}".
remote mural
ok you can just split the derivative by parts, but u also have to check what happens in x=0
so f(x) = x/2 + x when x>=0 (easier to get the derivative)
and f(x) = x/2 - x when x<0 (easier to get the derivative)
remote mural
its not incorrect, but could be more explicit
devout scaffold
ahh I see
Hmm
so I have to almost split the answer to the question into two different cases?
of x >= 0 and x < 0
remote mural
yes but u gotta check if its differentiable where it splits
can you see why there it is not differentiable at x=0?
devout scaffold
yeah because you're dividing by 0
remote mural
no
devout scaffold
I don't think I see why
oh wait
Is it because the derivative changes from that of one of the functions to that of the other?
remote mural
yes that a way to say that
there would be two different values depending (for the derivative, not the function because both approach 0) if you approach left or right
so there is no derivative (at x=0)
devout scaffold
ahh
that makes sense
so there are 2 derivatives?
Thank you, I think I understand :)
remote mural
no there are not 2 derivatives
i mean informally yes, but when that happens there is no limit
the definition is f'(a) = lim h->0 f(a+h)-f(a) / h
uu wait i forgot something
devout scaffold
yea
like the derivative is different when x >= 0 rather than when x < 0
if you split it into two cases
remote mural
just sharp point --> no derivative cuz the derivative of each sides are different
remote mural
np
devout scaffold
.close
calm coralBOT
calm coralBOT
Available help channel!
remote mural
How do I get [
V_0^+ \8{e^{-j\5{2\pi z}\lambda} - \41{37}\8{11+j8}e^{j\5{2\pi z}\lambda}}
]
into a form of $a+jb$
potent lotusBOT
remote mural
I can likely just expand each of the exponentials, but that probably will take a while. Is there some shortcut I can use here?
calm coralBOT
@remote mural Has your question been resolved?
remote mural
ok the form turns out to be
[
\42{37} V_0\8{4\6\sin{\4{2\pi z}\lambda} + 13\6\cos{\4{2\pi z}\lambda}} - j \48{37} V_0\8{6\6\sin{\4{2\pi z}\lambda} + \6\cos{\4{2\pi z}\lambda}}
]
potent lotusBOT
remote mural
I guess you just gotta brute-force it...
agile elk
calm coralBOT
agile elk
need help with this
calm coralBOT
@agile elk Has your question been resolved?
desert sierra
can anyne double check my solution in diff cal problems?
calm coralBOT
can anyne double check my solution in diff cal problems?
desert sierra
unkempt drift
honestly just ask one q at a time pls
desert sierra
its just one quest
versed zinc
Personally I skimmed and they look all fine, they’re all basic rules though so kinda hard to mess it up
One thing is that you really love to over complicate stuff
desert sierra
Arigathanks yousef
calm coralBOT
@desert sierra Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
muted cargo
can someone explain how to do part (iii)
calm coralBOT
can someone explain how to do part (iii)
tawdry garden
can someone explain how to do part (iii)
this parabola is symmetrical about x =3, an inverse doesn't exist if the function is not one-one
but still, what does this question want. I don't even get the first part
muted cargo
the first part is just restricting the domain of the function so that it is (3, infinity)
this makes the inverse a function
<@&286206848099549185>
leaden thunder
this makes the inverse a function
show the equation of the inverse function
muted cargo
y = √(2x-8) + 3
leaden thunder
y = √(2x-8) + 3
pick any value a < 3 and find f(a)
since f(a) is in the domain of f^(-1), then you can find its value.
the easy way to do this is just apply the definition of inverse function
calm coralBOT
@muted cargo Has your question been resolved?
calm coralBOT
muted cargo
pick any value a < 3 and find f(a)
ok i just found the answers and they say this:
.reopen
calm coralBOT
✅
fleet verge
Where did the 2 go?
calm coralBOT
@muted cargo Has your question been resolved?
muted cargo
.close
calm coralBOT
calm coralBOT
Available help channel!
eternal wagon
Part e
eternal wagon
I've been attempting this for the past hour and I still haven't found a solution
Here's some of my work
calm coralBOT
@eternal wagon Has your question been resolved?
calm coralBOT
@eternal wagon Has your question been resolved?
calm coralBOT
@eternal wagon Has your question been resolved?
calm coralBOT
@eternal wagon Has your question been resolved?
unkempt drift
Part e
try using log base 10 instead
so $a = \frac{1 + \log 3}{\log 2 + \log 3}$ and $b = \frac{3 \log 2 + \log 3}{\log 3 + \log 5}$
potent lotusBOT
south's secret twin brother
unkempt drift
but $\log 5$ is now $1 - \log 2$
potent lotusBOT
south's secret twin brother
unkempt drift
oh and you want to find $\frac{1 + \log 2 + \log 3}{2 \log 2 + \log 3}$
potent lotusBOT
south's secret twin brother
unkempt drift
,w a = (1 + y)/(x + y), b = (3x + y)/(y + 1 - x), solve for x
potent lotusBOT
calm coralBOT
calm coralBOT
Available help channel!
distant lagoon
Can someone please help me solve 5m/4 = 1-2m/3?
I cant seem to arrive to the correct answer
unkempt drift
Can someone please help me solve 5m/4 = 1-2m/3?
I cant seem to arrive to the cor...
is that $\frac{1 - 2m}{3}$
potent lotusBOT
south's secret twin brother
unkempt drift
or 1 - (2m/3)
distant lagoon
1-(2m/3)
prime yacht
Can you show your work?
distant lagoon
yep, so I did a couple things because Im not completely sure
First was 15/12 = 12/12 - 8m/12
and then I wasnt sure whether to transpose the 8m/12 to the left or not
so If I did that then 15m/12 -8m/12 = 12/12
which means that 7m/12 = 12/12
but then I couldnt figure out what to do from there, to get the correct answer
Could I have some help from that step, or have I already done something wrong?
unkempt drift
yep, so I did a couple things because Im not completely sure
First was 15/12 = ...
you need to add both sides by 8m/12, that's the problem
so 23m/12 = 12/12
and 23m = 12
distant lagoon
got it, thanks!
distant lagoon
you need to add both sides by 8m/12, that's the problem
wait, that cant be right?
wait it is
xD
sorry!
thanks!
.close
blazing sparrow
need help with 6a(maybe) and 6b. ik my 6b is wrong after using cross product formula to solve for the curvature. here is my work:
https://cdn.discordapp.com/attachments/1293680991025758269/1297441562355306578/IMG_1937.png?ex=6715f01d&is=67149e9d&hm=a9585c79fd011a0bf45e520d30ace6b66585db3f4878c75cf46c7532ff53d2e6&
calm coralBOT
need help with 6a(maybe) and 6b. ik my 6b is wrong after using cross product for...
@blazing sparrow Has your question been resolved?
calm coralBOT
@blazing sparrow Has your question been resolved?
blazing sparrow
<@&286206848099549185>
calm coralBOT
@blazing sparrow Has your question been resolved?
calm coralBOT
@blazing sparrow Has your question been resolved?
real veldt
what is the parametric form of the equation y=-coshx
calm coralBOT
what is the parametric form of the equation y=-coshx
eternal shard
what is the parametric form of the equation y=-coshx
The are many ways to go about it, the simplest would be just (t, -cosh(t))
real veldt
The are many ways to go about it, the simplest would be just (t, -cosh(t))
thanks i am just dumb in math i needed it to make a physics problem
.close
calm coralBOT
calm coralBOT
Available help channel!
warped solar
Hi, i need help to solve the point (iii)
calm coralBOT
Hi, i need help to solve the point (iii)
warped solar
We have a matrice and they are asking for which m, the equation system has solution, and if there is one, if she's a unique one or not
tried to use chatgpt to solve the problem but i don't get it
warped solar
we're still to the point which we haven't seen the determinant of the matrix, only know to make substitution in one to others one.
If there is really no other way, could you explain the determinant of the matrix in the last ressort?
Never heard of
calm coralBOT
@warped solar Has your question been resolved?
warped solar
.close
calm coralBOT
calm coralBOT
Available help channel!
amber wedge
f(x)=x^3+bx^2+cx+d
calm coralBOT
f(x)=x^3+bx^2+cx+d
amber wedge
i need to find a relation between b and c such that f(x) has a saddle point
prime yacht
Whats a saddle point
unkempt drift
i need to find a relation between b and c such that f(x) has a saddle point
you want f'(a) = 0 and f''(a) = 0 for some a then
unkempt drift
cool, so sub in x = -b/3
unkempt drift
so basically a point where f'(x)=0 , f''(x)=0 and f'''(x)!=0
actually the last condition doesn't work, third derivative not equal to 0
take y = x^5 at x = 0
that's why the 2nd derivative test is inconclusive
unkempt drift
<:catlove:920698762932920370>
np!
amber wedge
yeah the third derivative test doesnt always work
we can instead use the f'''(x) test
and check the sign of f"(x) left and right of the point
unkempt drift
and check the sign of f"(x) left and right of the point
yep exactly
amber wedge
generally
we can use this
for any n, if the first 2n derivatives at that point =0 and the 2n+1 !=0, then it's a saddle point
well now that i think about it
it's also inconclusive
cuz there are functions that have all derivatives=0 and still have a saddle point
well then
thanks again
.close
calm coralBOT
calm coralBOT
Available help channel!
zinc falcon
help with a please
calm coralBOT
help with a please
zinc falcon
i was able to get b
i found that the series gets a odd number added to the previous value everytime
but i'm struggling to get a explicit form for it
i just don't really know what steps to follow to find the explicit form
marble pendant
what is the asnwer of (a)?
zinc falcon
i don't know
zinc falcon
yeah
marble pendant
hint: ||each term of the sequence can be thought of the sum of that AP||
zinc falcon
ah you mean 2k+5 ?
marble pendant
k-1
zinc falcon
i don't get it
marble pendant
so write a series for that
have you learned this?
writing series for arithmatic series?
zinc falcon
yeah
marble pendant
okk
zinc falcon
a + bk
marble pendant
1 imo
zinc falcon
ah ok then makes sense
marble pendant
n >= 1
marble pendant
yup
zinc falcon
ohhh
marble pendant
1 + 5 + 7 + 9 ...
zinc falcon
the difference would be 2(k-1) + 5
but the initial number i'm not sure
but wait
how do i get 1
the first term of the sequence is 1
if i plug in 1 if would get 1+5
potent lotusBOT
Wumpus Man
zinc falcon
$\frac{n}{2}\left(2a\right)$
potent lotusBOT
eggman
zinc falcon
this?
marble pendant
$S_n = \frac{n}{2}\left[2a+(n-1)d\right]$
potent lotusBOT
Wumpus Man
marble pendant
this
zinc falcon
for n=1 you get 5
i think i found the solution
just take S_n = Sn-2 + Sn-1
no nevermind
but i think we can utilize Sn-1
nevermind thats recursive
ok
i just saw what you cooked
you need to add 1 to it
and you get every value
but how did you get that form
marble pendant
niceee
marble pendant
**Wumpus Man**
this form comes from a neat observation
if the ap is 3, 5, 7, 9, 11, 13
see 3 + 13 = 16
5 + 11 is also 16
so the sum of rthe term from start and end is constant
basically 2a + (n-1)d is just a_1 + a_n
multiply that with n/2
cause n/2 pairs
calm coralBOT
@zinc falcon Has your question been resolved?
calm coralBOT
@zinc falcon Has your question been resolved?
Available help channel!
Available help channel!
serene trail
Where do I go from here
calm coralBOT
Where do I go from here
strange lichen
no excuses
serene trail
I fixed it-
strange lichen
ok now what do u have
serene trail
5( m^2 -2m -15)
serene trail
It says to factor the GCF and trinomial- but I’m not entirely sure I remember how to factor the trinomial
strange lichen
ok lets look at the m^2 - 2m - 15 part
serene trail
Do I need to take the factors of 15 and make them add to 2?
Or is that smth entirely different
strange lichen
factors of -15 and make them add to -2
serene trail
Ok
That’s what I thought but I wasn’t sure
So that’s 3,-5
So they answer would be 5((m-3)(m+5))?
serene trail
Yeah you’re supposed to switch the signs..
strange lichen
try expanding (m-3)(m+5)
serene trail
That’s just what she told us to do- idk
strange lichen
try expanding (m-3)(m+5)
do this
strange lichen
simplify
serene trail
m^2 2m -15
strange lichen
m^2 + 2m - 15
strange lichen
ok lets look at the m^2 - 2m - 15 part
is that the same as this
serene trail
No-
serene trail
Flip the signs
strange lichen
ok
serene trail
And put the 5 on the outside?
strange lichen
ye
calm coralBOT
calm coralBOT
Available help channel!
sly tusk
bello
polar frost
hi
polar frost
I cant read that
sly tusk
holon
its blurry but
i need help understanding 2&3
-
log2^x + log2^(x+2) = 3 -
logb^x - logb^(x01) = logb²
mossy kayak
i would not use, eh, ^.
fleet verge
Log of what
sly tusk
dis how my teacher wrote the equation
logb^x - logb^(x01) = logb² dubass bitch gave nothing to work wit
mossy kayak
you should know log2(x) + log2(y) = log2(xy).
and log2(x) - log2(y) = log2(x/y).
Therefore, you get something like f(x) = k, solve for that.
mossy kayak
calm coralBOT
@sly tusk Has your question been resolved?
sly tusk
no
dull meteor
sly tusk
im cooked bro
sly tusk
<@&286206848099549185>
calm coralBOT
@sly tusk Has your question been resolved?
sly tusk
No
sly tusk
.close
calm coralBOT
calm coralBOT
Available help channel!
halcyon ore
calm coralBOT
halcyon ore
pls a graph is involved so its math
what do they mean it penetrate more deeply
as in its highest?
swift laurel
i think they are referring to the small peaks to the far left (very low distance)
calm coralBOT
@halcyon ore Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
jovial linden
pls help because i am stuck
calm coralBOT
pls help because i am stuck
golden sable
CRT
calm coralBOT
@jovial linden Has your question been resolved?
calm coralBOT
@jovial linden Has your question been resolved?
mental tendon
Chinese remainder theorem
calm coralBOT
mental tendon
19 * 29 * 11
calm coralBOT
Available help channel!
shy nova
sin(32) + sin(28) = cos(2)
calm coralBOT
sin(32) + sin(28) = cos(2)
shy nova
I need help with this proof