@ruby magnet Has your question been resolved?
#help-26
topaz sinewBOT
ruby magnet
<@&286206848099549185>
topaz sinewBOT
@ruby magnet Has your question been resolved?
night sonnet
do u have a formula sheet you refer too?
thick oyster
f(x) = 3x^1/4 - x^3/4
topaz sinewBOT
f(x) = 3x^1/4 - x^3/4
topaz sinewBOT
topaz sinewBOT
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supple bay
topaz sinewBOT
supple bay
Could someone please help me with this problem?
topaz sinewBOT
@supple bay Has your question been resolved?
spring zenith
<@&286206848099549185> can u guys explain proportionality to me in more detail pls
topaz sinewBOT
<@&286206848099549185> can u guys explain proportionality to me in more detail p...
tawny citrus
It just means that when one value grows, the other does aswell but with an added constant as a factor as far as im aware?
spring zenith
yea but i dont get it
tawny citrus
lets say x is proportional to y
spring zenith
ok
golden blade
1/2
2/4
3/6
are all proportional because they are the same ratio
tawny citrus
then x = ky and k is any Number
spring zenith
oh
tawny citrus
Just like a linear function
and when you devide both variables, they always = that konstant k
versed escarp
<@&286206848099549185> can u guys explain proportionality to me in more detail p...
Can you please close the other channel you opened
static marlin
1/2
2/4
3/6
are all *proportional* because they are the same ratio
Yes because 1/2 = 0,5 2/4 = 0,5 3/6 = 0,5
spring zenith
ok
tawny citrus
Yes because 1/2 = 0,5 2/4 = 0,5 3/6 = 0,5
Right and then you d have y = 0.5x , or the other way around, depending on your function
tawny citrus
no not specifically
spring zenith
and u can also do
spring zenith
oh so like 2 and 6
tawny citrus
right, just anyyyyy number
Its just when one variable grows, the other grows aswell but either slower (k < 1) or it grows faster (k>1) , it relates both Variables
spring zenith
ok thxs soooo much 4 ur time☺️
static marlin
oh so like 2 and 6
Tell me 2 random numbers
tawny citrus
hahaha
spring zenith
@static marlin 5 and 10?
spring zenith
ohhhhh thxs
spring zenith
☺️
tawny citrus
If you had a function y=1/2 x , the proportionalityfactor would be 1/2, because every time x increases in 1, y increases by a half of x
static marlin
<@757287173975441418> 5 and 10?
spring zenith
so u divide?
tawny citrus
and if you have a function with an inserted point like 10 = 5k, k= 10/5 = 2
static marlin
k is always the same number,
spring zenith
k will always be same then
tawny citrus
yes
In the same function atleast
when you get k, you can get any other value pair for x and y
spring zenith
ok what does k stand 4 then
tawny citrus
its just a random variable
spring zenith
oh
tawny citrus
you could also call it c or d
spring zenith
or z
static marlin
ok what does k stand 4 then
It’s the rate of x/y
spring zenith
ok
tawny citrus
constant = any number
usually people use k or c and other letters depending on the context
tawny citrus
yea just make sure its not x or y
tawny citrus
spring zenith
u really helped
tawny citrus
Glad to hear
static marlin
i get it now
How old are you tho? This was kind of a beginner unit in my country
spring zenith
🤩
tawny citrus
Same we did this in 7th grade but i didnt understand it then either hahaha
Never to late to learn math
static marlin
Never to late to learn math
Yeah tell me about it 😭
tawny citrus
@spring zenith you have to close the chat I think
tawny citrus
Yeah tell me about it 😭
real struggle
static marlin
real struggle
We do more math in the physics class than the math class
tawny citrus
We do more math in the physics class than the math class
Same our teacher gave us a quick explaination for derivs and integrals because math is always so behind physics haha
and Vectors
static marlin
Same our teacher gave us a quick explaination for derivs and integrals because m...
My teacher says “your ability to do math is so weak” instead of teaching it
tawny citrus
Oh damn
static marlin
He just tells us the formula and that’s it
tawny citrus
What is your nineth grade physics?
static marlin
Energy and electric
static marlin
Energy and electric
And tens of threads under these
tawny citrus
and mechanical energy is so annyoing
static marlin
Isn’t it like Kinetic e. + potential e.?
tawny citrus
Yea
tawny citrus
Thats definitly true
little lantern
but it's weird bc it's a separate approach
tawny citrus
Exactly
little lantern
the guy who invented energy i think fought with newton, his name was leibniz
tawny citrus
The fact that i can cross check with kinematics is so wierd
tawny citrus
the guy who invented energy i think fought with newton, his name was leibniz
aHAHaha
Those two
little lantern
The fact that i can cross check with kinematics is so wierd
truee
topaz sinewBOT
@spring zenith Has your question been resolved?
grand ether
I need help with this :
topaz sinewBOT
I need help with this :
grand ether
find : $\frac{(\cos\theta+i\sin\theta)^{4}}{(\sin\theta+i\cos\theta)^{5}}$
thorny flameBOT
yøung matr!x
grand ether
<@&286206848099549185>
torpid matrix
<@&286206848099549185>
convert the top and the bottom into a different form
does cos(theta)+isin(theta) ring any bells?
wild flume
hint: e^itheta
topaz sinewBOT
@grand ether Has your question been resolved?
spring zenith
<@1245428411732590714> Has your question been resolved?
yes
grand ether
does cos(theta)+isin(theta) ring any bells?
obviously, they are reversed
torpid matrix
obviously, they are reversed
both the top and the bottom are can be converted into the other form (see heavenly lambs answer) then exponentiated and combined
which part do you not know?
thorny flameBOT
yøung matr!x
grand ether
**yøung matr!x**
this is the denominator
according to the law of multiplication of comp
complex numbers
earnest apex
**yøung matr!x**
just put them in euler's form
grand ether
just put them in euler's form
didn't take that
earnest apex
wdym didn't take that
grand ether
wdym didn't take that
idk it's not in the lesson
ik what eulers number is
but it's not solved that way
torpid matrix
this is like almost certainly intended to be solved by converting to e^(itheta) form
grand ether
$(\cos\theta+i\sin\theta)^4=\cos4\theta+i\sin4\theta$
thorny flameBOT
yøung matr!x
earnest apex
Yeah that's from Euler's form
grand ether
then after this step ?
earnest apex
Write it in e^it notation
thorny flameBOT
yøung matr!x
earnest apex
**yøung matr!x**
How did your prof even teach you this without using Euler's form
earnest apex
**yøung matr!x**
Wrong, it's integral e ds
grand ether
How did your prof even teach you this without using Euler's form
I am a self studying high school student
grand ether
Here's Euler's form
please
earnest apex
cos t + i sin t = e^it
grand ether
**yøung matr!x**
.
earnest apex
cos t + i sin t = e^it
By this (cos t + i sin t)ⁿ = e^int = cos nt + i sin nt
Proof of the Euler's form may be found using Taylor series
earnest apex
but what about the denominator
My job is over, you think now
hollow axle
We model a speed control system for a bicycle using a chain, a front sprocket (P) with a radius R = 10 cm, and several rear sprockets (P₁) with different radii r₁ between 2 cm and 8 cm. The front and rear sprockets are connected by a non-slip chain. (See Figure 1)
- Let ω be the angular velocity of the front sprocket (P) and ω₁ the angular velocity of a rear sprocket (P₁) with radius r₁.
Show that: ω₁ = (R/r₁)ω (1 pt) - 2.1. Calculate the number of turns n₁ made by the rear sprocket P₁ with radius r₁ = 2 cm when the front sprocket makes one turn. (0.5 pt)
2.2. Let nᵢ be the number of turns made by the rear sprocket (Pᵢ) with radius rᵢ corresponding to the maximum value of rᵢ. Calculate nᵢ
topaz sinewBOT
We model a speed control system for a bicycle using a chain, a front sprocket (P...
fathom atlas
question, if i post multiple questions will they be answered here? (like 3)
earnest apex
Well I'm gonna try to solve this
lemme read it
Do you know why v_chain is constant
@hollow axle
earnest apex
no, because the chain is a rigid object
every point on the chain has to be moving with the same speed as every other point on the chain
i just revised my rotational mechanics a day ago, came in handy :)
hollow axle
And for the second Qs . What I did .is it right?
hollow axle
And that's what I did for the last Qs
earnest apex
And that's what I did for the last Qs
wrong, n_i won't be R/r_i * 2pi
what you've written is the number of radians
you need to remove that 2pi
Number of turns made is number of radians / 2pi
hollow axle
If I am looking for the radius ri corresponding to the maximum value of ni, how can I do it
earnest apex
If I am looking for the radius ri corresponding to the maximum value of ni, how ...
if r is a constant, to maximize n_i you need to minimize r_i
since n_i = r/r_i
hollow axle
if r is a constant, to maximize n_i you need to minimize r_i
So, r=2cm ??
According to what's given in the exercice
Because we have r between 2cm and 8
earnest apex
yeah
topaz sinewBOT
earnest apex
I truly appreciate your help. Thank you
np, im glad to help you
topaz sinewBOT
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viral mirage
can someone explain how they determined A and theta
topaz sinewBOT
can someone explain how they determined A and theta
@viral mirage Has your question been resolved?
topaz sinewBOT
@viral mirage Has your question been resolved?
topaz sinewBOT
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unique dew
topaz sinewBOT
unique dew
im thinking a long ass integral by parts
Shiii
finite storm
its v^3
loud oasis
you can reduce the number of integrations by parts by starting with a substitution
topaz sinewBOT
@unique dew Has your question been resolved?
wet holly
i solve for what?
M?
cuz if so Idk how I'd do that
u were asking for a friend?
idk bro
im in calc
tag heplers
yeah
never heard of it
placid turtle
Weight of M?
Well first you need to draw M
Then arrow from M pointing down
Label as W = Mg
Yeah
Draw arrow upward to the left
Which is the left rope
Should be 54 degrees with vertical
No two arrows up
Idk about that
But I do it
Same for right arrow
One down one up right and one up left
To represent tension force
Yeah?
Yeah?
Ok np
tight rivet
topaz sinewBOT
tight rivet
How come the denomiator also becomes 3-(4/n)?? shouldn’t it become 1/(3n-4) times 1/n? why does it cancel out
final jungle
You multiply 1/n to both the numerator and denominator, so it's (3n-4) x 1/n on the denominator and 2n x 1/n on the numerator
topaz sinewBOT
@tight rivet Has your question been resolved?
eternal grove
I don't understand this notation
topaz sinewBOT
I don't understand this notation
eternal grove
Can someone explain this in English
finite storm
[e = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + ...]
eternal grove
Why are there !
thorny flameBOT
k
finite storm
from mclaurin
eternal grove
What?
finite storm
mclaurin series
river marsh
English pal do you understand it
river marsh
i thought this guy was trolling at first but notation kinda got real
eternal grove
I'm serious lol
eternal grove
The picture I showed you lol idk
eternal grove
Yeah
river marsh
does e represent eulers number?
eternal grove
Yes
river marsh
oh wow
eternal grove
I never learned any of these series or notations
river marsh
,w sum 1/n!, n=0 to infinity
thorny flameBOT
true coral
the first thing to note is summation notation
basically what it does is run through every number from n = 0 to n = infinity by substituting n into the equation 1/n!
for example the sum of 1/n would then be 1/1+1/2+1/3+1/4 + ... + 1/infinity
if the sum was from n = 0 to infinity
that's basically what's happening
eternal grove
Yeah, but why are we doing this? It would end up being infinity anyway
The summation notation makes sense but it doesn't make sense why we are using it here
true coral
Yeah, but why are we doing this? It would end up being infinity anyway
the reason is because it's not infinity
if you look at it it sums to e
that's why we're doing it
true coral
With the weird E
that's the summation symbol
topaz sinewBOT
@eternal grove Has your question been resolved?
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@eternal grove Has your question been resolved?
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@eternal grove Has your question been resolved?
topaz sinewBOT
@eternal grove Has your question been resolved?
topaz sinewBOT
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remote grail
how do i find a maximum of a multivar function with boundaries for each var
remote grail
as i understood i have to take both partial ders and set em to 0
and solve system of eq
eager compass
Yes
eager compass
That‘s The First Part
eager compass
Do you mean $x^{2y} - xy^{2}$ or $x*{2}y - xy^{2}$
thorny flameBOT
FluxusX2
remote grail
so either x=0
then y=0
or y=0
then x =0
or x-2y=0
then x=2y
plug into y(2x-y)=0=>y(4y-y)=0 => 3y^2=0 y=0
so all answers are 0
for second eq too cuz symmetrical eq
or what do you call eq where you can change variaables and the eq deosnt change
yeah, symmertric
buuttt
wait
say x=1 y=1/2
1/2-1/4=1/2
so 0;0 is NOT the right answer
why
eager compass
You need to find values of x and y so that together the equation you have = 0
remote grail
eh?
solve the sys of eq you meant or
what
k walk me through it
or just tell me what's wrong with what i did
eager compass
You have your function f and first you take the partial derivative f_x and f_y then you search the solutions of f_x = and f_y = 0
Then you should have something like x = some value and y = some value so that P(x, y) are 0 when you use them in both partial derivatives
eager compass
So you should have f_x = 2yx - y^2 and f_y = x^2 - 2xy
eager compass
whats P(x,y)
A point at the coordinates x, y
remote grail
uhh
eager compass
youre just telling me things i just sent you
Yes I just want to clarify so we don’t get confused
remote grail
what
how can a point equal something
Then you should have something like x = some value and y = some value so that P(x, y) are 0 when you use them in both partial derivatives
explain
x is some value, yeah that is 0 , y too
eager compass
Your function f(x, y) = value. You set the coordinates of a point in your function and get a value out of it
eager compass
No no
remote grail
so?
eager compass
Forget P(x,y) it just confuses you
remote grail
that was my point
why would i need that
alr, so what do i do after solving sys of eq
eager compass
You want to search all x, y where f_x = 0 and f_y = 0
eager compass
why would i need that
Just some formal notation
remote grail
well YEAH<<< thats what i told you
solve sys of eq
yes
next?
plug and evaluate func?
eager compass
Yeah and you found x = 0 and y = 0
remote grail
...YEAhh
eager compass
Now you want to build the H-Matrix
eager compass
The Hesse matrix
remote grail
eh never heard of it
and i bet its not necc for finding the extrema of a func
its just as you said formal notation to make it confusing
eager compass
You want to do that to find out if it’s an extrema or a minima
remote grail
extrema are maxima and minima....
eager compass
Maxima I meant
eager compass
If you plug it in you get 0 what do you wanna find out with that?
remote grail
start with f(x,y)=(x^2)y-x(y^2)
eager compass
0, 0 is an extreme yes but you don’t know if it is a minima or maxima
Or do you really just need to say it’s an extrema?
remote grail
ok, now:
f_x=2xy-y^2
f_y=x^2-2xy
remote grail
alr, retelling you whole process until we reach disagreement
!
ok, so
let f_x=f_y=0
2xy-y^2=0
x^2-2xy=0
correct?
eager compass
Yes
remote grail
ok.
y(2x-y)=0
x(x-2y)=0
so from #1 y=0 then x=0 from #2
from #2 x=0 then y=0 from #1
from #1 2x-y=0 then 2x=y then x(x-4x)=0 | x^2(-3)=0 | x^2=0 | x=0 and y=0
from #2 x-2y=0 then x=2y then y(2x-y)=0 | y(4y-y)=0 | y^2(3)=0 | y^2=0 | y=0 and x=0
eager compass
Yes
remote grail
but say f(1, 0.5)=1x0.5-1x0.25=0.25
so this is more than f(0, 0)
so f(0, 0) is NOT the maximum
eager compass
Yes
eager compass
You told me extrema can be maximum or minimum
fallow heart
It could also be a saddle
eager compass
It could also be a saddle
Exactly
remote grail
so why did the process not work
fallow heart
so why did the process not work
What exactly do you think did not work?
remote grail
i heard its the right process
eager compass
so why did the process not work
It did work but your not at the end
remote grail
What exactly do you think did not work?
i did not find all the extrema
fallow heart
!original
topaz sinewBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
remote grail
f(x,y ) =x^2y-xy^2 how to find maximum
idk
i mean, im more curious why the process didnt work
not about solving the problem
and what to do if it doesnt work
what is the process then if this is not the correct one
eager compass
You did everything right. You found a counter example to show that it is not a maxima nor a minima so you could either assume it is a point of inflection or there is no extrema for this function
eager compass
what is the process then if this is not the correct one
Usually you do everything you did for now. You did the partial derivatives then solved the equations. Then what you usually wanna do is set the hessian matrix implement your values in the matrix you found where you think that there are the extremes and then you want to take the determinant of the matrix and depending of the result you will know if it is a maxima minima or point of inflection
remote grail
with 1 var func it is
look i mean when you solve it and get an answer, its always one of the extrema, when you dont get an answer theres no extrema
so i got an answer here
so it must be an extrema
but it is not
so this is not the correct process for doing it
because its not consistent
its not guaranteed to work
eager compass
what is that mateix
Look on google
remote grail
what is then?
ok, so let me get this clear: is what i did the correct process?
for finding the extrema of a 2 var func?
huuuuuuuuh
eager compass
ok, so let me get this clear: is what i did the correct process?
It’s the right beginning of it you need to understand what the hessian matrix is and then your got imo
remote grail
ehh
eager compass
I’m kind of busy rn so I can’t help you further rn. But if you need more help to understand write me a pm so I can answer it later
eager compass
so theres some algorithm that converts the sol i got into the extrema?
It tells you if it is an extrema
eager compass
It can also be a point of inflection
remote grail
ehh
isnt there an algorithm that finds only extrema?
because as i undersrtood there isnt
alr
eager compass
You need to do it with the hessian matrix
remote grail
so is there or not?
topaz sinewBOT
@remote grail Has your question been resolved?
nimble rover
I have homework due in 4 hours, and its 15 questions, can someone help me with this?
topaz sinewBOT
I have homework due in 4 hours, and its 15 questions, can someone help me with t...
clear lodge
you should have been given the formulas for the trig functions of the double angle
lusty marsh
if theta lies in q4, only cos and sec will be positive
clear lodge
nimble rover
thank you
clear lodge
you're explicitly asked to use the identities to compute your stuff
i guess they also assume you know the values of the trig functions for 30°, 45° and 60°
lusty marsh
first find sin theta from the given info
lusty marsh
if theta lies in q4, only cos and sec will be positive
do uk this?
nimble rover
:/
topaz sinewBOT
@nimble rover Has your question been resolved?
wanton tide
How do I integrate
$\int e^x \sin(3x) \sin(x) dx $
``` I've changed it to `cos(2x) - cos(4x)` but I don't know what to do next...xCirno
lusty marsh
maybe try putting $sin(3x)$ as $3sin(x)-4sin^3(x)$
thorny flameBOT
swerriee
dense lily
How about solving -½(cosP - cosQ)=sin3xsinx
wanton tide
maybe try putting $sin(3x)$ as $3sin(x)-4sin^3(x)$
hmm let me try
wanton tide
How about solving -½(cosP - cosQ)=sin3xsinx
yeah I can't figure out how to solve it with that form
wanton tide
oh
dense lily
I'm going to try it
spare monolith
If you do sin(2x+x), you're left solving $\int e^x sin^3x$, if that is any help.
thorny flameBOT
Good
wanton tide
is $\int e^x sin^3x$ solvable though?
thorny flameBOT
xCirno
wanton tide
I think the answer shouldn't be that long
lusty marsh
,w integral of e^x.sin(3x).sin(x)
dense lily
How about solving -½(cosP - cosQ)=sin3xsinx
Cos P - Cos Q = -2sin0.5(P+Q)sin0.5(P-Q)
wanton tide
My teacher told this, for the integration in the form of $\int(e^{ax}{f(x) + f'(x)}dx)$. Integrate only $\int(e^{ax}f(x) dx)$ with $u = f(x)$ and $dv = e^{ax} dx$ for integration by parts.
thorny flameBOT
xCirno
wanton tide
Cos P - Cos Q = -2sin0.5(P+Q)sin0.5(P-Q)
yeah I did that too, no chance
spare monolith
**xCirno**
,w \int exp(x) sin(x)^3
thorny flameBOT
spare monolith
It is, but it’s long.
dense lily
,w int e^x sin3xsinx
thorny flameBOT
dense lily
,w int e^xcos2x
thorny flameBOT
dense lily
,w -int e^xcos4x
thorny flameBOT
dense lily
yeah I did that too, no chance
Are you sure?
dense lily
Not really, that method actually works.
topaz sinewBOT
@wanton tide Has your question been resolved?
topaz sinewBOT
@wanton tide Has your question been resolved?
topaz sinewBOT
@wanton tide Has your question been resolved?
topaz sinewBOT
@wanton tide Has your question been resolved?
stone schooner
How do I integrate
```tex
$\int e^x \sin(3x) \sin(x) dx $
``` I've changed it t...
check this out
and let me know if you dont get anything
https://socratic.org/questions/how-do-you-integrate-e-x-cos-x
next rain
Always distribute before multiplying da brackets togetha?
topaz sinewBOT
Always distribute before multiplying da brackets togetha?
agile harness
what
next rain
desert goblet
[
\qty|2x - 6| < 0
]
topaz sinewBOT
\[
\qty|2x - 6| < 0
\]
thorny flameBOT
nick
torpid matrix
not rigorous but correct
desert goblet
not rigorous but correct
what could i do to make it better
torpid matrix
ie i think it should be fine for test corrections since it shows you know why
desert goblet
thank you
torpid matrix
"abs cant be negative" is not a well defined statement, you really mean something more like "the range of abs(f(x)) is R^+ U 0", so therefore...
idk im bad at analysis but your work is an explanation, not a proof
topaz sinewBOT
@wraith swan Has your question been resolved?
shadow salmon
Hm, i might have an idea.
So I’ll basically call a as the special element u got e from.
We have that for every b there exists y such that b = y*a.
Now notice that
y*a = y*(a*e) = (y*a)*e. (1)
But b = y*a for all b, so we have by (1) that
b = b*e for all b.
Ugh I guess I’ll have to live with the bad formatting
Hope it’s readable
Ah I see
Ur welcome!
topaz sinewBOT
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static venture
topaz sinewBOT
static venture
Can someone help me find what a and b are, these are simultaneous equations
placid drum
it might help to factor out the b term
in each equation
having it as a constant * b
static venture
Hmm ok
placid drum
u can also do elimination after multiplying the top equation by 2
static venture
I had this here
static venture
it might help to factor out the b term
static venture
Oh and then find b
By dividing the stuff next to b?
Yup I get the answer
Thank u so much 😄
.close
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unique river
topaz sinewBOT
unique river
can anyone solve this?
pearl peak
geometric series formula for the first bit, divide the top and bottom of the the first limit by x^3, and use lhopitals for the last bit
hard pendant
You are given the following identity cscA = sec(0.95). Given that angle a lies in the second quadrant, find the value of a that makes this true.
is 2.52 rad the correct answer in this scenario
topaz sinewBOT
You are given the following identity cscA = sec(0.95). Given that angle a lies i...
timid star
Yes
topaz sinewBOT
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oak cairn
topaz sinewBOT
oak cairn
Ok so i gotta solvethis
and this is what i finished with
so denominator is -4/3 and -1
and numurator is 0 and -2
bc -x(x+2)
but im rlly confused bc the teacher did this
but cant i still get the same answer without doing that???
except the problem is that im not getting the same answer
oops
nvm
bye guys
im tired
i just realized my mistake
AHAH
agile harness
all good
oak cairn
oh u have to flip the sign...
agile harness
indeed
glass maple
also (ditto)
oak cairn
ya but what if im just factoring it out tho
glass maple
must be an old teacher
agile harness
ya but what if im just factoring it out tho
well it’s not on the left anymore
so they clearly divided
oak cairn
and this is what i finished with
ok but what if i just left it like this tho
would i get the same answer
just -x^2 - 2x > 0
agile harness
no idea why you’re writing ditto but yea
oak cairn
im not writting that
its the teachers work
i just dont have my phone on me to send a pic of my work
wait so for inequalities i cant just factor out a -1
and if i do, i have to flip the sign?
agile harness
if you divide by a negative you must flip the sign yes
oak cairn
mhmi see ok one sec im gonna recheck my work
oh
wow
ok i got it
yep
interesting
ok thanks!
.close
lilac rover
Can anyone help?
topaz sinewBOT
Can anyone help?
snow brook
post le problem
wooden osprey
!da2a
topaz sinewBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
lilac rover
K
fading owl
fading owl
Do you know how to factorise quadratic equation?
lilac rover
Nope I’m in 6th grade and this is a advanced math practice sheet that I don’t understand
fading owl
Oh
lilac rover
I have to go in 10 minutes too so I think I’m just gonna ask someone tomorow
lilac rover
I’ll try
fading owl
I have to go in 10 minutes too so I think I’m just gonna ask someone tomorow
Can think of it later
🙂
lilac rover
Ok I gtg now
fading owl
Bye
lilac rover
By
snow brook
cya
topaz sinewBOT
@lilac rover Has your question been resolved?
graceful leaf
topaz sinewBOT
little pine
if you can convert the values on the left to a fraction, the value on the right is just it's denominator
graceful leaf
wait wot
thts hwo they did it
OH
I get what u just said
Ok ok
wait so 0.66 as a fraction
66/100
33/50
:/
hollow drum
0.66 is just about 2/3
hollow drum
And if you're allowed a calculator, you don't need to memorize anything
hollow drum
You want to multiply until you don't have a decimal, so with 2.66, start with 2. So 2.66 times 2 = 5.32, you still have a terrible decimal, so next try 3, so 2.66 * 3 = 7.98 and that's really close to 8 so there you go
You multiplied by 3 hence you do C_1 and multiply that 1 by 3
graceful leaf
ohhhh
Got it
tHank so much
so mcuh better than sitting here memorizing this 😭
.close
topaz sinewBOT
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uneven grotto
Lets say I can multiply two integers A and B, both in the range [1, 255]. What is the smallest composite (non-prime) number that cannot be obtained by multiplying A and B
topaz sinewBOT
Lets say I can multiply two integers A and B, both in the range [1, 255]. What i...
uneven grotto
My thinking is that it is 2 * 257 or 514 since 257 is the smallest prime number above 255. Would this be correct?
little pine
why not 256?
sweet shard
,calc 2 * 128
thorny flameBOT
Result:
256
I think this is right. You just check that 257 itself is prime
topaz sinewBOT
@uneven grotto Has your question been resolved?
uneven grotto
gotcha, thanks
low monolith
how to find y using 3x - y =2 with x= 2
topaz sinewBOT
how to find y using 3x - y =2 with x= 2
agile harness
substitute x = 2
golden blade
algebra
low monolith
this is linear equation
golden blade
mb
low monolith
3(2) - y = 2
hard ravine
so expand and solve
topaz sinewBOT
@low monolith Has your question been resolved?
toxic sphinx
topaz sinewBOT
toxic sphinx
can someone please solve this question, i want to know if i got it right
pearl fog
what did you get?
sweet shard
can someone please solve this question, i want to know if i got it right
Not how this server works
Just show your work
toxic sphinx
what did you get?
x^2-888x+3344=0
pearl fog
huh this doesent have a real solution
toxic sphinx
huh this doesent have a real solution
oh
i made it up
i just wanted to test my solving skills
bc
pearl fog
😭
toxic sphinx
im not very good at this
so
you could say
i have a
skill issue
badum tshhhh
fallow igloo
sweet shard
i made it up
I don't recommend lying to helpers if you want help
topaz sinewBOT
@toxic sphinx Has your question been resolved?
viral fulcrum
is 6-x = 6+6x in mod7?
warped thistle
is 6-x = 6+6x in mod7?
Yes
neon iron
All the undergrad folk
how accurate is this curriculum? I just want to pursue this for the purpose of knowledge and not actually doing a degree or smth….just wanted to expand what I know
neon iron
I’ve done OSSU for computer science and I’ve found that to be pretty nice
But what I’ve heard is that it’s not even close to an actual CS degree
What about this one?
topaz sinewBOT
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ivory sorrel
topaz sinewBOT
toxic sphinx
I don't recommend lying to helpers if you want help
i legit made it up, why are you being so stuck up
oh sorry a dense set
ivory sorrel
Let $T(x,y,z) = (2x-4y+3z,6x)$.
\
$T(x_1,y_1,z_1)+T(x_2,y_2,z_2)= (2(x_1+x_2)-4(y_1+y_2)+3(z_1+z_2),6(x_1+x_2) = T(x_1+x_2,y_1+y_2,z_1+z_2)$
thorny flameBOT
A dense set
alpine mist
For the reverse direction you can choose certain vectors to show that properties of linear transformations only hold if b and c are 0.
ivory sorrel
If T(x,y,z) = (2x-4y+3z+b,6x+cxyz) were linear, then $T(0)=0_v$. Clearly $T(0,0,0) \neq (0,0)$ if $b \neq 0$
\
At the same time linearity would mean that $T(x_1+x_2,y_1+y_2,z_1+z_2) = T(x_1,y_1,z_1)+T(x_2,y_2,z_2)$ We thus hypothesize that $(2x_1-4y_1+3z_1,6x_1+cx_1y_1z_1)=(2(x_1+x_2)-4(y_1+y_2)+3(z_1+z_2),6(x_1+x_2)+c(x_1+x_2)(y_1+y_2)(z_1+z_2)$.
\
thorny flameBOT
A dense set
ivory sorrel
They clearly aren't the same for all vectors unless c=0
alpine mist
you should be a little more careful, that works for some vectors. So you'd need a 'for all vectors' somewhere in there.
otherwise, that seems fine.
you can also construct a counter example for when c != 0.
topaz sinewBOT
ivory sorrel
Thanks!
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solid zephyr
topaz sinewBOT
solid zephyr
how do i use limit comparison test
i compared it to 1/2^n
but idk how to take the limit with a factorial
clear lodge
you'd show that n!>2^n
mortal steeple
clear lodge
same with 2 and 3, but he's talking limit
topaz sinewBOT
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civic cairn
topaz sinewBOT
civic cairn
I do not understand how to do question 7 but i know how to do question above that
here is the answer key
tardy wave
approximus prime
topaz sinewBOT
@civic cairn Has your question been resolved?
topaz sinewBOT
@civic cairn Has your question been resolved?
crude thunder
when i have projection onto line, would the term pp^t/p^tp cancel to 1 ? in my textbook they just switch it as p^tx/p^tp but i dont see why we dont just cancel it out
topaz sinewBOT
when i have projection onto line, would the term pp^t/p^tp cancel to 1 ? in my t...
tough nest
$a a^T \neq a^T a$
thorny flameBOT
Katharine
crude thunder
**Katharine**
ive read, that the upper term is called dyade
can you please show me what would the upper term be equal to in case ov a = 2 1 -3?
im not really sure how to calculate it
tough nest
what kind of vector is a
vertical?
let me say it this way
let a be a 1xn vector
then $a a^T$ is a scalar
thorny flameBOT
Katharine
smoky sparrow
if $a$ has dimensions $m \times n$, then $(m \times n) (n \times m) \to (m \times m)$
but $(n \times m)(m \times n) = (n \times n)$
the dimensions are totally different!
tough nest
and $a^T a$ would be a nxn matrix
tough nest
those things flip if a is a nx1 vector
smoky sparrow
a should be a vector in this situation so n = 1
so you get the matrix $a a^t$ multiplied by the column vector $b$
what happens is that you get another column vector as $y$, with the same dimensions as $b$
thorny flameBOT
south's secret twin brother
smoky sparrow
specifically, a a^t will be m by m, and b will be m by 1
so their product is an m by 1 vector
topaz sinewBOT
@crude thunder Has your question been resolved?
terse bronze
topaz sinewBOT
terse bronze
im unsure about my ans to this one
I graphed the absolute function and found the max value within the range to be 4
so would it just be 4m/s
smoky sparrow
,w d/dt (4t e^(-t^2) - 1) = 0
thorny flameBOT
smoky sparrow
so would it just be 4m/s
no, check your work again
t = 1/sqrt(2) is a critical point and it's also a local maximum
(as $t \to \infty, v(t) \to 0$ so it can't be a local minimum)
thorny flameBOT
south's secret twin brother
smoky sparrow
(given that v(t) is positive there)
topaz sinewBOT
@terse bronze Has your question been resolved?
terse bronze
@smoky sparrow
topaz sinewBOT
<@1151031274413228043>
terse bronze
but we're just trying to find when the absolute value of the function is greatest
not necessarily the local max or local min
so when we graph the abs function find where that value is greatest for speed?
what is wrong with my approach?
smoky sparrow
ah good catch
smoky sparrow
I think you just graphed it wrong
but yeah we do have to check the critical points and the endpoints
then take the absolute value
in this case the maximum speed is |v(0)| = |-1| = 1
topaz sinewBOT
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chilly walrus
topaz sinewBOT
chilly walrus
do we really need MVT for this? doesn't this just follow from the fact that f is strictly monotone?
BWOC, assume $\exists x_1, x_2 \in I, x_1 \neq x_2$ s.t. $f(x_1) = f(x_2) = 0$. But because $f$ is strictly monotone, it is injective on $I$ so $f(x_1) = f(x_2) \implies x_1 = x_2$, a contradiction
thorny flameBOT
artemetra
chilly walrus
like i get how to prove it using MVT but wouldn't the above approach also work just as well?
obsidian solstice
like i get how to prove it using MVT but wouldn't the above approach also work j...
Yes, it would work and you don't even need continuity
topaz sinewBOT
topaz sinewBOT
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little iron
is this a real parabola? I have never seen a parabola like this
is chat GPT trolling or am I dumb?
topaz sinewBOT
is this a real parabola? I have never seen a parabola like this
is chat GPT trol...
topaz sinewBOT
little iron
oh ok ty
neon iron
is this a real parabola? I have never seen a parabola like this
is chat GPT trol...
What the hell
💀
neon iron
Chat gpt on some weird stuff
little iron
Chat gpt on some weird stuff
fr
little iron
ty
topaz sinewBOT
Available help channel!
echo granite
i dont know how to solve questions in this form
topaz sinewBOT
i dont know how to solve questions in this form
echo granite
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
frosty iron
try to do something with the third and second equation
echo granite
okk but should i tryna convert it to row echalon form or
frosty iron
have no idea what that is lol
echo granite
😭
frosty iron
sorry
echo granite
its alr
frosty iron
isnt it just linear equations or am i misunderstanding
echo granite
yes
crisp bloom
isnt it just linear equations or am i misunderstanding
well it asks for possible values of c
thats where the difficulty is
echo granite
exactly
frosty iron
oops mb
candid salmon
If u are relating it to row echelon form
You know theres 3 types
Turn the equations into a matrix and try figure out what c’s you need to fit each of the types of solns
If u arent using row echelon form then u can do it a different way but im assuming u learn row echelon form and need to apply it here
echo granite
thank u for advice im working on that right now thanks 🙂
topaz sinewBOT
@echo granite Has your question been resolved?
candid salmon
ok i just got home and looked and it is quite hard
i thought u could do it that way but its unnecessarily hard compared to using the det
for a system to have a unique solution the det of A must be non zero
so instead of doing ref and working stuff out just work out the det and youll get an equation for C right
you need a c where det A is NOT 0
now you can take the c's that do make det A = 0 and sub them in to see which ones fit each type of equation @echo granite
echo granite
oh ok i see
candid salmon
it should simplify it to a 3 min question