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#help-26
topaz sinewBOT
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manic parcel
can someone help me figure out what is wrong with m answers
topaz sinewBOT
can someone help me figure out what is wrong with m answers
manic parcel
1 sec
im getting a screneshot
i did all the math plugged it into calculator and all that shit and ive done it i kid you not fucking 10 times and cannot get it to work
i plugged the values into the position function then used the formula (f(b)-f(a))/b-a to get these answers
ive done this multiple times and gotten same answers and idk whats wrong witht hem
been working on calc stuff for 5 hours now and i cannot for the life of me figure this one oyt.
<@&286206848099549185>
topaz sinewBOT
@manic parcel Has your question been resolved?
manic parcel
how
somber socket
Re plug into calc
somber socket
Yes
manic parcel
i fucking couldnt read my own handwriiting
holy fuck thanks man
bro it doesnt end
theres more
sdjafjeig
the instantanious velocity at t=1 is 92 right?
somber socket
No
somber socket
Yep
topaz sinewBOT
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Available help channel!
deft holly
very new to integration
topaz sinewBOT
very new to integration
agile harness
what’s your question
agile harness
try rewriting the x^1/2 and x^3/2 in terms of u
deft holly
if i do that, does it come out as an abs value?
agile harness
does what come out as an absolute value
nocturne orchid
once you sub u in, what do you notice about numerator and denominator in terms of derivatives and what does that mean?
deft holly
actually nah, could i get an explanation for why it cant be a negative u?
like
abs value
agile harness
actually nah, could i get an explanation for why it cant be a negative u?
$\sqrt{x^2} = x$
thorny flameBOT
knief
nocturne orchid
cool bot
agile harness
its the principal root
agile harness
latex
nocturne orchid
my first thought would to do this but idk what to do with it
what do you get when you change all x to u and change the dx to be in terms of du?
agile harness
so false bruh sqrt (x^2) = |x|
principal root
agile harness
so false bruh sqrt (x^2) = |x|
are you saying sqrt(25) = |5|?
verbal shadow
no
nocturne orchid
principal root
👍
deft holly
verbal shadow
principle root means that you're not doing -sqrt(x^2)
deft holly
do i substitute again?
nocturne orchid
yup
deft holly
or am i doing smth wrong
deft holly
okok
nocturne orchid
simplifies down very nicely
agile harness
principle root means that you're not doing -sqrt(x^2)
ok sure but as it applies to this problem the | | is irrelevant
nocturne orchid
the c 😢
deft holly
ill add it later lmao
deft holly
ok sure but as it applies to this problem the | | is irrelevant
does the negative not matter in integration?
what are the cases where we just take the principle root
nocturne orchid
does the negative not matter in integration?
are you asking why we arent integrating with -sqrt(x) being the numerator?
deft holly
-u as the numerator
nocturne orchid
-u as the numerator
why would we?
nocturne orchid
why is that
theres no reason to take the negative, the problem specifically assigns the principle root, so we just say u=sqrt(x) in other words and worked from there
wanting to do u=-sqrt(x) is pointless here as far as i see
deft holly
how are we able to tell it assigns the principle root. is it just because the original q has sqrtx only?
nocturne orchid
how are we able to tell it assigns the principle root. is it just because the or...
it doesnt say +/-, it is merely a sqrt
deft holly
so its because the original q only has sqrtx
nocturne orchid
imagine it like 1-1+sqrt(x), its a positive sqrt
deft holly
.close
topaz sinewBOT
topaz sinewBOT
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placid fern
.help
topaz sinewBOT
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- clopen:
.close,.reopen - consensus:
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.tag - help:
.help - version:
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Type .help <command name> for more info on a command.
placid fern
?help
placid fern
- Explain what it means to say that
lim and lim
x-->2- f(x)=1 x-->2+ f(x)=5
in this situation is it possible that lim x--> f(x) exists? explain.
i dont understand the book answer? can sm1 explain?
merry hill
for the limit to exist at a point
both LHL (left hand limit) and RHL (right hand limit) at that point should be equal
merry hill
2. Explain what it means to say that
lim and lim
x-->2...
here LHL = 1 and RHL = 5
which are obviously not equal
so limit doesnt exist at x=2
placid fern
ohh alr
what abt the first part
why r they saying that x approaches 1 from left y should approach 3?
since the limit equations are saying that x is approaching 2 not 1
merry hill
since the limit equations are saying that x is approaching 2 not 1
oh that
maybe you are checking the answer to wrong question or smth
placid fern
nope it is that one
merry hill
then either misprint in question or answer
topaz sinewBOT
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Available help channel!
half field
Yo
topaz sinewBOT
@half field Has your question been resolved?
fringe grove
you need to adjust the limits of integration for the u sub
urban barn
quick question but the points on the shaded lines are not included right?
fiery saddle
topaz sinewBOT
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spiral canopy
Can anyone explain why is the answer D? Does it have something to do with the domain?
topaz sinewBOT
Can anyone explain why is the answer D? Does it have something to do with the do...
topaz sinewBOT
@spiral canopy Has your question been resolved?
topaz sinewBOT
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crude crystal
topaz sinewBOT
crude crystal
this is what i did
but the answer is a+b+c/3
i know that we can find answer using binomial approximation
but i just wanna know what is wrong with this method
solid matrix
but i just wanna know what is wrong with this method
The last step
Expand the denominator
hoary venture
am i missing something? if a, b, and c are constants than the limit should simplify to 0
sick escarp
Why
hoary venture
because infinity + a constant is infinity
sick escarp
Where's an expression of that form mentioned here
hoary venture
idk bro im 17
sick escarp
neon iron
guess what I am 14
topaz sinewBOT
wary tulip
am i missing something? if a, b, and c are constants than the limit should simpl...
yes you are missing something
neon iron
do you understand the problem
i understand
crude crystal
what am i missing
bro do you know how to solve that indeterminate form
hearty turret
the reason why ur method doesn't give u the right answer is bcus
crude crystal
the reason why ur method doesn't give u the right answer is bcus
thanks i got it
hearty turret
ah k
wary tulip
what am i missing
look at it in desmos with a particular a,b,c or something
hoary venture
so im wrong
but what am i missing
in general, an infinitely large sum plus a definite amount is still an infinitely large sum right?
lim x->infinity (x+1) is just infinity right?
crude crystal
yo that expression is of the form infinity-infinity
so it is an indeterminate form
you can't solve for limit like that
hoary venture
how
crude crystal
so you have to convert it to some other form
hoary venture
its not over infinity
crude crystal
its not over infinity
mb i actually am doing lot of questions forgot which question i was talking about
so its infinity - infinity
so you gotta convert to infinity/infinity or 0/0 form
and
then
convert it again
to a determinate
form
to solve
the limit
hoary venture
thats only for l hopitals
infinity - infinity is not indeterminate
infinity/infinity and 0/0 is indeterminate
timber falcon
infinity - infinity is not indeterminate
it is though
both n-n and n-n^2 are infinity - infinity and one gives 0 and other -infinity
hoary venture
thats because infinity - infinity isnt infinity - infinty^2
sick escarp
infinity/infinity and 0/0 is indeterminate
That's just two of many indeterminate forms
hearty turret
infinity - infinity is not indeterminate
me when $\lim_{x \to \infty} (x+1) - x = 0$ bcus $\infty - \infty = 0$
thorny flameBOT
LY
timber falcon
thats because infinity - infinity isnt infinity - infinty^2
infinity^2 is the same as infinity
hoary venture
infinity^2 is the same as infinity
the way i learned it infinity^2 is conceptually infinitely bigger than infinity. so infinity - infinity^2 is essentially and practically -infinity
and practically it works the exact same, just more effeciently
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crude crystal
infinity - infinity is not indeterminate
uh whats bro saying
topaz sinewBOT
uh whats bro saying
crude crystal
That's just two of many indeterminate forms
exactly 7 indeterminate forms
hoary venture
infinity - infinity is 0
crude crystal
no
hoary venture
if you keep my previous message in mind
#help-26 message
hoary venture
conceptually and practically, it is
crude crystal
soo..
hoary venture
infinity - infinity = 0
infinity^2 - infinity = infinity^2
^ this is true in any limit
thats how i learned it for AP precalc and AP calc
hoary venture
lim x-> infinity (x - x) is 0
hoary venture
it just is?
crude crystal
bro think there are infinite natural numbers and there are infinite integers, but the second infinity is bigger than the first
hoary venture
what limit represents that bro
crude crystal
so how can you argue that infinity - infinity is 0
hoary venture
show me the limit
hoary venture
bro think there are infinite natural numbers and there are infinite integers, bu...
that represents this
lim 2x + x = 2infinity + infinity = infinity
x->infinity
crude crystal
lim 2x + x = 2infinity + infinity = infinity
x->infinity
yes that works
if you add infinities
its not indeterminate
but if you subtract
it is indeterminate
see this
7 indeterminate forms
hoary venture
i mean i understand its largely regarded as indeterminate. im just saying the way I learned it, it isnt indeterminate.
and my way works exactly the same just faster
instead of memorizing formulas, just think of it conceptually
crude crystal
then how would you solve that
hoary venture
solve what
crude crystal
the other
question
that i sent you
you got wrong
answer
right
when you used
your concept
hoary venture
if a b and c are constants then im right
hoary venture
oh i see
hoary venture
the reason you cant disregard a b and c is becaus e after taking the cube root, you subtract x, and this subtraction causes the constants to become significant.
so my way still holds true, its just not as intuitive because of the cbrt
crude crystal
hearty turret
the reason you cant disregard a b and c is becaus e after taking the cube root, ...
but ur literally wrong lol
hearty turret
but ur literally wrong lol
answer is a+b+c/3
crude crystal
answer is a+b+c/3
yeah
hearty turret
so clearly the constants are less insignificant as u think
hoary venture
so clearly the constants are less insignificant as u think
idk if you read my message or not, but like i said, they are significant, its just not as intuitive because of the cbrt
the reason you cant disregard a b and c is becaus e after taking the cube root, you subtract x, and this subtraction causes the constants to become significant.
reread this gang
hoary venture
you too bro you need to read better
hearty turret
the reason you cant disregard a b and c is becaus e after taking the cube root, ...
ah k yeah that's the reason why you can't disregard the constants in this case
but like infinity - infinity is still an indeterminate form
hoary venture
yeah, but the base logic of my method still applies regardless
crude crystal
you too bro you need to read better
kay bro
i dont get it
imma go
i have a lot to study
hoary venture
good luck brah
hearty turret
yeah, but the base logic of my method still applies regardless
as in what is ur method?
intuitively it's fine to think about it as i.e. infinity^2 - infinity = infinity etc.
or like infinity + 1 - infinity = 1
but ultimately, ur intuition only goes so far
hearty turret
what did you do after this
like i don't think it's intuitively obvious the answer should be a+b+c/3 in this case
also it doesn't translate to a good write-up
hearty turret
i mean i understand its largely regarded as indeterminate. im just saying the wa...
also whoever taught u that it isn't indeterminate is just wrong
glass maple
i mean
this isnt proper
but u can apply amgm for 3 terms
to evaluate this limit
amgm applies as long as all terms are real positive
@crude crystal do u still have any questions , if not, dont forget to close channel
crude crystal
like i don't think it's intuitively obvious the answer should be a+b+c/3 in this...
true
you have to solve
topaz sinewBOT
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crude crystal
to find
crude crystal
.close
topaz sinewBOT
neon iron
to find close
topaz sinewBOT
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burnt swift
Find the expression of the linear transformation $f$.
(a) $f: \mathbb{R}^3 \to \mathbb{R}^4$ such that
[
f(1,0,0) = (2,1,-1,1), \quad f(0,1,0) = (3,-1,1,0), \quad \text{and} \quad f(0,0,1) = (0,0,4,1).
]
(b) $f: \mathbb{R}^3 \to \mathbb{R}^3$ such that
[
f(1,1,-1) = (0,3,1), \quad f(1,0,1) = (2,-1,1), \quad \text{and} \quad f(1,1,0) = (3,2,4).
]
(c) $f: \mathbb{R}^2 \to \mathbb{R}^{2 \times 2}$ such that
[
f(1,-1) = \begin{pmatrix} 2 & 1 \ 3 & 0 \end{pmatrix} \quad \text{and} \quad f(1,1) = \begin{pmatrix} 0 & 1 \ 2 & 1 \end{pmatrix}.
]
thorny flameBOT
ඞඞඞ
topaz sinewBOT
**ඞඞඞ**
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
@glass maple
glass maple
sorry let me get paper, i cant do this without writing anyhting down
glass maple
<@586297444434706446>
give me a moment
burnt swift
Ok i will grab paper aswell let me see your drawing
glass maple
Ok i will grab paper aswell let me see your drawing
ok i back, sry took longer than i expected cause i ran into my parents talking
burnt swift
Where were we
glass maple
my method might not be 'conventional' but here is what i would do
so we are solving a)?
we want to find f:R^3 => R^4
one nice thing the quesiton gives you straight away is that (1,0,0) and (0,1,0) and (0,0,1) are all linearly independent
can u think of why this might be really useful
burnt swift
No
glass maple
ok, let me ask this another way,
do you know by just looking how many rows and columns f will have>
burnt swift
3
glass maple
3?
wintry canyon
**ඞඞඞ**
f(x,y,z) = xf(1,0,0) + yf(0,1,0) + zf(0,0,1)
this is true because f is a linear transformation, and the 3 given vectors form a basis of R³, aka we know how to express any triplet (x,y,z) in terms of those vectors
glass maple
that was what i was trying to allude to
wintry canyon
ah i'm sorry do you want me to delete so you can continue explaining?
burnt swift
No idea what you guys are saying
You are al jumping to conclusions
Without any explanatory whatsoever
glass maple
ok i ill write down
sec
does this make sense?
ik the writing is a bit cramped but bear with
burnt swift
It does not
burnt swift
You did a vector full of dots man
glass maple
the dots is just placeholder
burnt swift
The fuck
glass maple
sry thats improper
thats not really pertinent to solving the question
its just meant to be a 4x1
burnt swift
You guys asume im Einstein
glass maple
can you understand the second line?
if we treat (1,0,0) as (x,y,z)
(2,1,-1,1) = (2x, x, -x, x) since y and z are both 0
burnt swift
Why do you use transpose
burnt swift
The vectors are in rows but in your drowing is columns
glass maple
wdym?
burnt swift
burnt swift
glass maple
dots is just placeholder, i wrote it hurriedly without thinking about it being proper
glass maple
wait actually it doesnt really matter
they have given it as a vector
since the commas
u can write it vertically or horizontally
i preferntially write it vertically
can i just ask you trust the process for now
it will make sense
burnt swift
Ok so transpose symbol is unnecessary
glass maple
no you dont need transpose since its written just as a vector
burnt swift
Is a row vector
glass maple
ok, just transpose it after im done
for the sake of showing you the logic i think using column is nicer
because we aren't used to reading certain things horizontally
burnt swift
glass maple
yes or no
burnt swift
Yes
glass maple
can you understand all of this?
glass maple
if we replace 1 by x, what do you think the output would be for f(x,0,0)
burnt swift
Why
glass maple
so we can generalise it in the form for f(x,y,z) at the end
if that confuses you, just consider it as xf(1,0,0) instead
burnt swift
glass maple
i dont understand where you dont understand
i multiplied it by an arbitrary scalar x
burnt swift
glass maple
i left a question mark because i hope you can find that at the end
becaues it is the last bit
burnt swift
The sum of matrix multiplications
glass maple
it hinges on whether you actually understand what is happening
the quesiton mark is just (transformation u want) * (x,y,z)
burnt swift
I don't get it
glass maple
I don't get it
^
burnt swift
Yes
burnt swift
What is the ?
glass maple
that is for you to find because you just litearlly have to sum all 3 expressions as is
ive even written them anove
*above
burnt swift
Is the question over
glass maple
yes
like thats the end of it for part (a)
this is what the matrix is
transposed it back to how u wanted it
burnt swift
I want that website
glass maple
do u still have more questions
if u do, u might have to ask someone else, i have to depart for now
topaz sinewBOT
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Available help channel!
plucky bluff
I don’t know how to solve this inequality, any help is greatly appreciated
topaz sinewBOT
I don’t know how to solve this inequality, any help is greatly appreciated
@plucky bluff Has your question been resolved?
plucky bluff
<@&286206848099549185>
woeful stone
!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
gilded pawn
I don’t know how to solve this inequality, any help is greatly appreciated
What do ya know about x?
Is it positive?
plucky bluff
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
plucky bluff
What do ya know about x?
Is it positive?
Wdym?
gilded pawn
$\frac{\surd{(x^2 + 1)}}{x+2} < 1$
$\implies\surd{(x^2 + 1)} < (x+2)$
thorny flameBOT
derTeufeL
plucky bluff
Isn’t x+2 strictly negative?
plucky bluff
**derTeufeL**
It should change the sign right?
fallow heart
Isn’t x+2 strictly negative?
That's another option you have to take into account, yep
fallow heart
**derTeufeL**
So if x+2 was > 0 (hence for x > -2) you got x > -3/4 from here
Now you have to suppose that x + 2 is < 0 (hence x < -2) and see what you get
You should get x < -3/4
Therefore the solution to that inequality is x < -2 or x > -3/4
plucky bluff
My textbook says otherwise
fallow heart
My textbook says otherwise
Uh sorry the denominator was x + 2
mortal steeple
ie x<2 and x>=2
fallow heart
Let me redo the calculations
mortal steeple
As the root is always positive, you don't have to worry about it
C1: x<-2
root(x2 +1) > x+2
All values satisfy as positive numbers are greater than negative ones
C2: x>=-2
root(x2 +1) < x+2
As both numbers are positive, you can square both sides
x2+1 <= x2 + 4x + 4
x >= -3/4
Ans from C1 is x<-2 and from C2 is x >= -3/4
fallow heart
Therefore the solution to that inequality is x < -2 or x > -3/4
@plucky bluff does this correspond to what your textbook says now?
plucky bluff
<@1169030606856921128> does this correspond to what your textbook says now?
Nope sadly
mortal steeple
Ans from C1 is x<-2 and from C2 is x >= -3/4
This?
plucky bluff
It’s x<-2 or x>-3/4
@fallow heart @mortal steeple I think there might be only 1 case as the numerator is always positive and the denominator must be negative
mortal steeple
This would have been the case if there was a 0
But there is a 1
So 0.5 is also valid
Therefore both can be positive
fallow heart
It’s x<-2 or x>-3/4
Yeah I forgot a minus but that corresponds to what I found
plucky bluff
Yeah I forgot a minus but that corresponds to what I found
Oh that’s great
mortal steeple
C1: x<-2
root(x2 +1) > x+2
All values satisfy as positive numbers are greater t...
Fixed my calculation too
topaz sinewBOT
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Available help channel!
unique quarry
topaz sinewBOT
finite storm
what have u tried
unique quarry
sin compound angle
finite storm
try rearranging the first equation
unique quarry
sinx * cos pi/3 + cosx * sin pi/3
unique quarry
sinx * 1/2 + cosx * sin root3 /2
unique quarry
2sinx * sin pi/3
unique quarry
2sinx * root3/2
finite storm
yes
so we have
$\frac{1}{2}\sin(x) + \frac{\sqrt{3}}{2}\cos(x) = \frac{2\sqrt{3}}{2}\sin(x)$
thorny flameBOT
Average Calc Student
finite storm
what do u think we should do that
unique quarry
this is hte bit i'm stuck on
finite storm
lets remove the fraction first, shall we?
unique quarry
sinx + cosx * root 3 = sinx * root 3
finite storm
$\sin(x) + \sqrt{3}\cos(x) =2\sqrt{3}\sin(x)$
thorny flameBOT
Average Calc Student
unique quarry
divide by root3 cos?
finite storm
u have tanx, right?
unique quarry
yes
topaz sinewBOT
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strong sable
here the left limit exists doesn't mean that 1 and 2 also exist, why? isn't the left limit 3f'(x) and the 1 is 2f'(x), the 2 is f'(x), so aren't they both f'(x)?
topaz sinewBOT
here the left limit exists doesn't mean that 1 and 2 also exist, why? isn't the ...
strong sable
but isn't that they're all f'(x)? just differ by multiplying a constant
odd pagoda
the left one doesnt depend on f(x). the two on the right do. so the value of f(x) could mess stuff up
strong sable
what does the left one depend on then?
hearty turret
here the left limit exists doesn't mean that 1 and 2 also exist, why? isn't the ...
oh yeah LHS is not sufficient for f'(x) to exist
bcus i.e. i could have f(x) = x^2 for all x != 0 but f(0) = 1
then clearly f is not diffable at 0 but LHS limit = 0
strong sable
in this case what's the limit on the right side?
hearty turret
in this case what's the limit on the right side?
those limits don't exist
it'll be an infinity-infinity scenario
strong sable
2x-2x?
hearty turret
$\lim_{h \to 0} (\frac{2h-1}{h} + \frac{1-h}{h})$
thorny flameBOT
LY
strong sable
why isn't it f(x+2h)-f(x)=(2h)^2-1 since f(x)=x^2
hearty turret
why isn't it f(x+2h)-f(x)=(2h)^2-1 since f(x)=x^2
oh whoops yeah ur right, i forgot what i defined f as
hearty turret
hmm so it turned out to be 4h-1/h + 1/h-h=3h=0
oh whoops yeah if u add them back up then yeah it's fine
hearty turret
hmm so it turned out to be 4h-1/h + 1/h-h=3h=0
but basically u can't split the limit cus otherwise u'll end up with infinity-infinity
strong sable
4h-1/h is infty right?
hearty turret
- infinity in this case
strong sable
here the left limit exists doesn't mean that 1 and 2 also exist, why? isn't the ...
so here in the example you gave, RHS is f'(0) right? And 1 & 2 are f'(0) too??
hearty turret
so here in the example you gave, RHS is f'(0) right? And 1 & 2 are f'(0) too??
1 and 2 are not defined cus i've moved f(0) upwards
quasi prairie
topaz sinewBOT
quasi prairie
what’s the fastest way i can do this?
it would help if somebody wrote down how to do a and then i should be able to solve the other two
quasi prairie
what is GDC?
graphical display calculator
quasi prairie
binomial expansion
but how? using pascal’s triangle?
odd forge
you can use (x+y)^n expansion or this one
hollow drum
but how? using pascal’s triangle?
This would be the easiest since you can write the rows down instead of memorizing the above
odd forge
I thought
quasi prairie
This would be the easiest since you can write the rows down instead of memorizin...
so then do i have to draw it during the test as well? if such a question appears
odd forge
I thought you already knew binomial expansion using so I gave the above formula
hollow drum
so then do i have to draw it during the test as well? if such a question appears
If you don't recall the rows then drawing it would be easier
quasi prairie
I thought you already knew binomial expansion using so I gave the above formula
well yes i do but doesn’t that take some time to write using that formula
odd forge
yes
I think you will learn about this later which involves combinations
for now construct pascal's triangle
hollow drum
well yes i do but doesn’t that take some time to write using that formula
Like here's an example, that you can do within like a minute
Then you just simplify the values
hollow drum
Ie 2^3 = 8
3 * 2^2 * x = 12x
etc
quasi prairie
this question has +/-
where do i add that in the equation
hollow drum
this question has +/-
My guess is your practice wants you to do (1 + x)^3 and (1 - x)^3
quasi prairie
My guess is your practice wants you to do (1 + x)^3 and (1 - x)^3
is this approach right or am i overcomplicating it?
there’s two parts, one for +x and the other for -x
hollow drum
is this approach right or am i overcomplicating it?
Yeah that's right
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royal sky
if the car is going around steady why is it accelerating
topaz sinewBOT
if the car is going around steady why is it accelerating
bleak pond
What is 6 exponet 7
prisma mesa
the velocity vector changes it's direction
so the velocity actually changes
although speed stays constant
if it wasnt accelerating, you wouldnt feel anything while sitting in the car
verbal shadow
if the car is going around steady why is it accelerating
circular motion is always accelerating cuz the direction of movement is changing
smoky sparrow
if the car is going around steady why is it accelerating
cause the car isn't travelling in a straight line
prisma mesa
but when turning, you get pushed to the side, that happens because the car accelerates
smoky sparrow
you can take the difference of velocity vectors near each other to approximate the acceleration vector
royal sky
ahhh okay okay
smoky sparrow
like so
if you do this for any point on the circle
you'll find it always points towards the centre
smoky pumice
if the car is going around steady why is it accelerating
If you feel the motion then the car is accelerating, and let common sense take over from there.
topaz sinewBOT
smoky sparrow
np
pseudo sonnet
thorny remnant
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long ocean
Did I do this right
topaz sinewBOT
Did I do this right
long ocean
I wasn't sure how to find the normal line if tangent is 0 but I just did x = pi since it is the only vertical line I know
vernal matrix
A line perpendicular to, say, y = -1 in this case is x = [something], and you want that line to pass through (pi, -1), hence you want x = pi as the normal 
topaz sinewBOT
@long ocean Has your question been resolved?
neon iron
Of a group of patients in a medical center, it was found that 40% have fever, while 30% have cough and 50% have other ailments. What percentage of the total patients have fever and cough at the same time?
A) 10%
B) 20%
C) 25%
D) 30%
E) 15%
topaz sinewBOT
Of a group of patients in a medical center, it was found that 40% have fever, wh...
neon iron
F = 2P/5
C = 3P/10
O = P/10
F + C + O = 120%P
I don't know if I can be certain that is 20%
Or if it's actually wrong
dense lily
I don't know if I can be certain that is 20%
20% of people have more than one ailment
finite storm
Fever or cough is 50%?
neon iron
20% of people have more than one ailment
Mm ye
neon iron
Fever or cough is 50%?
?
neon iron
20% of people have more than one ailment
Then how do I know which ones have fever and cough
dense lily
Are you sure this is the original question
neon iron
So the other 50% must have either fever or cough, no?
50 % have others, meaning neither fever nor cough I think
dense lily
50 % have others, meaning neither fever nor cough I think
Yes
finite storm
Yes
neon iron
and from the other 50% some have fever and cough, some only one of each
finite storm
Yes
dense lily
Oh wow that's it lol
neon iron
40% + 30% = 70% "should be the 50%" so Ig it's indeed 20%
dense lily
40% + 30% = 70% "should be the 50%" so Ig it's indeed 20%
Yes
finite storm
Yeah
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ember mirage
hi, does anybody know how to demonstrate the haversine formula to calculate the distance between two points on a sphere?
topaz sinewBOT
hi, does anybody know how to demonstrate the haversine formula to calculate the ...
sweet shard
hi, does anybody know how to demonstrate the haversine formula to calculate the ...
What do you mean demonstrate
fair thorn
i think they mean provide a proof
ember mirage
yes
cunning kayak
aha proof
topaz sinewBOT
@ember mirage Has your question been resolved?
stone sluice
hello
stone sluice
can someone help me please
i tried some methods at the first one but did not get to any result
second one i don’t even know how to start
topaz sinewBOT
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@stone sluice Has your question been resolved?
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surreal grove
Can someone help me start this question? Im confused by how theta j are defined. “0j(vi)=0 unless i=j, 0j(vj)= 1” i suppose this is referring to the fact that different components of theta and v are orthogonal to each other but i dont get why the same component’s inner product gives 1, it just makes me think of the fact that both should be normal (unit) vectors, but im not sure
topaz sinewBOT
Can someone help me start this question? Im confused by how theta j are defined....
surreal grove
😩😩😩
surreal grove
Please do
undone thistle
i didn't actually cook i just have a convenient book lying around called finite dimensional vector spaces
and i think it has this as a standard proof
but i don't wanna spoil it
so i'm tryna understand it so i can give you hints
💀
do you just want to see the solution and try figure out what it means by yourself
surreal grove
Sure
surreal grove
Alr i’ll read it later and hopefully that will help me understand this question better
undone thistle
👍
undone thistle
np boss
surreal grove
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burnt swift
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burnt swift
<@&286206848099549185>
burnt swift
<@&286206848099549185>
dim(S')=3
dim(W)=3
dim(H')=4
S∩T={0}
S'∩T={0}
T∩W ≠ {0}
dim(S)+dim(T)=dim(H) ⇒ 3 + dim(T) = 4
dim(S')+dim(T)=dim(H') ⇒3 + dim(T) = 4
S ⊆ H
T ⊆ H
S' ⊆ H'
T ⊆ H'
dim(T)=1
<@&286206848099549185>
burnt swift
dim(S')=3
dim(W)=3
dim(H')=4
S∩T={0}
S'∩T={0}
T∩W ≠ {0}
dim(S)+dim(T)=dim(H) ⇒ 3...
@haughty drum
burnt swift
dim(S')=3
dim(W)=3
dim(H')=4
S∩T={0}
S'∩T={0}
T∩W ≠ {0}
dim(S)+dim(T)=dim(H) ⇒ 3...
@static lava
@cold wagon
<@&286206848099549185>
brittle pine
hey
river dust
hi
river dust
i would like to understand the range of a function
wooden osprey
what's your question
topaz sinewBOT
@river dust Has your question been resolved?
frozen copper
like how can i find the range?
is this integration or partial fractions or?
topaz sinewBOT
@river dust Has your question been resolved?
hoary venture
but ultimately, ur intuition only goes so far
you cant actually give me an example of it not working tho
topaz sinewBOT
you cant actually give me an example of it not working tho
hoary venture
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hoary venture
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hoary venture
idk how to interpret this
would i need to find the second derivative for the rate at which the spread of the virus is changing?
sweet shard
Flue firus
hoary venture
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tiny cairn
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next rain
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sudden temple
you can't factorize x^2+1 over reals
next rain
you can't factorize x^2+1 over reals
I don't understand
We had two x^2+1, we unraveled one, but left the other one as is
sudden temple
We had two x^2+1, we unraveled one, but left the other one as is
that was x^2 - 1 not x^2 + 1
next rain
that was x^2 - 1 not x^2 + 1
Why does it matter?
sudden temple
you can't factorize x^2+1 over reals
because of this
next rain
Why can't we?
sudden temple
if you factorize x^2 + 1 further you'll get (x+i)(x-i)
worn aurora
Why can't we?
because it will be x^2=-1 and you can’t take the square root of a negative number unless you wanna enter the complex numbers
next rain
if you factorize x^2 + 1 further you'll get (x+i)(x-i)
Why is this bad, wouldn't we want to get as bare bones as possible, so we can cancel out da denominator?
sudden temple
Why is this bad, wouldn't we want to get as bare bones as possible, so we can ca...
there is no denominator to cancel it with
worn aurora
Why is this bad, wouldn't we want to get as bare bones as possible, so we can ca...
i stands for imaginary numbers and the equation you solving with is real numbers
next rain
there is no denominator to cancel it with
So hypothetical if there was, would we unravel it?
worn aurora
so basically each got their own realm
sudden temple
So hypothetical if there was, would we unravel it?
if it already had complex linears(imaginary to be more precise here)
then you could definitely factorize it over imaginary linears for simplification
rotund valley
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gray ridge
My answer is different from my friends and I cant find the issue
I can't seem to find an error.
one ambiguous thing is that if |z|=1 is counterclockwise
what's the difference between yours and your friend's?
rotund valley
Maybe their answer start with -8/3
rotund valley
I can't seem to find an error.
one ambiguous thing is that if |z|=1 is countercl...
Or my memories are wrong
But its okay I just wanted to check my solution
Thank you
gray ridge
Cheers!
topaz sinewBOT
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rigid relic
Hi guys, I have a problem understanding a topic in linear algebra, specifically the change of basis. Just so you know, I'm a beginner in this area. I've been working through some questions from ChatGPT (yea probably not a good idea), and here's what I've gathered: with two different basis coordinate systems, we can identify a vector expressed in one basis and convert it to another. I understand that this involves multiplying the change-of-basis matrix by the vector. However, I’m confused about when we need to invert the change-of-basis matrix. In question 3, it seemed like no inversion was required, while in question 4, it was necessary. I’m wondering if I’m missing some fundamental concepts or if there’s a misunderstanding on my part regarding this process, or maybe chatgpt is screwing up my understanding. I hope I’ve explained my problem clearly.
topaz sinewBOT
Hi guys, I have a problem understanding a topic in linear algebra, specifically ...
thick lily
Hi guys, I have a problem understanding a topic in linear algebra, specifically ...
the way I think of it is to put the basis vectors in a matrix. For instance, for question 4 you basically want to find constants $a,b$ such that $$\begin{pmatrix}1 & 2 \ 1 & -1\end{pmatrix} \begin{pmatrix}a \ b \end{pmatrix} = \begin{pmatrix}3 \ 5 \end{pmatrix}$$
thorny flameBOT
Merosity
thick lily
that make sense, how the (a b)^T vector is really just the same vector but in the B' basis because it's a(1 1)^T + b(2 -1)^T
let me just write that clearly since it looks a little muddy writing it that way
$$a\begin{pmatrix}1 \ 1 \end{pmatrix} + b \begin{pmatrix}2 \ -1 \end{pmatrix} = \begin{pmatrix}3 \ 5 \end{pmatrix}$$
$$\begin{pmatrix}1 & 2 \ 1 & -1\end{pmatrix} \begin{pmatrix}a \ b \end{pmatrix} = \begin{pmatrix}3 \ 5 \end{pmatrix}$$
thorny flameBOT
Merosity
thick lily
first line is saying on the right hand side you have v in the B basis with the left side in the B' basis, but we don't know what the vector (a,b) is yet
second line I just factor that vector components out into the vector itself times the matrix of the basis B'
so now it's clear if we want a, b we need to multiply by the inverse on the left to get our answer
so to answer you other question about needin gthe inverse or not, it's really a difference of whether the unknown vector is one or the other there, if that makes sense.
I dropped a lot of stuff on you so just think about it and ping me if you have any troubles
rigid relic
**Merosity**
ahhh i see it now... thanks for this picture. I was having a hard time visualizing it numerically
.close
topaz sinewBOT
thick lily
ahhh i see it now... thanks for this picture. I was having a hard time visualizi...
cool, you're welcome
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jolly meadow
I don't understand multiplication, in the conceptual sense, can someone explain it to me
is there a word for multipllication like PER is for division
topaz sinewBOT
I don't understand multiplication, in the conceptual sense, can someone explain ...
jolly meadow
I don't really understand the
use of tables for multiplication, think like in phyiscs
what does distance = speed multiplied by time mean?
I understand that speed is the amount of distance per time increase
I can transfer it into the enlish language
not the same with multiplication
what does speed x time mean!!
YAY someone came
loud oasis
speed is distance/time, so (distance/time) * time = distance
jolly meadow
yeah but how does that convert to words
jolly meadow
I don't understand multiplication, in the conceptual sense, can someone explain ...
.
for example the distance per interval of time is speed
but what is speed x time in words?
linguistically what is it saying
I need to get my foundational arithemtic straight
well if anyone knows the answer make sure to ping me
🦗
no one came..
.close
topaz sinewBOT
verbal crater
well if anyone knows the answer make sure to ping me
i found an answer that makes sense to me on reddit lmao
jolly meadow
.reopen
topaz sinewBOT
✅
verbal crater
so basically multiplication in physics just means direct proportionality
means if this thing gets bigger, then the result also gets bigger
example distance = speed * time
if your time is large, means you had more time to travel
thus your distance is large
jolly meadow
so it's like for the amount of distance = The amount of speed accumulated for every interval of time
and for divison it is: speed is the amount of distance travelled per time interval that has been taken
does that make sense I'm pretty sure it does!
jolly meadow
so basically multiplication in physics just means direct proportionality
indeed it is very related to propotionality
verbal crater
so it's like for the amount of distance = The amount of speed accumulated for ev...
i mean it sounds wrong and right at the same time to me
jolly meadow
i mean it sounds wrong and right at the same time to me
wait aren't per and for every the same XD
jolly meadow
or is it
dun dun dun xdd..
dude gettting a conceptual understanding of maths is so hard when there's no literature around it
it's only taught procedurally in 99% of things
I was learning about cognitive science and I saw that solving math wasn't the problem for me it was more about reading maths
when I see x^2 I think of quadratic equations and how to solve them
BUT I don't think about a square number
nor a square
same with factors, I recently learned about the conceptual meaning
that it's something that's perfectly fits into something
and some other conceptual attributes too
all my life it's just been procedures
I think this helps though so thanks, I'll try and semantically understand my equations from now on
it's especailly important in half conceptual topics like physics
.close
topaz sinewBOT
verbal crater
yeah multiplication in physics doesnt really mean repeatedly adding
since units are involved
much easier to think if i increase this thing will the other increase or decrease
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thorn kernel
s
little pine
depends, if it's going up it's positive
if it's going down it's negative
little pine
oh mb
that's the rise
thorn kernel
is run always positive
little pine
run you can decide the sign/direction
if you want to go from left to right then it's positive
if you want to go from right to left, then negative
merry hill
why does this even matter
if you take two points (-1, -3) and (-2, -4)
both rise and run are negative
-4-(-3) and -2-(-1)
or both are positive if: -3-(-4) and -1-(-2)
thorn kernel
run you can decide the sign/direction
if you want to go from left to right then ...
but i got to solve for slope
craggy haven
you'll get the same result
merry hill
you'll get the same result
yes, so why does the positive negative thing matter
thorn kernel
this math teacher is picky
little pine
but same m, which is the important one
craggy haven
$\f42 = \f{-4}{-2}$
thorny flameBOT
hayley is not layla
thorn kernel
but same m, which is the important one
so it doesnt matter
if its negative or positive
heyy
little pine
yea
thorn kernel
OK
merry hill
i think its just like if the line is sinking then rise is negative which makes slope negative but if line is rising then rise is positive which makes the slope positive (so run is positive in both cases)
but in numbers it doesnt matter
if you do it right you will get the same result either way
topaz sinewBOT
@thorn kernel Has your question been resolved?
junior linden
Find the equation of the lines containing the bisectors of the angles formed by the lines 2x-y=-1 and x+2y=1
topaz sinewBOT
Find the equation of the lines containing the bisectors of the angles formed by ...
azure cedar
junior linden
Ok
junior linden
Ok
junior linden
Thanks bro
neon iron
Hey
junior linden
Hey