ty
#help-0
alpine sable
alpine sable
.close
lone heartBOT
rocky grove
And #latex-testing e
lone heartBOT
Available help channel!
warped topaz
lone heartBOT
https://gyazo.com/d73d6e0cfe20d8fdcae1bab46b54995b.png
rocky grove
Oooo
warped topaz
If anyone is here for the question I asked earlier, this is kinda the follow up I guess
rocky grove
Hmm could you post the original if it's important?
warped topaz
how do I know whether I should do (2,3) - (1,5) or (1,5) - (2,3)
rocky grove
how do I know whether I should do (2,3) - (1,5) or (1,5) - (2,3)
For the slope, it won't matter much. You will get the same slope either way
warped topaz
Hmm could you post the original if it's important?
It was just about how to tell which point to minus which
rocky grove
Either through $\frac{5-3}{1-2}$ or $\frac{3-5}{2-1}$
warped topaz
but to get the vector?
ocean sealBOT
VulcanOne
rocky grove
It was just about how to tell which point to minus which
Ooo I remember it now
warped topaz
yee
idk how to make vectors in latex but it will be -2 over 1 vs 2 over -1 depending on which one I subtract from the other
rocky grove
$\begin{bmatrix}
-2 \
1
\end{bmatrix}$
ocean sealBOT
VulcanOne
warped topaz
ye
that or the minus on the bottom
depending on which way I do it
so how can I tell which way to do it?
which is (a,b) and which is (c,d)?
rocky grove
Hmm
Usually there should be a phrase saying where it begins
Or where it ends
Because of this ambiguity
And I don't wanna make assumptions here but I guess it's safe to assume that the first point is the beginning
warped topaz
Ok
warped topaz
so the question is a mistake? Theyre always supposed to give us the direction?
rocky grove
A beginning or end, or they told you to assume that the first given point in order is the beginning
wary stream
For the question you posted above, it's not a mistake since it doesn't deal with vectors
warped topaz
Are you sure? This whole chapter is on vectors...
wary stream
It's a line that passes through those two points
Lines are infinite
All you need to do is to find the slope, and use point slope
warped topaz
hmm ok
weird that they would have a question not related to vectors in this section
wary stream
Don't forget a vector has magnitude and direction
rocky grove
weird that they would have a question not related to vectors in this section
Well you can have eigenvectors, which are vectors that have the same direction but have different scales
warped topaz
Well you can have eigenvectors, which are vectors that have the same direction b...
I havent covered that yet haha
rocky grove
So expressing them by line is sometimes better
rocky grove
I havent covered that yet haha
It's gonna be fun lol
warped topaz
So expressing them by line is sometimes better
ye I will do this
thank you so much for your help!
❤️
.close
lone heartBOT
rocky grove
lone heartBOT
Available help channel!
past current
lone heartBOT
past current
how would yall go about doing this one?
tacit arch
you can simplify by dividing both sides by 4. then notice that the arguments for both cos and sin are the same
$\tan(x) = \sin(x)/\cos(x)$
ocean sealBOT
riemann
lone heartBOT
@past current Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
gleaming flame
i dont get this
lone heartBOT
i dont get this
viral pagoda
gleaming flame
im sorry i dont get it
pliant cedar
$\frac{1}{x^4}=x^{-4}$
ocean sealBOT
SilverSoldier
pliant cedar
can u integrate $x^{-4}$
ocean sealBOT
SilverSoldier
gleaming flame
oh
ocean sealBOT
gleaming flame
shut crest
How 1/x wolf tripping
lone heartBOT
@gleaming flame Has your question been resolved?
tacit arch
How 1/x wolf tripping
Is it?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Just curious, is x/2 equivalent to 1/2 x?
lone heartBOT
Just curious, is x/2 equivalent to 1/2 x?
alpine sable
Idk how to use the Text generator bot
carmine reef
$\frac x2 = \frac 12x$
ocean sealBOT
monikanicity
alpine sable
**monikanicity**
yes like that
ocean sealBOT
haygiya
spiral lily
$\frac{x}{1}=x$
ocean sealBOT
haygiya
ornate ginkgo
Is $\frac{2sin^2(\frac{x}{2})}{2cos^2(\frac{x}{2})} = 2tan^2(\frac{x}{2})$
ocean sealBOT
ColdTee
ornate ginkgo
Or $\frac{2sin^2(\frac{x}{2})}{2cos^2(\frac{x}{2})} = tan^2(\frac{x}{2})$
ocean sealBOT
ColdTee
spiral lily
2's will cancel out
ornate ginkgo
**ColdTee**
This one is correct then?
spiral lily
$\frac{2}{2}\cdot\frac{\sin²(x)}{\cos²(x)}$
ocean sealBOT
haygiya
spiral lily
**ColdTee**
this one is correct
ornate ginkgo
How did they $2tan^2(\frac{x}{2})$ to sec^2(x/2) - 1
ocean sealBOT
ColdTee
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
ornate ginkgo
carmine reef
What is that last one?
ornate ginkgo
Is it from sec^2(x) - 1 = tan^2(x) cause i don't understand the inverse that the took
pliant cedar
arctan x = secx?
spiral lily
this is wrong
pliant cedar
what is the question
spiral lily
its tan(x/2) not 2tan(x/2)
ornate ginkgo
Its the integration of 1 - cos(x)/ 1 + cos(x)
pliant cedar
oh
so $\frac{1-\cos x}{1+\cos x}=\frac{2\sin^2\frac{x}{2}}{2\cos^2\frac{x}{2}}=\tan^2\frac{x}{2}=\sec^2\frac{x}{2}-1$
ornate ginkgo
ocean sealBOT
SilverSoldier
ornate ginkgo
I didnt understand that they wrote 2tan^2(x/2) and from tan^-1x = sec(x) they wrote
Sec^2(x/2) - 1
pliant cedar
I didnt understand that they wrote 2tan^2(x/2) and from tan^-1x = sec(x) they wr...
these are all wrong
alpine sable
how does it go from step 1 to step 2?
lone heartBOT
how does it go from step 1 to step 2?
hallow ember
well there is a trigometric identity that says 1 = sin^2 + cos^2
alpine sable
there is supposed to be a minus sign there?
hallow ember
i have to imagine so
alpine sable
ok, so just a missing minus sign
hallow ember
it would make it work
alpine sable
over here how would I convert it because nothing is squared
so I can't use an identity I think
hallow ember
i think its has to do with the unit circle
i dont believe an identity could help here
but i have no clue how to use the unit circle, its just my best guess so i cant really help
alpine sable
rip
alpine sable
for part a, I have to make it sin(80), but idk how to do that in terms of p
stuck cape
do you know identities sin(a+b) sin(a-b) cos(a+b) cos(a-b)
slim holly
Assertion: If Product of two numbers is 2890 and their HCF is 17, then their LCM is 450.
Reason: LCM is always greater than HCF.
alpine sable
Assertion: If Product of two numbers is 2890 and their HCF is 17, then their LCM...
i think ur in the wrong channel
slim holly
BRUH!
stuck cape
$1-cos^{2}(x) = sin^{2}(x)$
ocean sealBOT
ayushch80
alpine sable
$1-cos^{2}(x) = sin^{2}(x)$
I know this
hallow ember
stuck cape
where should i go to ask for help
stuck cape
I know this
$1-cos^{2}(10) = sin^{2}(10)$
ocean sealBOT
ayushch80
stuck cape
$cos^{2}(10) = p^2 -1$
ocean sealBOT
ayushch80
stuck cape
$cos(10) = \sqrt{p^{2}-1}$
ocean sealBOT
ayushch80
stuck cape
**ayushch80**
use this
alpine sable
**ayushch80**
so this is supposed to be $\sqrt{-p^2+1}$
ocean sealBOT
_____
stuck cape
yes
halcyon fox
Pythagoras therom
lone heartBOT
Pythagoras therom
alpine sable
Pythagoras therom
$a^2+b^2=c^2$
ocean sealBOT
_____
indigo thorn
This is an LPP question in both pictures i just want to know how they come up with this points i highlighted
ornate condor
plain sundial
lone heartBOT
pliant cedar
this looks wrong, alpha/3 and beta/3 are the roots of the equation in terms of m
alpha/3 + beta/3 must equal the -(coefficient of x)/(coefficient of x^2) of ur equation in terms of m
tacit arch
(alpha + beta)/3 = -b/a from the quadratic formula. You forgot the minus sign and have the 3 in the wrong place
pliant cedar
btw why r u calling the sum of roots POR and the product of roots SOR
tacit arch
PumOfRoots
lone heartBOT
@plain sundial Has your question been resolved?
vale wigeon
don't ping moderators for math help.
also, are we to understand that you want somebody to do this entire worksheet for you?
ok, in that case please be more specific about which of these problems you need help with
lilac rain
ok
lilac rain
how do I write a value ranging from -3 to 4 using < > symbols? Is it like:
-3 < 0 < 4 ?
frosty solstice
how do I write a value ranging from -3 to 4 using < > symbols? Is it like:
-3 <...
does the value include -3 and 4?
rustic ruin
-3<x<4
rustic ruin
ok, thank you.
just in case, this is valid only if it does not include -3 and 4
median osprey
.close
lone heartBOT
lilac rain
.reopen
lone heartBOT
✅
rustic ruin
if it includes -3 and 4, -3<=x<=4
lilac rain
-3 < =
hm, ive seen a symbol where < is underlined, is that the same as <= ?
rustic ruin
yup
dim coral
how did they get the negative for the 2 cos 2(pi/2)?
lone heartBOT
how did they get the negative for the 2 cos 2(pi/2)?
median osprey
how did they get the negative for the 2 cos 2(pi/2)?
Cos 2*π/2= cos π = -1
dim coral
oh
dim coral
Cos 2*π/2= cos π = -1
do you have this memorized?
how were u able to just know it off the top of ur head
dim coral
yeah but like dont you gotta go out of ur way to memorize them
median osprey
You have to only memorize angles and their sines cosines, etc from 0 to π/2 rest can be calculated by imagining
dim coral
You have to only memorize angles and their sines cosines, etc from 0 to π/2 rest...
im not quite sure what u meant by angles and their sines and cosines wdym by thay
median osprey
yeah but like dont you gotta go out of ur way to memorize them
What do you mean by this ?
Then
dim coral
What do you mean by this ?
i was refering to something like this
median osprey
Yes you will have to memorize it
dim coral
You have to only memorize angles and their sines cosines, etc from 0 to π/2 rest...
so these are the values you were refering to? like memorize their angles and their sines and cosines?
median osprey
Yes and by the help of these angles you can even find sin, cos of angles beyond this .Like 3π/4, 7π/6, etc.
dim coral
Yes and by the help of these angles you can even find sin, cos of angles beyond...
ah alright i got
it
thx
.close
pallid sphinx
can someone help me with this question?
lone heartBOT
can someone help me with this question?
solemn juniper
what's giving you issue?
mortal trellis
Remember the relationship between eigenvalues and trace/det
lone heartBOT
@pallid sphinx Has your question been resolved?
pallid sphinx
Remember the relationship between eigenvalues and trace/det
yea.. that's where i stuck
is a+b = 3 or -2?
compact hawk
How complex is to create an algorithm (or formula) which converts a real number (like 1.4142135623730951) into a fraction of integers or a fraction of integers and square roots?
(1.4142135623730951 = sqrt(2)/2 instead of 1.4142135623730951 = 70710678118655/500000000000000)?
(i know that 1.4142135623730951 is a real number but it could be approximated, i mean : 1.4142135623730951 is more 'equal' (is nearer) to sqrt(2)/2 than 70710678118655/500000000000000)
alpine sable
do you mean given a rounded real number find an irrational number that it could be?
rancid hazel
do you mean given a rounded real number find an irrational number that it could ...
i think he means that he's trying to find a formula or an algorithm that turns real numbers into a sequence of fractions.
abstract isle
Because in the exercise they said that y=tan*-1(x) soo when u replace it in the equation u get cos(tan*-1(x))=cos(y)
rancid hazel
How complex is to create an algorithm (or formula) which converts a real number ...
quantum isn't 1.4142135623720951 sqrt2 instead of sqrt(2)/2?
compact hawk
quantum isn't 1.4142135623720951 sqrt2 instead of sqrt(2)/2?
yea, sorry. I was thinking to an other problem while i as writing
rancid hazel
is alright buddy
compact hawk
i think he means that he's trying to find a formula or an algorithm that turns r...
yea
rancid hazel
anyways there are certain ways to approximate a real number
but it actually depends on the number
rose sigil
the original problem seems like the “opposite” of that?
compact hawk
yea i mean that also 1.41 is sqrt(2) (approximated)
i am looking for a formula which converts a number (could be 1.41 or 1.41142135) to it's fraction representation (in that case both 1.41 and 1.41142135 are approximable to sqrt(2))
rancid hazel
i am looking for a formula which converts a number (could be 1.41 or 1.41142135)...
there's exactly a formula i know
it's one of my favorites
compact hawk
By talking of math formulas i think that there is no one which converts both 1.41 and 1.41142135 to sqrt(2) but it could be possible to do with programming, for example :
if numerb_taken_in_input == 1.41 or number_taken_in_input == 1.41142135 then the number is sqrt(2)
rancid hazel
By talking of math formulas i think that there is no one which converts both 1.4...
yeah you're right
compact hawk
By talking of math formulas i think that there is no one which converts both 1.4...
but the problem of this condition (don't take this example as programming question) is that also 1.411421 is sqrt(2)
so the solution would be to approximate every number inputted to a calculator with 2 digit number
rancid hazel
what you could do is round up the number to let's say 3 digits, so 1.411421 to 1.41
and then say that if numerb_taken_in_input == 1.41 then the number is sqrt(2)
compact hawk
but to check which number correspond to 1.141421 the only solution should be to generate fractions until the fraction generated is approximated to that number, like :
Number = 1.4114
for each number in that range of numbers : 0-200:
if sqrt(number) == Number: the program is finished
i am talking too much about programming, but it's required to explain myself
rancid hazel
oops
compact hawk
i mean that to get the fraction representation of a number taken in input from the user (like a calculator does) you should try to generate random fractions until you find the one which result is 1.4114 and that is not possible to do because this program would take much time
you got it?
rancid hazel
yeah
but couldn't you say that you don't do an algorithm that does it from 0-200 but instead do it into a certain group of numbers, because you know 1,41 is between 1 and 2. that means that number that you're trying to find is a number somewhere between 1 and 4. that when sqrted becomes 1.41...
hollow sparrow
i mean that to get the fraction representation of a number taken in input from t...
just try to see if the number have a Repeating decimal like for N digit
compact hawk
just try to see if the number have a Repeating decimal like for N digit
What do you mean?
rancid hazel
he means a number like 0,25252525...
hollow sparrow
just fking use exponential : 1.41^2
but how to know the right exponential
rancid hazel
just fking use exponential : 1.41^2
yeah but what if you got a nummber where if sqrt is still an irrational number?
compact hawk
but the problem persists if the number is not a square root, like sqrt(2)/2
compact hawk
yeah but what if you got a nummber where if sqrt is still an irrational number?
yea
however, i am not here to find a formula for that. i was just curious if there is a known formula for it
rancid hazel
(sqrt(2)/2)²=1/2 which is not an irrational number
compact hawk
Well, i don't think that a so complex algorithm can be created, because python algorithm returns 70710678118655/500000000000000 as the convertion in fractions of 1.41142135
rancid hazel
however, i am not here to find a formula for that. i was just curious if there i...
i think the only formula i know is the infinite continued fraction.
compact hawk
isn't there the reverse formula of that?
Like getting sqrt(2) by knowing the result (1.4114)?
ocean sealBOT
Mehdi_Moulati
lone island
How complex is to create an algorithm (or formula) which converts a real number ...
you can't
the good new is
you don't need to
rancid hazel
you don't need to
reason?
lone island
computers were made to approximate this stuff
the original problem was "how do we represent these real numbers in a manner that let us work with them and give use the results we want sufficiently accurately"
the reverse problem serves no purpose
also
there's no way to separate between sqrt(2)/2 and actually 70710678118655/500000000000000)
what if you wanted the latter?
maybe you'd say "I just need an answer that's close enough"
compact hawk
Yea
lone island
then 70710678118655/500000000000000 is close enough
better yet
1.4142135623730951 is close enough
compact hawk
Hmm what if we just simplify the fraction?
lone island
1.4142135623730951 is close enough
(or however the computer represents that in memory)
lone island
Hmm what if we just simplify the fraction?
what
rancid hazel
Hmm what if we just simplify the fraction?
then you get 141421356237.../1000000000...
lone island
I don't know what that has to do with what I said
hollow sparrow
I don't know what that has to do with what I said
i guess he want to simplify the approximation of the sqrt
compact hawk
Because today's algorithms represent sqrt(2) with this fraction :
70710678118655/500000000000000
lone island
it does?
compact hawk
Because today's algorithms represent sqrt(2) with this fraction :
70710678118655...
I see that both numbers can be divided for 2
lone island
the nominator is odd lel
rancid hazel
Because today's algorithms represent sqrt(2) with this fraction :
70710678118655...
what type of algorithms?
lone island
by 5 you meant?
compact hawk
Yea I am stupid
compact hawk
what type of algorithms?
fractions.Fraction() function in python (idk algo name)
lone island
you can look at the reference to figure out how it works
rancid hazel
fractions.Fraction() function in python (idk algo name)
doesn't python have a way to simplify fractions?
next brook
How complex is to create an algorithm (or formula) which converts a real number ...
You might want to look at continued fractions, which provide a way to find the "best" fractions appoximating a given real, where "best" means that no other fraction with smaller denominator gets closer.
compact hawk
You might want to look at _continued fractions_, which provide a way to find the...
Thanks
next brook
This leads to successive "best" approximations for sqrt(2): 3/2, 7/5, 17/12, 41/29, ..., 22619537/15994428, ...
compact hawk
Ok, thank you guys.
You answered my question 🙂
How do i close this chat?
next brook
Type .close.
viscid pawn
Ok, thank you guys.
You answered my question 🙂
How do i close this chat?
like dat
.close
lone heartBOT
viscid pawn
have a good day
lone heartBOT
Available help channel!
quiet knoll
a
rancid hazel
what is your problem?
quiet knoll
hello
im a 7th grader and ijust came back from a math exam and there is this question
that is confusing all of my friends and family when i told them it
rancid hazel
tell it please?
quiet knoll
and i myself didnt figure it out
the tempature of mashhad is -3 celcius
the tempature of tehran is 4 degrees celcius less than tabriz
the tempature of tabriz is the average of tehran and mashhad - 5 degrees
what is the tempature of tabriz?
rancid hazel
haha
quiet knoll
we are learning about algebra and x and y and such things
rancid hazel
the tempature of mashhad is -3 celcius
the tempature of tehran is 4 degrees celc...
wait is mashad -5 degrees or -3 degrees?
quiet knoll
wait is mashad -5 degrees or -3 degrees?
they didnt tell temp of mashhad
wait
no
they didnt tell temp of tabriz and tehran
quiet knoll
wait is mashad -5 degrees or -3 degrees?
mashhad -3
pseudo ice
Worded weirdly
quiet knoll
Worded weirdly
english is not my first language
and it was put weirdly in the exam aswell
its 5 less than the average of tehran + mashhad,
pseudo ice
Wondering if it’s “[the average of tehran and mashhad] - 5 degrees” or “the average of tehran and [mashhad - 5 degrees]”
viscid pawn
you pick 3 equations out of this :
a = tempMash = -3
y = tempTehran = TempTabriz - 4
x = tempTabriz = ((TempMash + TempTehran)/2) - 5
quiet knoll
Wondering if it’s “[the average of tehran and mashhad] - 5 degrees” or “the aver...
1st one
[tehran and mashhad] - 5 degrees
hollow sparrow
[tehran and mashhad] - 5 degrees
[tehran and mashhad] /2- 5 degrees
rancid hazel
and you want to find temp tabriz right?
viscid pawn
you pick 3 equations out of this :
a = tempMash = -3
y = tempTehran = TempTabri...
in this case x = (-3 + x - 4)/2 -5
rancid hazel
bruh how do you type so fast
quiet knoll
i dont understand anything you guys are saying i just am extremely curious about the answer
💀
viscid pawn
idk if you guys find the same
rancid hazel
i got it
quiet knoll
what is it??
rancid hazel
shadow how do you type so fast lol
rancid hazel
wait shadow you made a mistake
quiet knoll
please ping me when you find the answer
viscid pawn
old on
yeah
mb
in this case x = (-3 + x - 4)/2 -5
so if i pick the x/2 out it's 1/2*x = -17/2
x = -17
rancid hazel
exactly
viscid pawn
does that sound right to any other helpers ?
and then you know that Tehran temp = -21
rancid hazel
maybe put x as temp tabriz
quiet knoll
oh
viscid pawn
rancid hazel
np
viscid pawn
no problem dude 🙂
viscid pawn
just type .close
lone heartBOT
viscid pawn
no problem dude, have a good day 👍
lone heartBOT
Available help channel!
alpine sable
I wanted to know if there are any distinct non-zero integers a, b, c such that this expression is also an integer.
viscid pawn
can't just you kick the square roots out ?
rancid hazel
easy say that a=1 , b=1 and c=1
viscid pawn
easy say that a=1 , b=1 and c=1
then it's equal to 1
alpine sable
easy say that a=1 , b=1 and c=1
Distinct integers
rancid hazel
can't just you kick the square roots out ?
you can't this is a sum not a multiplication
viscid pawn
alpine sable
can't just you kick the square roots out ?
Kick?
viscid pawn
you can't this is a sum not a multiplication
but if you go ^2 on both sides
it's still the same
viscid pawn
I wanted to know if there are any distinct non-zero integers a, b, c such that t...
both being 1, 2 etc
you get it ?
alpine sable
No
viscid pawn
if you pick all of them with the same value you can have IN solutions
vale wigeon
you want distinct a, b, c such that sqrt( (a^2+b^2+c^2)/3) is an integer, yes?
alpine sable
if you pick all of them with the same value you can have IN solutions
But they'll not be distinct
kindred anchor
alpine sable
Also I don't know if that's even possible, I just made that up on my own
So if not, is there a way to prove that it's not possible
rancid hazel
do a, b and c have to be integers?
alpine sable
do a, b and c have to be integers?
Yes
vale wigeon
wait shit
ocean sealBOT
Result:
25
3 should be in root
vale wigeon
yes
rancid hazel
sqrt(75)/sqrt(3)=5
vale wigeon
,calc sqrt(1^2+5^2+7^2)/sqrt(3)
ocean sealBOT
Result:
5
there you go
vale wigeon
here you go
alpine sable
Oh yeah, thanks
stoic folio
This isn't right, is it: https://imgur.com/qrGJ1sE
vale wigeon
@stoic folio open your own channel
stoic folio
Can you post the template for that please I've never done so.
alpine sable
Shall I close this now?
vale wigeon
Can you post the template for that please I've never done so.
read #❓how-to-get-help
there's no command, you just post in a free channel
@alpine sable if you have nothing else to ask then close
alpine sable
.close
stoic folio
Oh, I see what I did wrong, there are open help channels above.
stoic folio
.close
twin arrow
Good morning and happy new year.
What's the character used for partial derivatives? What's the LaTeX syntax?
lone heartBOT
Good morning and happy new year.
What's the character used for partial derivativ...
@twin arrow Has your question been resolved?
bright remnant
lone heartBOT
bright remnant
The answer is a, but im getting b
median osprey
Yes the given answer is correct
Please tell how are you getting b
The unit of time in graph is ms
bright remnant
The unit of time in graph is ms
median osprey
It's wrong a is not equal to v/t it's equal to dv /dt
You will have to calculate the area of graph
F=mdv/dt
mdv=F dt
Integrate put respective limits m=1 here
v= area of graph( velocity at any instant is the area till that time)
at t=0 v=0
Now simply calculate the area till 0.2 seconds using 1/2 base* height
You will get 8m /s
Velocity
bright remnant
F=mdv/dt
mdv=F dt
Integrate put respective limits m=1 here
v= area of graph( vel...
idk what the limits are bro
is it 0 & 200
bright remnant
m is outside the intrgral, right?
median osprey
Yes you can take it out as it's a constant
And moreover it's value is 1
Integral of Fdt will give you area of the graph
So in other words you have to simply calculate the area
Making sure time is in seconds
1/2*80×0.2= 8m/s
bright remnant
Integral of Fdt will give you area of the graph
ok sure but when i input everything i still get 16
median osprey
1/2*80×0.2= 8m/s
.
bright remnant
1/2*80×0.2= 8m/s
ok but how does an integral give me the 1/2??
median osprey
ok but how does an integral give me the 1/2??
It is the area of graph Fvs T
Integral Of Fdt means area of F vs T graph
Between respective limits
bright remnant
i get that
but when you actually write the integral and do everything
there is no 1/2
median osprey
1/2 is coming because I am calculating the area of traingle in graph
We already figured out that v will be equal to area till 0.2 s
So now time to calculate area
Integration was just to show that area=v
If we were given relation between F and t then we could have directly solved through integration
But here there is no relationship between F and T
So we have to rely on graph
As the meaning of integral Fdt is the area covered by curve between the respective limits
If you read properly these things must have been mentioned in your text book , proof may not be though
But it must be there in some form of statement
lone heartBOT
@bright remnant Has your question been resolved?
lone heartBOT
@bright remnant Has your question been resolved?
median osprey
What doubt do u have boi
I wrote a whole long Paras while explaining
Just ask in which part are you facing problem
@bright remnant
bright remnant
What doubt do u have boi
im sorry but im extremely busy with something
thats critical to me at the moment
would you mind showing some working out?
with the integration and stuff
i get that you have to find the area and that u use calculus
median osprey
Ok i am sending you pics in your dm
bright remnant
I just want to be able to apply this in any situation
lone heartBOT
@bright remnant Has your question been resolved?
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alpine sable
vale wigeon
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misty oak
hi, i don't understand this step which i marked with a red arrow. From my understanding this will be used the chain rule to show that f(x) =ax^n -> it's derivation f'(x anx^(n-1) os valid for real numbers. What i don't understand is how a*1/q arises.
abstract fractal
It's just the power rule for derivatives, since 1/q is rational
pseudo ice
Did they prove that x^{1/q} differentiates to (1/q)*x^{1/q - 1} before that point? If so that’s just chain rule
abstract fractal
Oh, they're differentiating a function with a rational power
So 1/q being rational doesn't really matter lol
pseudo ice
Yeah my reading of OP’s post is that they start with it for n being natural/integer and then work from there to get it for all real numbers(?)
lone heartBOT
@misty oak Has your question been resolved?
misty oak
Did they prove that x^{1/q} differentiates to (1/q)*x^{1/q - 1} before that poin...
do you mean this?
lone heartBOT
do you mean this?
pseudo ice
do you mean this?
Hmmm not quite - that seems to be proving for integers given it being true for naturals
pseudo ice
hi, i don't understand this step which i marked with a red arrow. From my unders...
Does anything come after that but before your one here?
pseudo ice
do you mean this?
If you give me a second, I’ll typeset what I was expecting to see
lone heartBOT
@misty oak Has your question been resolved?
pseudo ice
Set $f(x) = x = x^{\frac{q}{q}} = \left( x^{1/q} \right)^{q}$ for some integer $q$
Then $f'(x) = 1$, but also $f'(x) = q \left( x^{1/q} \right)^{q - 1} \left(\dv{}{x} x^{1/q} \right)$ by chain rule and what we already know
Simplify and equate, you have $1 = q x^{1 - \frac{1}{q}} \left(\dv{}{x} x^{1/q} \right)$, therefore $\dv{}{x} x^{1/q} = \frac{1}{q x^{1 - \frac{1}{q}} } = \frac{1}{q} x^{\frac{1}{q} - 1}$
@misty oak
ocean sealBOT
chartbit
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dire gale
f(x)=x^(4)-1,0<=x<=10
lone heartBOT
f(x)=x^(4)-1,0<=x<=10
dire gale
is this a one to one function?
daring zenith
yes
dire gale
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lone heartBOT
misty oak
**chartbit**
no i did not see this, but the video where i posted the steps out was part of a video about the chain rule, but the step x^{1/q} ^q was not a part
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south timber
Hi, I need to determine the intervals of monotonicity and extremum of the function
south timber
idk if there are any formulas or barely know anything about this topic due to the fact that I was too sick to attend my classes, can anyone help
thorn kindle
It's just asking you to determine the sign of the first derivative
south timber
oh, didnt know that, so it will be 3x^2-4, right?
rocky grove
Yep
south timber
and from where do I get the sign of it
south timber
the original question is to determine the intervals of monotonicity and extremum of the function (question is in polish so i just translated it, hope i did it right)
rocky grove
Monotonicity hmm
Well extremum is easy
You determine when the derivative is 0
And see what x makes the derivative = 0
south timber
so i got x=-2sqr3/3 or x=2sqr3/3
rocky grove
Hmm I now understand monotonicity
Ok so you determine if the derivative gives negative values or not
south timber
how do i know that? cause one of my x is negative and the other one is not
rocky grove
how do i know that? cause one of my x is negative and the other one is not
Nope not like that
It's gonna be quickest with a graphing calculator
But I don't think it is allowed
So an easy way to check is you pick an x value between your critical points (x values that make the derivative = 0)
south timber
so can I pick 1 for example?
south timber
so i got x=-2sqr3/3 or x=2sqr3/3
cause i think my critical points are these and they equal -1.15 and 1.15
south timber
okay and what do i do with that 1
rocky grove
Try it on your derivative
south timber
i got -1
rocky grove
If it gave you a negative, then it is decreasing in the interval between the critical points
south timber
can i write it like this? f(x)(arrow down) x=(-2sqr3/3;2sqr3/3)
rocky grove
$x \in (-2\frac{\sqrt{3}}{3}, 2\frac{\sqrt{3}}{3})$
ocean sealBOT
VulcanOne
rocky grove
With the f(x) arrow down
Or you can write decreasing when $x \in (-2\frac{\sqrt{3}}{3}, 2\frac{\sqrt{3}}{3})$
ocean sealBOT
VulcanOne
south timber
ohhh, ok, and it will be rising from -infinity to the -2sqr3/3 and from 2sqr3/3 to +inf?
rocky grove
And increasing when $x \in (-\infty , -2\frac{\sqrt{3}}{3}) \cup (2\frac{\sqrt{3}}{3} , \infty)$
rocky grove
ohhh, ok, and it will be rising from -infinity to the -2sqr3/3 and from 2sqr3/3 ...
Yep
south timber
ohh, okok, and what will be the extremum of the function
rocky grove
Evaluate the original function at the critical points you got
You'll get your y values
Use them to label the points as maxima and minima
tacit arch
$\cup, \bigcup$
ocean sealBOT
riemann
south timber
so i need to put 2sqr3/3 into my first function?
ocean sealBOT
VulcanOne
rocky grove
$\cup, \bigcup$
Tysm
rocky grove
so i need to put 2sqr3/3 into my first function?
Yep both the (2sqrt(3))/3 and it's negative counterpart
south timber
and do i need to put it exactly or can i put 1.15?
rocky grove
Well does the question accept approximation?
rocky grove
Wait
You can store the value of (2sqrt(3))/3 into a letter
Let's say A
And plug in A instead of (2sqrt(3))/3
south timber
so i got -16sqr3/9 +5 and 16sqr/9+5
rocky grove
So 8.079 and 1.92?
south timber
wait, the second one is 16sqr3/9 +5
south timber
So 8.079 and 1.92?
yeah i got this
rocky grove
Okay
Okay
Now you have
(-1.15, 8.079) as a maximum and (1.15, 1.92) as a minimum right?
south timber
they can be wrong tho cause he makes a lot of mistakes
south timber
yeah i also think i am right
so i will try to make the second question and will text in few min, will it be alright?
rocky grove
Sure
lone heartBOT
@south timber Has your question been resolved?
south timber
k, so i got it i think
so i got y(arrow up) if x=(-2,0) and y(arrow down) if x=(-inf,-2)u(0,inf) (not including -1, cause x =/=-1)
and fmax=0 and fmin=-4
rocky grove
so i got y(arrow up) if x=(-2,0) and y(arrow down) if x=(-inf,-2)u(0,inf) (not i...
The increasing part is actually 2 intervals
And (-2, 0) is not the interval
rocky grove
You have to consider also that there might be discontinuities
Like at x=-1
Which will make the function become undefined
south timber
oh, didnt know that
south timber
oh, so the lim for x-->-1 (-)?
rocky grove
Yeah
south timber
and do i do that for the frst function?
south timber
or for the derivative
south timber
k, so to which point is this done good and from where is it bad
rocky grove
Your increasing and decreasing
south timber
and are the extremum also bad?
rocky grove
They aren't, but they are switched
The minimum you wrote is the max
And the maximum you wrote is the min
south timber
oh, and how do i know which one is min and which is max
rocky grove
You check your decreasing and increasing intervals
Like (-inf, -2), the derivative gives you positive numbers
Then at (-2, 0), -{-1}, it gives you negative numbers
And (0, inf), it gives positive numbers
south timber
ohhh, k i know where i did wrong, thank you
rocky grove
south timber
so from limes i got -inf and inf
rocky grove
limes?
south timber
lim
rancid hazel
vulcan i find it strange that you're helping someone with math while listening to fnaf 1 ambience
south timber
we call it limes at my college classes, is it wrong?
south timber
vulcan i find it strange that you're helping someone with math while listening t...
I'm listening literally now to fnaf music also, so respect
rocky grove
vulcan i find it strange that you're helping someone with math while listening t...
I wanna get into a certain mood to feel the need to study
Lol
I was listening to REPULSIVE - 1908 (Vol. II) and it evolved from there 
But ngl, FNAF ambience makes me feel serious
rancid hazel
it's the intense music keeping you up
south timber
so what do i do with my limits?
south timber
i got inf and -inf
rocky grove
That's in the original function?
south timber
yeah
rocky grove
Hmm
Well true
But
I think I messed up
You should use the limit in the derivative
rocky grove
This means that your function is decreasing
south timber
in -1?
rocky grove
In the region around -1
rocky grove
It tells you that x = -2 is a transition point from an increase to a decrease
And x =0 is a transition point from a decrease to an increase
rocky grove
Yep
south timber
so wait
ill try to write it
so i got y(arrow up) if x=(-inf,-2)u(0,inf) and y(arrow down) if x=(-2,-1)u(-1,0)
yes?
rocky grove
Yep
rocky grove
Oki
south timber
k, so i got my derivative and its e^x+xe^x
and my x's are x1=do not exist and x2=-1
south timber
and what now
rocky grove
Wait you take the limit to check which x will make e^x = 0
south timber
it does?
rocky grove
Yeah
south timber
idk really what it is but yeah, keep going
ocean sealBOT
VulcanOne
south timber
ok
rocky grove
Check for each interval
south timber
and i need to know which decrease and which increase?
rocky grove
And see if you have a maximum or not
rocky grove
and i need to know which decrease and which increase?
Yep
south timber
so i need to put -1 in the place of x?
rocky grove
That will give you the extreme
south timber
and do i put it in the first function or derivative
rocky grove
Where do you find the maximum y and minimum y?
south timber
literally have no idea
rocky grove
That finds you the minimum/maximum
south timber
so i get 1/e?
rocky grove
-1/e yeah
rocky grove
Oki ^-^
south timber
and thats my max?
rocky grove
Now we wanna know if -1/e is a minimum or a maximum.
south timber
yeah
rocky grove
We check the intervals and plug a value in between them inside the derivative
To know where the increase is and the decrease is
south timber
We check the intervals and plug a value in between them inside the derivative
literal magic words
rocky grove
Like a number between (-inf, -1) and see if it gives a positive or a negative
south timber
like 0?
rocky grove
Same thing for a number between (-1, inf)
south timber
and i put it in derivative, right?
rocky grove
Yeah
south timber
i got 1
rocky grove
So the interval (-1, inf) is increasing
south timber
ohh, and the -inf,-1 will be decreasing?
rocky grove
Yeah if you tried it, it will give a negative
south timber
and what will be my min
rocky grove
Any transition point from a decrease to an increase
Your x=-1
On its left, is it increase or decrease?
south timber
decrease
rocky grove
And on its right?
south timber
increase
rocky grove
Why?
rocky grove
Correct
south timber
cause its on the bottom
rocky grove
It's a minimum
south timber
but yeah, its min cause its on the bottom
rocky grove
Which means that it is the point which makes the function go from decrease to increase
south timber
yeah
south timber
-1,inf
south timber
-inf,-1
south timber
yes yes
know its time for the d)
now
k my dude cause its literally 23;00, imma head to sleep, but thank yoou for your help, hope your pillow is cold on both sides
/close
south timber
.close
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rose rivet
lone heartBOT
tacit arch
i wouldn't do it that way
when you find $\tan(3 \theta + 20) = \sqrt{3}/3$, use the periodicity of tangent
ocean sealBOT
riemann
rose rivet
yeah which is 30
tacit arch
that's not the periodicity
rose rivet
whats periodicity
tacit arch
$\tan(x + \pi) = \tan(x)$ for all $x$ in the domain of tangent
ocean sealBOT
riemann
tacit arch
,w plot tan(x) for pi/2 < x < 7pi/2
ocean sealBOT
tacit arch
,w plot tan(x) for 0 < x < 3pi
ocean sealBOT
rose rivet
what would you do next
tacit arch
whats periodicity
$\tan(x + n \pi) = \tan(x)$ for any integer $n$ and $x$ in the domain of tangent
ocean sealBOT
riemann
tacit arch
when you find $\tan(3 \theta + 20) = \sqrt{3}/3$, instead of just $3 \theta + 20 = 30$, you need to add $n \cdot 180$ to the right side
ocean sealBOT
riemann
tacit arch
$3 \theta + 20 = 30 + n \cdot 180$
ocean sealBOT
riemann
rose rivet
3?
rose rivet
3 values
tacit arch
what are they?
rose rivet
one second
tacit arch
you can just check them by plugging it in
whatever theta you find, verify it by calculating tan(3 theta + 20) and see if you get sqrt(3)/3
tacit arch
now find all integers n where theta is in your limits
.
your limits being 0 <= theta <= 180
worn hearth
Just a general question guys, i am just not 100% sure of this but if the denominator of a said function is just a number(never 0), can we be 100% sure that the graph has no vertical asymptote
mossy laurel
If the numerator has none too yes
worn hearth
excuse me but, wdym?
tacit arch
excuse me but, wdym?
$\frac{x^2-1}{x-1}$
ocean sealBOT
riemann
tacit arch
at first glance, you would think there's an asymptote at x-1=0, or x=1
but there isn't because $x^2 - 1 = (x-1)(x+1)$
ocean sealBOT
riemann
tacit arch
so a factor cancels and the fraction simplifies to x+1
worn hearth
Exactly so, if we put a function in its most simplified form to where it doesn't have a denominator, we can be 100% sure that the function lacks a vertical asymptot right?
stoic folio
I'm not clear on whether or not the default unit is angle or radians when using the Microsoft .NET 7 System.Math static type functions in PowerShell 7.2.8. Does anybody know?
stoic folio
I did, I used Microsoft's PowerShell 7.2.8 and then I used their calculator's "sin" button on a 45 degree angle. They didn't match up. So, I'm confused.
alpine sable
so what did sin(45) give?
stoic folio
0.850903524534118
alpine sable
thats radians
stoic folio
Ah, okay, I'm not to that in trigonometry just yet. I wonder if I can flip a switch to have it do degrees for me.
stoic folio
I'll look, at least you confirmed it's giving answers back in radians. I figured something was up when they didn't match right.
Thank You
.close
lone heartBOT
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daring rapids
can someone teach me how to solve equations like this (91.67% * 100% ) + (8.33% * 22%)
last ether
Fraction multiplication ig
daring rapids
????
wary stream
Convert to fractions
last ether
You can represent each percent as a fraction
daring rapids
oh ok
wary stream
Or use a calculator if that is allowed
lone heartBOT
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past current
would anyone kindly help me w this qstn pls ?
lone heartBOT
would anyone kindly help me w this qstn pls ?
past current
it looks as though it's a simul eqn at first but I don't think it is
limpid turret
calculus?
Ask yourself this question
Which point must always be on the line mx-y-2=0 regardless of m?
past current
is there such point?
limpid turret
yes
past current
(0,-2)
limpid turret
yes
Now, for some point (x0, y0) on the circle, consider what the equation of its tangent line must be
Then, that tangent line must go through (0, -2)
past current
does "touches" mean tangent?
limpid turret
yes
past current
this is the closest page I can find in the textbook
pliant cedar
do u know the formula fr the distance from a point to a straight line
past current
Oh is this algebra?
not sure what the difference is tbh
limpid turret
between algebra and calculus?
past current
yes
past current
do u know the formula fr the distance from a point to a straight line
I would assume something to do with finding the line's perpendicular but I'm not sure what the formula is
pliant cedar
I would assume something to do with finding the line's perpendicular but I'm not...
yes
do u know how to find the perpendicular of a line?
so if u have a line ax+by+c=0, the distance to the line from the point (p, q) is
$\frac{|ap+bq+c|}{\sqrt{a^2+b^2}}$
ocean sealBOT
SilverSoldier
past current
What's the derivative y=sqrt(4-x²)?
y' = (2x)^(1/2) ?
I know how to find the derivative of simpler expressions but not sqrt over two terms