so like x = arcsin(1+ sqrt 2) and x = arcsin(1- sqrt 2)?
#help-10
chilly lark
chilly lark
oh!
timid silo
Okay so now
We need to make sure that 1+sqrt(2) and 1-sqrt(2) fit the domain we defined above for the arcsin function
What was the domain we defined for the arcsin function leila?
chilly lark
[-1, 1]
timid silo
Yep!
So we just have to find out if 1+sqrt(2) and 1-sqrt(2) are inside that domain
So take sqrt(2) as 1.4 for simplicity sake
What do you have approximately for both of them
chilly lark
2.4 and -0.4?
chilly lark
nope!
timid silo
Exactly !!
So that solution is an extraneous solution
So we just have to worry about the -0.4 one
obtuse pebbleBOT
@chilly lark Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
chrome star
obtuse pebbleBOT
chrome star
Ik how to factor the denominator but Idk how to factor the numerator
I tried the cube factoring but it won't work
timid silo
Is that a 9x or a 4x
chrome star
9x
timid silo
Ik how to factor the denominator but Idk how to factor the numerator
First factor the obvious first factor, x
The x^3 term has a common factor of x with the term -9x
So factor it
chrome star
Ahh gcf?
timid silo
,rcw
chrome star
Disregard x(x-9x)
warm shaleBOT
timid silo
Breh
chrome star
But there's nothinf to cancel
chrome star
Yeahhh?
timid silo
The factoring is wrong
chrome star
Why?
timid silo
,w expand (x+7)(x-3)
warm shaleBOT
timid silo
Isn't really 9x
timid silo
Yeah no worries then yeah you are right
chrome star
Ohhhhhhhhhh
timid silo
Do u see how? Haha
timid silo
Ding ding
jolly ginkgo
Good handwriting
chrome star
Should I substitute the x to 3 now?
chrome star
Good handwriting
Haha thank you
jolly ginkgo
Sure
timid silo
Should I substitute the x to 3 now?
Yeah
timid silo
Woooo
chrome star
Is it correct?
timid silo
Yeah sorry if I sounded a bit rude, have a nice day :3
chrome star
.close
timid silo
how can i remove the log from both sides?
obtuse pebbleBOT
how can i remove the log from both sides?
sage geode
Exponentiate as you would do normally
log_c(a) = log_c(b) so c^log_c(a) = c^log_c(b) or simply a = b
timid silo
log_c(a) = log_c(b) so c^log_c(a) = c^log_c(b) or simply a = b
so to remove the log i have to apply always the exp?
sage geode
Yeah
sage geode
Yes
timid silo
perfect, thank you!
sage geode
Also make sure that a and b are both positive
timid silo
Also make sure that a and b are both positive
yes
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
.close
small scaffold
obtuse pebbleBOT
small scaffold
Where on earth did the 2y go, and where did the lnk come from?
timid silo
ln1 is written as lnk
small scaffold
why is it ln 1?
timid silo
why is it ln 1?
-ln(1-y^2) = ln(1/1-y^2) = ln1 - ln(1-y^2)
small scaffold
okay, where did the 2y go?
obtuse pebbleBOT
@small scaffold Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
frosty valve
need some explanation again:')
obtuse pebbleBOT
need some explanation again:')
frosty valve
i was guided
got the answer but not sure how things work
i still don't get why it's 34/3
royal basin
no.
alpine raven
Plz dont use chatgpt here ffs
royal basin
<@&268886789983436800> chatgpt abuse
royal basin
then you are unwelcome here.
warm canopy
I think mods aren't around I pinged them for this in another channel
frosty valve
what's that
alpine raven
an AI
frosty valve
i still don't get why it's 34/3
this
plucky swan
I think mods aren't around I pinged them for this in another channel
where
alpine raven
so yea can anyone explain:)
so an arithmetic progression is written like this :
$T_n = T_1 + (n-1)d$
warm shaleBOT
Ｈｅｒｅｌｓ
alpine raven
the first term is $T_1 = 8$ and the last term $T_n = 34$
warm shaleBOT
Ｈｅｒｅｌｓ
alpine raven
not really n but thats an n we want to find
frosty valve
found the n ald
frosty valve
i still don't get why it's 34/3
.
plucky swan
<#486844829209198613>
ah okay i missed that somehow
alpine raven
i was guided
do we know d ?
frosty valve
do we know d ?
alpine raven
cant see*
timid silo
AP? 👀
frosty valve
cant see*
so i first did 34=8+(6-1)d and it was wrong, so they told me to replace 34 with 34/3
alpine raven
S6 = 6*(8+T6)/2 = 58
with that
timid silo
so i first did 34=8+(6-1)d and it was wrong, so they told me to replace 34 with ...
What you did shouldnt be wrong
I'm getting 26 = [n-1] x 2/3
alpine raven
,w 6(x+8) = 116
warm shaleBOT
alpine raven
with that you can have d and its over
timid silo
There are 2 main formula's
a,n = a + [n-1] x d
Where a,n is the desired term, a is the first number of the AP, n is the numbers and d is the common difference
All the other sums you will have will revolve around the same, but will have twists
frosty valve
these 2 are the same right?
n/2(a+l)
n/2[2a+(n-1)d]
timid silo
Yes
But the second one is used the most. As if you dont have the last term you can directly do the second one
frosty valve
obtuse pebbleBOT
high lily
do you know the expression/formula for the sum of the first n terms in an arithmetic series?
frosty valve
do you know the expression/formula for the sum of the first n terms in an arithm...
sn formula?
high lily
yes
frosty valve
n/2[2a+(n-1)d]
high lily
yeh
so you have
S_n = n/2[2a+(n-1)d]
and you know everything except for the n you're being asked to find
plug in those values and solve for that n
royal basin
you do not "move" anything anywhere.
frosty valve
you do not "move" anything anywhere.
so how do i continue?
royal basin
expand carefully
frosty valve
i still don't get it💀
sorry, do u mind if i ping u later if this channel closes?bc im being called
sorry im back
@royal basin
is the expanding something like this
high lily
where's the rest of it
tame narwhal
solve it like you would solve any algebraic equation
frosty valve
where's the rest of it
stuck
high lily
whether its valid depends on what else you plan on writing
these are just expressions
what we're tying to get you to do is no different to expanding something like
a(b+c)
frosty valve
but there's another bracket in the bracket
high lily
don't let fractions / large expressions intimidate you
well take it one step at a time if needed
frosty valve
so (n-1)5/2 is c?
high lily
yes
you can view it like that if you are struggling to combine multiple steps
(and is recommended until you get comfortable enough)
frosty valve
like this?
high lily
no
high lily
the whole right side, yes
high lily
looks ok so far
frosty valve
ik i shouldn't be confused by fractions but i am💀
high lily
if you can simplify
$$2 \times \frac{3}{7}$$
you shouldn't really have an issue here
warm shaleBOT
ℝamonov
high lily
,w 5/2*n^2 + 23n/2 - 5580 when n=45
warm shaleBOT
high lily
,w sum from 1 to 45 of 7 + (n-1)*5/2
warm shaleBOT
high lily
looks good
frosty valve
i also got a negative num while factorising
ik that's impossible but is there a way to check it
high lily
check what
high lily
ik it's not
there's no need to check then
the negative value for n does not make sense in the context of the problem
frosty valve
alr ty😅
high lily
though you'd show the factorisation within the work and state reasons for the exclusion
instead of jumping straight from the quadratic equation to the final solution by what seems to be magic
frosty valve
sorry, so how do i state reasons
high lily
something like since n>1, should be sufficient
frosty valve
i see, ty
haughty onyx
hi
haughty onyx
i have no clue where to start here
they didnt give us any training yet and just asked us to attempt
ive tried 2 cases where numerator <0 and denom >0
and vice versa
royal basin
you want $\frac{x(k-x)-400}{x^2 - x + k - 38} < 0$ to be true for all $x$...
warm shaleBOT
Ann
royal basin
pretty sure this means both the numerator and denominator will have to have negative discriminants so they don't have any roots
haughty onyx
ohhh
so i take discriminant of numerator <0 for one case and discriminant of denominator <0 for another case?
and find largest k?
royal basin
those won't be cases
you will have two inequalities, each with its own solution set, and you will want the largest integer in the INTERSECTION of those
haughty onyx
ohh okay tysm
lean spear
H
lean spear
tame narwhal
you missed a term I think, that's why
lean spear
?
tame narwhal
use the product rule twice
lean spear
im not sure why
tame narwhal
"not sure why" what?
lean spear
why product rule twice
tame narwhal
First apply the product rule to $(t) \cdot (e^t \cot(t))$
warm shaleBOT
cwatson
tame narwhal
Then you'll have to apply the product rule for $e^t \cot(t)$
warm shaleBOT
cwatson
lean spear
what about -csc(t)
tame narwhal
try following what I suggested, write it all out, and see what you get
tame narwhal
what was your original answer, that you said was marked wrong?
lean spear
tame narwhal
ok, it should be $e^t \cot(t) + te^t \cot(t) - te^t \csc^2(t)$
warm shaleBOT
cwatson
tame narwhal
You missed the squared part of $\csc^2(t)$ in the last term
warm shaleBOT
cwatson
tropic leaf
f(n+1) = [f(n)]^2 + 1
obtuse pebbleBOT
f(n+1) = [f(n)]^2 + 1
tropic leaf
how do I proove there is no f from integer to integer
there is no integer function f
f(n+1) = [f(n)]^2 + 1
f(n) = [f(n-1)]^2 +1
f(n-1) even -> f(n) odd -> f(n+1) even
obtuse pebbleBOT
@tropic leaf Has your question been resolved?
timid silo
how to solve 1,4 ,5 and 6?
obtuse pebbleBOT
how to solve 1,4 ,5 and 6?
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
Could you solve it please
grizzled shore
!nosols
obtuse pebbleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
grizzled shore
So no, we can’t just do your homework for you
simple iron
I'll tell you how to solve it
you solve it by yourself
The fastest way to learn something is by doing it on your own
So I'll tell you the concept
And if you're able to do the sums on your own then you're set for the test
So these questions are implicit functions
Implicit functions are functions of functions
Basically multiple functions combined to form one whole single function
First question of example
There is an exponential, a trigonometric function and an algebraic function
You have to differentiate this whole thing
There's two ways you can do this
One is by using the chain rule
The other directly by the outer inner method
I prefer the direct meth
Method**
timid silo
What's the direct method?
simple iron
You start differentiating the function from outside to inside
SO in the case of the 1st question
timid silo
I think using chain rule is better
timid silo
I'm gonna try using chain rule
simple iron
That’s just the chain rule
Well chain rule you start from the inside
grizzled shore
It’s just rewording
simple iron
And while doing the direct method you start from outside
@timid silo do you have the answer key??
simple iron
how to solve 1,4 ,5 and 6?
The 5th question is it prove dy/dx+ sin4x or sin^4(x)???
simple iron
-12xcsccot(2+3x^2) . csc(2+3x^2)
Yes combine both cosec to get cosec squared
Write answer in simplest possible terms
simple iron
i got -sin4x cos2x
Okay
simple iron
Yep
timid silo
alright
im stuck on question 4 though
i used the quotient rule
but i got a complete diff answer
simple iron
Don't covert in terms of cos
simple iron
I got sec^2 (root x) tan (root x)/(root x)
simple iron
Nope
First the exponent gives 2 sec root x then differentiate sec you get sec root x tan root x and then differentiate root x
You get 1/2 root x
Cancel 2 from numerator and denominator
timid silo
we do use quotient rule though, right?
timid silo
what question is this
simple iron
Question 4
timid silo
wait let me try to solve without looking at ur paper LOL
simple iron
What grade are you in?
timid silo
11th
simple iron
question where did 1/2 root x come from
Dy/dx(root x)= 1/2 rootx
timid silo
Huh
simple iron
Differentiate using the first principle and check for yourself
timid silo
Wait wdym
simple iron
square root x is 1/2x^-1/2 right
Well that's one way to write it as well
timid silo
i thought we didnt have to differentiate
simple iron
i thought we didnt have to differentiate
You do
timid silo
so first we rewrite sec root x as
simple iron
simple iron
It's from my 11th grade textbook
timid silo
i have
trigonometric derivatives and implecit differentiation
and youtube isnt helping somehow
cant find any good math teachers
simple iron
Khan academy
Are you good at functions?
What country are you from?
is the syllabus difficult?
Learn all 6 trig derivatives
And do you know first principle of differenciation?
timid silo
Are you good at functions?
i'm pretty good won't say im bad
timid silo
What country are you from?
iraq
simple iron
Okay then that's okay
timid silo
is the syllabus difficult?
nope but my teacher brings hard questions
so im just solving as much as i can
simple iron
Ah that's okay
simple iron
nope but my teacher brings hard questions
Okay
Are you good with manipulating trig functions?
Just keep doing implicit functions
timid silo
Are you good with manipulating trig functions?
what's that?
timid silo
@simple iron can i solve number 2 with chain rule?
timid silo
im trying to get better this year so im alright
okay
does it become 2sinxcosx -cscxcotx?
simple iron
It's an exponential function and algebriac function
timid silo
where did cosx come from?
so the question is (sinx +cscx)^2 right
then we do 2sinx right
and sinx is cosx
so 2sinxcosx?
timid silo
@simple iron thanks
obtuse pebbleBOT
Available help channel!
lapis vortex
help please I just need to be helped with the steps
obtuse pebbleBOT
help please I just need to be helped with the steps
lapis vortex
<@&286206848099549185>
fierce lagoon
!15m
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
sick jewel
what do you want to find?
lapis vortex
the area
fierce lagoon
The area of a kite is half the product of the diagonals
sick jewel
then find the area of triangle AOD = triangle COD
fierce lagoon
So basically 1/2 • AC • BD
lapis vortex
so then 30 ?
sick jewel
30 is the area for triangle COD = AOD
sick jewel
Bruh don't just tell him the answe
sry
lapis vortex
it's ok
fierce lagoon
So basically 1/2 • AC • BD
@lapis vortex did you do what I told you to do
lapis vortex
I tried
fierce lagoon
What is AC
lapis vortex
12
fierce lagoon
What is BD
lapis vortex
12
fierce lagoon
So what is 1/2 • 12 • 12
manic mango
Proof that for every triangle that is true 1<cos(α)+cos(β)+cos(γ)<=3/2
obtuse pebbleBOT
Proof that for every triangle that is true 1<cos(α)+cos(β)+cos(γ)<=3/2
manic mango
I tried doing it and cant figure out how to
obtuse pebbleBOT
@manic mango Has your question been resolved?
shadow lava
obtuse pebbleBOT
shadow lava
something is not right here, when I plug in x to the original equation I get different answers for both sides
dark stirrup
,w (-2ln(2)-7ln(3))/(2ln(2)-ln(3))
warm shaleBOT
kind hawk
should be $\frac{-2\ln2-7\ln3}{2\ln2-\ln3}$ instead of $-\frac{2\ln2-7\ln3}{2\ln2-\ln3}$
warm shaleBOT
Denascite
shadow lava
**Denascite**
i don't see the difference?
kind hawk
the location of the minus
dark stirrup
$-(a-b)=-a+b \ne -a-b$
warm shaleBOT
SWR
shadow lava
ya
OK I need to remember that
I can't just pull first minus sign from numerator like that and put it in front of a rational
well, sometimes I can lol
like -7/3 is -(7/3)
but only because it's monomial on top and bottom?
with polynomial it's different?
or even -7/(x+3) I don't know if I could also write it -(7/x+3)?
is it implied distribution to numerator or denominator?
trim portal
or even -7/(x+3) I don't know if I could also write it -(7/x+3)?
you can write that
warm shaleBOT
MathIsAlwaysRight
trim portal
is also equal to that
shadow lava
so what's the rule when i'm allowed to move the - sign at beginning of numerator or denominator to be in front of the fraction?
because sometimes it works, sometimes it doesn't
in my case above it doesn't
trim portal
as long as it's in front of WHOLE the numerator in parenthesis or WHOLE the denominator in parenthesis, you can
shadow lava
oh I see, I see
thank you
that makes better sense
so 7/(-x+3) would not work
that's like saying 7/(3-x)
so brackets are super important for fractions
can make a big difference, with or without
i always thought brackets were implied with fractions
like they are always there
invisible
trim portal
what you could do is 7/(3-x)=7/-(x-3)=-7/(x-3)
shadow lava
like a jail for the entire numerator and denominator
shadow lava
what you could do is 7/(3-x)=7/-(x-3)=-7/(x-3)
oh..
so brackets are optional for fractions, adding them around the entire numerator, or entire denominator doesn't make any difference
because it's already implied?
it's like giving double brackets (())
trim portal
so brackets are optional for fractions, adding them around the entire numerator,...
if it's in text you should definitely add them
$\frac{x+1}{x+2}$
warm shaleBOT
MathIsAlwaysRight
shadow lava
if it's in text you should definitely add them
wdym by in text?
trim portal
wdym by in text?
If you write x+1/x+2 I am not sure if it's x+(1/x)+2 or x+(1/(x+2)) or whatever it is
trim portal
**MathIsAlwaysRight**
but when you use texit, you dont need to use parenthesis
shadow lava
ya
shadow lava
**MathIsAlwaysRight**
but when writing it like this, no need for brackets
trim portal
yeah, if you write it on paper you dont need to use parenthesis
shadow lava
you can just assume brackets are there with fractions. always and forever. the entire numerator is being divided by the entire denominator. we just don't show the brackets
when there is a divisor line
by default
but still important to use brackets where necessary
ty that helps me to understand what's really going on
do you think math could be easier to teach if we always used brackets for numerator and denominator? even in fraction form when writing it. or it would be worse?
trim portal
do you think math could be easier to teach if we always used brackets for numera...
I dont think it would be easier
shadow lava
you can just assume brackets are there with fractions. always and forever. the...
i think for a lot of new students maybe they don't understand this part
the complete implications of that, maybe
shadow lava
I dont think it would be easier
or do you mean more work to write it?
always with paranthesis
warm shaleBOT
MathIsAlwaysRight
trim portal
The parenthesis are just unnecessary I guess
shadow lava
that part yes, but signs could still be a tad bit confusing, as per the above example
trim portal
**MathIsAlwaysRight**
if it was possible with signs, it would imply that what I've written would be also true
I wouldnt complicate the notation too much
shadow lava
OK heheh, just curious if it could be any better for those starting out..
I think the big one everyone agrees on is sin^(-1). Bad bad bad.
Bad notation.
trim portal
This was confusing me too, but after few examples you get familiar with the notation
trim portal
I think the big one everyone agrees on is sin^(-1). Bad bad bad.
well it may be confusing, but it's not too bad
shadow lava
lol it doesn't mean 1/sin
shadow lava
lol, only 1 extra character
actually it's much easier to write arcsin than sin^(-1) in latex
sin^(-1) is now 2 characters longer than arcsin
trim portal
raising function to negative one is general notation for inverse, but I've never seen arc outside trig
the ^-1 later becomes a general notation for inverse
tardy epoch
lol it doesn't mean 1/sin
Understandable confusion. It's widely accepted that sin^(-1) is awful notation
tardy epoch
arcsin and csc is best and clear
trim portal
well i guess im in the 1% of people who dont mind it
tardy epoch
For function inverse and multiplicative inverse, respectively
shadow lava
well i guess im in the 1% of people who dont mind it
well you can thank this guy for it
https://en.wikipedia.org/wiki/John_Herschel
according to Google..
trim portal
I will keep using sin^(-1) together with asin
asin is acceptable, it's at least not so long
tardy epoch
Oh asin is also good
I'm afraid it'll be confused with a * sin for a constant a, but context usually rules that out
shadow lava
ya I would assume it as a * sin too, dunno if I've seen it written that way before
my instructors usually just write it as arcsin, so it's crystal clear
lol are mathematicians really this lazy to avoid writing "rc"?
arcsin is less confusing, no need to double check if "a" is a constant, if (^1) is an inverse, it just means arcsin
I dunno why John Herschel even invented this notation to begin with
like if there is anything you can do with sin^(-1) that you can't do with arcsin?
and now it's like a cancer in all of math, can't get rid of it
balmy steeple
I have a quick question:
obtuse pebbleBOT
I have a quick question:
balmy steeple
lets say that F(t, P(t)) = f(t,P(t))-g(P(t))
what would the partial derivative of F regarding t be?
When I do it, I think that I have to derive both f() and g() since they both depend on t. But in the solutions the result is simply f't(t, P(t) with no g() at all. Why is that?
Also the task states that P is defined "implicitly" through t, and sometimes it is written just P, sometimes P(t).
<@&286206848099549185>
hard anvil
<@&286206848099549185>
im gonna try help
balmy steeple
nice
balmy steeple
deriving I guess
hard anvil
lets say that F(t, P(t)) = f(t,P(t))-g(P(t))
ok that's the question
right?
ok leme try then
balmy steeple
the entire block yes. the last sentence is just additional info.
idle sandal
g() is just a constant so when differentiating with respect to t it’s zero
balmy steeple
g() is just a constant so when differentiating with respect to t it’s zero
but its g(P(t))? how is it a constant then?
idle sandal
Though it’s been ages since I took diff eq so could be wrong
balmy steeple
Though it’s been ages since I took diff eq so could be wrong
how is it a constant though?
<@&286206848099549185>
idle sandal
Sorry let me think a sec
balmy steeple
np
obtuse pebbleBOT
@balmy steeple Has your question been resolved?
obtuse pebbleBOT
@balmy steeple Has your question been resolved?
obtuse pebbleBOT
@balmy steeple Has your question been resolved?
vast linden
what would the partial derivative of F regarding t be?
if you do partial derivatives, then you assume that all the other variables are constant, and that’s why you only derive f’(t, P(t))
however you can also try to have a total derivative with respect to t, and it’s marked as $\frac{d}{dt}$ instead of $\frac{\partial}{\partial t}$
warm shaleBOT
rkky
vast linden
and then you’ll get f’t(t, P(t)) + f’P(t, P(t)) * P’(t) -g’(P(t)) * P’(t)
balmy steeple
alright thanks, let me ask a super quick follow up question though:
in the case of f(x,y) = 3x^2+5y where y is a function of x
the partial derivative regarding x would still be simply 6x then?
vast linden
exactly
balmy steeple
Okay thanks
I am testing something out rn to check whether I fully understood it, so I may write something in a few minutes again
I think I got it, thanks for clearing it up
.close
shadow lava
obtuse pebbleBOT
shadow lava
For #1 I always remember this (easy)
but for #2 I keep forgetting..
Anybody else the same way? Can you convert #2 to #1 if you forget?
sonic anchor
from 2 -> 1 take log_a for both sides
shadow lava
oh interesting..
wait, how would you take it for both sides?
log_a(a^(log_a(x)) = log_a(x)
log_a(x) = log_a(x)
sonic anchor
ok maybe its not exactly 2->1 but it atleast should convince you that 2 is true
which is the best way to remember something imo
shadow lava
it's confusing lol. I feel like I'm doing logarithm in reverse
reverse engineering it
for #2
nocturne minnow
Looking at 1 vs 2, you have log(a^x) vs log(x), and for log(x) you can't have negative numbers
shadow lava
not log, log_a(a^x)
nocturne minnow
Or were you not referring to the domain?
shadow lava
log by default is log_10
nocturne minnow
log by default is log_10
I know
shadow lava
but you said log(a^x)
nocturne minnow
I was not feeling to type out _a
shadow lava
wild swallow
in math, log is always natural log
shadow lava
who put X for this?
sonic anchor
but its just that they are inverses
shadow lava
in math, log is always natural log
???
static beacon
in math, log is always natural log
Not really
atomic agate
in math, log is always natural log
log is always base 2
wild swallow
yes really
static beacon
log is normally base 10
nocturne minnow
in math, log is always natural log
That's math software though, log on calculators defaults as log_10
static beacon
ln is natural log
shadow lava
log is base 10
wild swallow
not software
atomic agate
log is always base 2
log is binary by default
wild swallow
in general
wild swallow
log is used for natural
shadow lava
no.
static beacon
nope
nocturne minnow
not software
Then explain log vs ln on physical calcs
shadow lava
and log is used for base 10
atomic agate
Then explain log vs ln on physical calcs
its the same
static beacon
Casio calculators log = base 10
nocturne minnow
its the same
No it's not
shadow lava
yes
wild swallow
that's because its catered for non math people
static beacon
have yall not used a calculator?
shadow lava
Then explain log vs ln on physical calcs
they are literally different buttons on calculators
wild swallow
in pure math almost always log = natural log
static beacon
in pure math almost always log = natural log
no its not
wooden cipher
If you watch 3b1b's video on the triangle of power, he states that base 10, e, and 2 are used for logs in different contexts
sonic anchor
have yall not used a calculator?
,w log(e)
warm shaleBOT
wild swallow
the computer scientists want base 2
shadow lava
in pure math almost always log = natural log
oh now it's "almost always", we have backed down from original statement lol
nocturne minnow
And I'm referring to physical calculators, like ti calculators where it has log and ln, where log is log_10
static beacon
And I'm referring to physical calculators, like ti calculators where it has log ...
exactly
shadow lava
static beacon
same with casio
static beacon
real question is why u on light mode
shadow lava
real question is why u on light mode
just to get asked
wooden cipher
Bros pulling up receipts 💀💀
sonic anchor
i agree with snow, i have never seen anyone use log for log_10
inside math context
but a lot of people on here do so i just go with it
cause it doesnt matter
what you call something lol
as long as you are clear its what oyu mean
shadow lava
i agree with snow, i have never seen anyone use log for log_10
wtf
static beacon
i agree with snow, i have never seen anyone use log for log_10
what?
wild swallow
who cares about always vs almost always it's like there's gonna be a few use cases but it's rare
static beacon
That is such a lie
wooden cipher
Ive seen it for a precalc class and never again
nocturne minnow
i agree with snow, i have never seen anyone use log for log_10
Calculators
wild swallow
for the engineers
sonic anchor
i have never used a physical calculator
shadow lava
literally all calculators approved for math exams are log base 10
wooden cipher
ANYWAY
shadow lava
if you wanna change the base there is another button, log[]
wooden cipher
Why do you ask?
shadow lava
where you can use your own base
nocturne minnow
If you've used ti calcs then you know that calculators use log as log_10
sonic anchor
If you've used ti calcs then you know that calculators use log as log_10
but ive never used one
wild swallow
mathematicians don't design calculators
sonic anchor
also physical cals are not for pure mathematicians
static beacon
Casio fx 83-gtx standard GCSE and a level calculator : https://gyazo.com/46abb6ceaf3245465cc8e9de5598d5e1
nocturne minnow
but ive never used one
And that's the reason why
shadow lava
i never see anyone use a physical calc lol
lol i feel like i'm in the Twilight Zone
timid silo
potential bingo square unlocked!
"Argument about whether log is base e,2, or 10"!
static beacon
i never see anyone use a physical calc lol
you even been to class bro>
sonic anchor
you even been to class bro>
yes.
sonic anchor
i know what it looks like. i just never see anyone use it in a maths class
and ive never used it myself either
static beacon
so what do u use in exams?
shadow lava
lol i feel like i'm in the Twilight Zone
fading quest
its just notation, generally i find that log without any base has about the same chance of referring to natural log as base 10
nocturne minnow
i never see anyone use a physical calc lol
You're not millennial then
static beacon
:
fading quest
also physical calcs are incredibly common for exams
static beacon
Yea
fading quest
which i believe my calc also has log for base 10 and ln for natural base
nocturne minnow
That is an absolute lie. There is no way you are 23 and have not used a physical calc
static beacon
That is an absolute lie. There is no way you are 23 and have not used a physica...
He would've for exams
fading quest
if you dont do math related exams you probably never need a calculator
static beacon
hes cappin
fading quest
a physical one at least
shadow lava
static beacon
Maths is mandatory in my country and probably most others
until 16
in which the test u take u need a calculator
nocturne minnow
If you don't do any stem classes, then you'll never need a physical ti calc that stem uses, like casio or ti 84
shadow lava
https://tenor.com/view/travis-scott-floki-inu-excited-ready-for-battle-raid-gif-...
ask a question on Discord they said...
fading quest
If you don't do any stem classes, then you'll never need a physical ti calc that...
business also needs it
like accounting
timid silo
i love how this channel just turned into a big pissing match 
what even was the question
shadow lava
what even was the question <:xd:1071205372989288468>
I don't even remember anymore
sonic anchor
what even was the question <:xd:1071205372989288468>
how to remember that log_a and a^ are inverses
nocturne minnow
Business has their own economics related calc
fading quest
Business has their own economics related calc
quite sure they also use scientific calculators
sonic anchor
i used maple in highschool and in elementary, we used geogebra for graphs and no calculators
nocturne minnow
quite sure they also use scientific calculators
They have a ti ba 2 plus
static beacon
i used maple in highschool and in elementary, we used geogebra for graphs and no...
What about exams?
sonic anchor
What about exams?
highschool exams was maple and no calcs for elementary exams
fading quest
They have a ti ba 2 plus
i dont think its that specific. literally just google "calculator for economic exam" and plenty of scientific calculators show up
nocturne minnow
highschool exams was maple and no calcs for elementary exams
Your school trusted you that much to not roam on the inter webs for answers?
sonic anchor
maple is an application. wifi is turned off that dya
static beacon
highschool exams was maple and no calcs for elementary exams
I refuse to beleive in 23 years of living you've never used a physical calculator
fading quest
in my uni the only requirement is that its just a regular scientific calculator with no special functions. there are thousands of different calculators i can use. id reckon its the same for business
static beacon
in my uni the only requirement is that its just a regular scientific calculator ...
BRO THAT IS THE OPPOSITE TO MINE, only 2 are allowed
shadow lava
trig questions are a lot easier with calculator. i know the unit circle, but an approved exam calculator tells me and it's much faster
frosty spoke
never needed a calculator for an exam in any of the STEM classes I took
static beacon
never needed a calculator for an exam in any of the STEM classes I took
what
frosty spoke
except for one bullshit class in economics
fading quest
BRO THAT IS THE OPPOSITE TO MINE, only 2 are allowed
sounds like a murica moment
frosty spoke
my whole guideline was
if you needed a calculator with functions restricted that a laptop could provide
the class probably was a joke
shadow lava
static beacon
ah, well uk is basically the same
its stupid because in a level (exams end of highschool) we were allowed to have BETTER calculators
as in they have more functions
nocturne minnow
Anyways this has gone off the rails, peace out
shadow lava
Anyways this has gone off the rails, peace out
says the train conductor himself
static beacon
yea
sonic anchor
i will not correct my proffessor for example
static beacon
it means base 10
sonic anchor
when he uses log for natural log
and say pysical calc disagrees with youi
its moronic
mathj is more than this
fading quest
if i see log alone i will generally ask what base it is since its extraordinarily common for teachers to use log for base e
sonic anchor
stop getting hung up on thsi stuff
fading quest
which i honestly find kinda dumb, ln is slightly less effort and removes any potential confusion
shadow lava
if i see log alone i will generally ask what base it is since its extraordinaril...
why not write it ln if it's base e? it's one less character and professors usually love less work
fading quest
yeah thats what im saying, i would not write log ever for base e
static beacon
why not write it ln if it's base e? it's one less character and professors usua...
that is the question
fading quest
but a lot of people do
static beacon
but tbf
nocturne minnow
if i see log alone i will generally ask what base it is since its extraordinaril...
If I see log alone, I normally assume log_10 because apparently I'm one of the few people who uses a physical calc where it uses log as log_10 and ln as log_e so I'm used to that notation based on physical calcs
sonic anchor
i do 💀
static beacon
Most programs (non calcs) do take log as base e
sonic anchor
i like log better
fading quest
If I see log alone, I normally assume log_10 because apparently I'm one of the f...
i did until i joined this discord
and now ive seen so many log being base e
that i need to ask
static beacon
If I see log alone, I normally assume log_10 because apparently I'm one of the f...
i agree and so does 99% of the british population
fading quest
if people just stopped using log for base e then id always assume base 10. but thats just not the case
sonic anchor
i rarely see people use log with different than base e
maybe thats just why
i like log as base e
frosty spoke
yeah it looks too much like in
sonic anchor
yes log looks prettier
frosty spoke
I feel like you see log_10 a lot in things like engineering
but with things involving calculus, then it's log_e
sonic anchor
I feel like you see log_10 a lot in things like engineering
ye im pure math so maybe thats the disconnect
fading quest
guess it makes sense why im middle ground then. physics moment 
frosty spoke
log_2 is very popular in computer science
static beacon
but with things involving calculus, then it's log_e
so if you were asked to like integrate 1/x you'd say log(x)
warm shaleBOT
nocturne minnow
log_2 is very popular in computer science
If there was a duh emoji, I would have used it because base 2 is binary related
static beacon
fading quest
you can easily see why i would just ask what base it is instead of just assume its base 10. personally i dont see a reason to use log for natural since there is literally no downside and a slight upside (avoiding confusion) to using ln over it
sonic anchor
but its just a notational definition lol
notational definitions vary even from paper to paper
like how you type out vectors
frosty spoke
some notation is truly awful
nocturne minnow
Also a good chunk of the internet searches, I'm looking at, uses log as log_10
sonic anchor
you can easily see why i would just ask what base it is instead of just assume i...
you are 100% right
but i will still use log as base e liol
shadow lava
sonic anchor
i just like it more
also when you are speaking
i just say log
so i also typ elog
yknow?
static beacon
NAW THE CLOCKS WENT foward and now its 2 am
fading quest
i always say "el en" when referring to natural log. so i guess thats a slight reason to use "log" instead since its 1 syllable instead of 2
really micro managing the efficiency of a potential lecture there
nocturne minnow
I'm sticking to what I know and is used to and that's log is log_10 and ln is log_e, you guys do you
static beacon
i always say "el en" when referring to natural log. so i guess thats a slight re...
'lin' is what i say
sonic anchor
people only care on the internet anyways it seems
fading quest
people only care on the internet anyways it seems
and people who skip classes and get confused by notation
sonic anchor
did you actually get an answer to your question
shadow lava
no but I will close this now
static beacon
thanks for the super checkmark <@318024849333288960>
it was too cancel out all the x's
shadow lava
I gotta go the gym lol
static beacon
i gotta go to sleep#
shadow lava
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
untold mica
Hi. Doing disk and washer methods and not sure how to do the formula.
obtuse pebbleBOT
Hi. Doing disk and washer methods and not sure how to do the formula.
untold mica
The original equations are y=1/(1+x), y=0, x=0, x=3
timid silo
The original equations are y=1/(1+x), y=0, x=0, x=3
y = 0 is a flat line, so it's just [f(x)]^2
timid silo
Hi. Doing disk and washer methods and not sure how to do the formula.
you forgot the $\pi$
warm shaleBOT
hannibal
untold mica
Oops. Got it now
untold mica
But the circles are in terms of y, so to find the radius you need to use x
Input x, output y
Am I wrong?
obtuse pebbleBOT
@untold mica Has your question been resolved?
untold mica
<@&286206848099549185>
untold mica
Maybe?
spring marsh
Didn’t realize
river hare
spring marsh
We can tinder stand this stuff
spark field
obtuse pebbleBOT
obtuse pebbleBOT
spark field
1st one converges becuz cn is just constant
2nd series converges because its just a constant * a constant?
3rd doesnt because it alternates
same for 4th?
civic zealot
your justifications don't make sense
what do you mean it's a constant? or constant times a constant?
and when x = -4, the series is alternating and the series converges.
spark field
what do you mean it's a constant? or constant times a constant?
Cn is a constant
civic zealot
each term is constant, but the terms are not all the same...
spark field
each term is constant, but the terms are not all the same...
oh so how do we do this
its centered around
1.5
civic zealot
you know when $x=-4$ the series is convergent. So, necessarily, $\lim_{n\to\infty}c_n(-4)^n =0$. So $0\leq|c_n| <4^{-n}$
warm shaleBOT
Zybikron
spark field
you know when $x=-4$ the series is convergent. So, necessarily, $\lim_{n\to\inft...
but they also said 7
so would it be
-4<x<7
is it not that?
civic zealot
ah, true, so you can say something like $7^{-n}\leq |c_n| < 4^{-n}$
warm shaleBOT
Zybikron
spark field
ah, true, so you can say something like $7^{-n}\leq |c_n| < 4^{-n}$
where did the -n come from
@civic zealot
obtuse pebbleBOT
@spark field Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
https://i.imgur.com/qZO5QLE.png
tame relic
how does he get -55?
-350/-4 just gives me 87.5
cant wrap my head around it
oh my god
Im too tired
its okay bro sorry to waste your time
Just realized my error
latent walrus
no worries
obtuse pebbleBOT
tame relic
thanks again
obtuse pebbleBOT
Available help channel!
warm siren
<@&268886789983436800> why did my question chhanel turn to hidden?
obtuse pebbleBOT
<@&268886789983436800> why did my question chhanel turn to hidden?
idle thunder
<@&268886789983436800> why did my question chhanel turn to hidden?
it must have timed out
were you asking about the centroid question or something else?
warm siren
no something else