pi is 1/2 of the way around the circle
#help-0
ionic jewel
(where it says -1)
wait this is linear approximations
lemme find the relevent formula
same answer
in the case of sin it means they have the same height
but please look up linear approximation to learn more
it's not hard, it's just easier to explain with graphs and stuff so a webpage would be better than me
no, you should learn how linear approximations actually work and apply it to your problem
it's basically using the derivative at a point you know (x=2 in this case), and linearly extending that to guess and points that are very close (x = 2.001)
i learned it in calc 1
it's reasonable to know if you know derivatives and have a bit of critical thinking, the topic isn't complex
no
okay
I'm gonna call it theta
instead of x
does ur class use radians or degrees
radians obviously for this I'm dumb
anyways
since theta is in the first quadrant, you know $0\leq \theta \leq \frac\pi2$
ocean sealBOT
bunny
ionic jewel
do you agree with this so far?
not you
yours has no theta or pi
clyda please just look it up, i can't explain it as well as a good video or website
you agree?
okay
so now we have
we are doing pi minus theta
so
$\pi-0 \geq \pi-\theta \geq \pi-\frac\pi2$
which is
ocean sealBOT
bunny
ionic jewel
sure if you want
what?
do you not see what or not how it's not in the second quadrant?
yes that's the power rule for derivatives
yes that is good
check the inequalities direction
lol yw, hopefully that actually helped
pi minus theta is greater than or equal to pi/2
okay
so what i did
take the original inequality
with the 0 to pi/2
then you want it to be pi - theta
so you can multiple everything by negative 1
then add pi
but either way this is just a proof that it's right
it's not actually understanding
it's basically subtracting the angle from pi, If that makes sense
because we want it to be pi minus theta
each of the three terms
and that's why you have to flip the less than to greater thans
when you multiply inequalities by a negative number
brittle mantle
When y’all are done can I get help with smth pls 👩🏽🔬
ionic jewel
no not at all
brittle mantle
Wait wrong channel I think
ionic jewel
$0\leq \theta \leq \frac\pi2$
ocean sealBOT
bunny
ionic jewel
start with this one
then do what i said
it'll show that pi-theta is in the second quadrant
Ignorw the sin and cos for now
ionic jewel
When y’all are done can I get help with smth pls 👩🏽🔬
pick an empty channel
brittle mantle
What do I say there
brittle mantle
you post your questions
I have no math equations I need help learning smth
ocean sealBOT
TheMane3
ionic jewel
yes, but change the middle one to pi-theta, and simplify the rest, then you can see that (pi-theta) is in quadrant 2
i mean i guess it seems okay, but i wouldn't mention linear approximations unless you know how to do them
ocean sealBOT
TheMane3
ionic jewel
look at the last term
pi-pi/2 = pi/2
once you do that, do you agree that angles between pi/2 and pi are in the second quadrant?
i mean if you ever happen to need to prove it, you can do something like that
this worked specifically because you had theta and wanted pi-theta
but you don't really seem to understand why it works
here let me try an easier idea here
let's say you have a number
it's between 0 and 1 inclusive
lets call it x
what range of values could you get if you do 2-x?
what
why is 0.01 the smallest?
what about 0.001?
or 0.0000000000001
I've changed the problem to make it easier
x is now between 0 and 1 inclusive (could be 0 or 1)
now what is the range for 2-x
you what
2 - 0 = 0
would you like you rethink this
no not quite
what's the new range
not 0 to 1
yes fantastic
now let's say our x is between 0 and pi/2 (inclusive again)
what's the range of pi - x?
it's pi
pi is a number
you can do the same work as last time
why is this one so much harder?
well
<=, but yes
who cares
leave it in terms of pi
i don't care
ok
which is?
what's pi - pi/2?
okay
and pi-0 is pi
so the range is pi/2 to pi
right?
so the range is pi/2 to pi
wow this sounds an awful lot like the second quadrant
(it is)
that's why pi - x is in the second quadrant
ok
wait
what
that's a nonsensical statement
perhaps you mean to say (pi+x) is in the first quadrant, or x is in the first quadrant
no stop
sin(something) can't be in a quadrant
sin(something) evaluates to a number
the stuff you put inside the sin can be a quadrant
yes
sin(anything) isn't in a quadrant
uh
i don't think that's true
pi+x is in the third quadrant
pi - x is in the second
sin is positive for values in the second, but negative for values in the third
if x is first quadrant, all of those other ones are true, yes
would be sin(-x)
uhhhhh
well there's a few ways to prove it
but it should intuitively make sense if you can think about it on the unit circle
pi+x is third quadrant, x degrees away from the x-axis
-x is in the 4th quadrant, x degrees away from the x-axis
No but close
it's because the distance from pi+x to the x axis is the same as the length from -x to the x axis
remember sin is the y value, or height, or distance from the x axis
yes
yes
that is true
I'm not sure what that means so glad u got it urself lol
,w -sin(x) = sin(-x)
ocean sealBOT
ionic jewel
sin is an odd function so that's why that property works
my bad it's not strictly distance
the sign also matters
sin is positive in quadrant 2 remember
so it can't be equal to the same thing in quadrant 3
what we can say is that sin(pi+x) = - sin(pi-x)
yep
feel free to check both of those in wolfram
oh no
no no no
let's think about this for a second
where is 2pi?
yep
2pi = 0
so...
sin(2pi-x) = sin(-x)
yes
yep
bleak igloo
Is the discussion going on here should I ask in another channel
ionic jewel
signed distance to the y axis is right
ionic jewel
Is the discussion going on here should I ask in another channel
new channel
bleak igloo
ok
ionic jewel
yes, you can also think of it as the x value
(like cos(0) = 1 because it's the point (1,0) and 1 is the x value)
but continue
uhh
pi + x is in the third quadrant
-x is in the 4th quadrant
cos is positive in one of those and negative in the other, so not quite
hint: ||cos is positive in the 1st and 4th quadrants|| DONT CLICK IF YOU WANT TO FIGURE IT OUT URSELF
yeah ur right anyways tho
,w cos(pi+x) = cos(pi-x)
ocean sealBOT
ionic jewel
tangent is sin(x)/cos(x)
yea
uh huh
well
that's true but it's not the intended solution
find another one
bleak burrow
ionic jewel
those are both in the 4th quadrant
cos is positive in one other quadrant as well
yea
yes
okay but
that's still not the intended solution
despite being true
well let's think about it
what is sin(pi+x) equal to?
wait
this ain't gonna work out like this
okay scratch that
is sin positive or negative for pi+x?
okay
how about cos for pi+x
steel monolith
find the sum of the following APs 2,7,12.......,to 10 terms
ionic jewel
yes
so then for tangent
you have tan(pi +x) = negative/negative = positibe
so what other quadrant is tangent positive in?
hint:||it's where both sin and cos are positive||
yes
so tan(???)
,w tan(pi+x) = tan(x)
ocean sealBOT
ionic jewel
woah hold on
this ain't true
yes
no
that doesn't exist
you just care about the sign of tangent
yep
you want the other quadrant where tangent is negative
also wrong channel
hold the area near the message
if mobilw
on PC there's a drop-down on the right of the message
well idk what to tell u
just go find a new channel I'm working with mane
speaking of which, what's your answer mane
go ahead and check it with wolfram
ocean sealBOT
ionic jewel
go find a document of limit properties
marsh shard
Pleasee help me someone
austere elk
go find a document of limit properties
Can u give me a example of what the answer of a would be
Cuz I’m still kinda confused
austere elk
@alpine sable yeah thank you, i was overthinking it. It’s so easy and I was just thinking there was something else to it
stone scroll
Please help me know what the right answer is
My teacher said that my answer is wrong
stone scroll
I think 36
unborn kernel
but 360/5 divided by 1/2
gives 144
one calculator of mine shows 36 and the other 144
stone scroll
360/5 is 72
undone dock
Why times?
minor heath
yh but 360/5 divided by 1/2
god use your order of operations
unborn kernel
when you divide by faction
minor heath
(360/5)/2=36
undone dock
360/5 ÷ 2/1
=360/5 × 1/2
unborn kernel
my alevel calculator shows 144 and my gcse shows 36
unborn kernel
same
ocean sealBOT
minor heath
there
unborn kernel
then why wold my a level calculator show 144
stone scroll
Help hehehe
unborn kernel
because those kinds think of 360/(5/2)
oh i see thanks
minor heath
remember that y=f(x)
stone scroll
Oh I get it, it says relative not absolute
valid bone
Hey guys I have a question. f(x) has a domain of [-2,4]. What is the domain of f(x+3)
<@&286206848099549185>
shell widget
@valid bone f(x+3) means the function is shifted 3 units to the left.
So the domain will be shifted 3 units to the left.
valid bone
So would it be [-5,7]?
shell widget
No
valid bone
[-5, 1]?
shell widget
Yes
valid bone
Thank you
shell widget
np
ocean sealBOT
shell widget
the middle part?
noble crypt
well if you're talking about $\frac{(t+1)-2}{t+1}=1$ part then it's cause -1 can also be represented as +1 - 2
ocean sealBOT
わたし
noble crypt
the same way 3 can be represented as (5 - 2)
chilly panther
Yeah.... my head is so in algebra mode for some reason I saw that as -2(t+1) thank you 🙏🏻
noble crypt
no problem
plucky sun
I tegers
dry jay
How can i factor this expression fast without foiling all the terms?
minor heath
How can i factor this expression fast without foiling all the terms?
$x^2-y^2=(x-y)(x+y)$
ocean sealBOT
G3oG0dly
teal epoch
Can someone explain this. Like what is that sign?
The big sign? like the one between m=1 and 3?
vagrant rover
Yeah that one
teal epoch
Well that's sigma
It's usually used for summation notation
vagrant rover
What is summation notation?
wind bane
a convenient and condensed way of writing out the addition of many terms. for example, $1+2+3+\dots+n=\sum_{k=1}^nk$
ocean sealBOT
coycoy
teal epoch
What is summation notation?
In simple terms, it is the sum of a sequence
teal epoch
Do I substitute 1 in place of each m?
Since it starts at 1 and ends with 3, substitute all (integer) values that is within its range, and add them all up.
For this case, you only have to substitute 1, 2, and 3.
vagrant rover
oh so substitute 1,2,and 3 in place of M in (2m + 1)^m-1. And then add the three results together?
teal epoch
oh so substitute 1,2,and 3 in place of M in `(2m + 1)^m-1`. And then add the thr...
That's right.
teal epoch
One example how to do these things:
$\sum_{k=1}^3{2k}\implies 2(1)+2(2)+2(3)\implies2+4+6\implies12$
ocean sealBOT
Callaway
teal epoch
And when we substitute 1,2, and 3 we get a sequence, right?
no
in your case $(2m+1)^{(m-1)}$ is the sequence
vagrant rover
**Callaway**
Ahhh alright alright
ocean sealBOT
Callaway
vagrant rover
Oh, okay
So what if we have a sequence of numbers, such as 1,2,3,4,5 and we want to find the sum of the sequence? Are we forced to manually add each integer together or is there a faster way to do it using an equation? @teal epoch
teal epoch
So what if we have a sequence of numbers, such as `1,2,3,4,5` and we want to fin...
hmm.
well sometimes there some notation that has a faster way than doing it manually and sometimes there are no choices but to manually substitute it to the expression
for this case I don't think there's a faster way
teal epoch
So what if we have a sequence of numbers, such as `1,2,3,4,5` and we want to fin...
what do you mean sequence of numbers such as 1, 2, 3, 4, 5?
is it 1+2+3+4+5 or the numbers you're going to substitute like this?
$\sum_{k=1}^5{2k+1}$
ocean sealBOT
Callaway
vagrant rover
what do you mean sequence of numbers such as 1, 2, 3, 4, 5?
is it 1+2+3+4+5 or t...
2,4,6,8,10
A sequence
not for substitution @teal epoch
teal epoch
A sequence
oh i see
teal epoch
hmm.
well sometimes there some notation that has a faster way than doing it man...
welp uh same response ig
vagrant rover
hmm.
well sometimes there some notation that has a faster way than doing it man...
ah alright, tysm
umbral orchid
Let G be a group of order 315 which has a normal Sylow 3-subgroup. Prove that Z(G) contains a Sylow 3-subgroup of G and deduce that G is Abelian
is the first condition necessary here?
The Sylow 3-subgroup has order 9 so it must be Abelian and be a subgroup of its centralizer
severe hearth
Can someone please help me with the transition matrix
umbral orchid
mfw I forgot everything after passing LTAM😆
ember ether
hello i have a question about fuctions
so when you draw a function
you need x to get f(x) the image
but if x is a none decimal number
how are you going to know where x is
like if x = 0,9999999999999999999999....
glass lichen
well that's x=1
glass lichen
$0.\overline{9}=1$
ocean sealBOT
Mosh
glass lichen
but if you mean something like x=sqrt(2), then just eyeball it w/ a decimal approximation
ember ether
and if it's a number like Pi how are you gonna knw now
glass lichen
pi ~ 3.14
ember ether
yes
glass lichen
so put it just after the x=3 mark..
ember ether
then tracing your function won't be exact right ?
glass lichen
nope
glass lichen
unless it's trig in the case of pi 
ember ether
yeah thanks
i like math a lot but i ask to much questions because i wanna know everything
so we just trace what about look like the function so we can study it
sleek elbow
i like math a lot but i ask to much questions because i wanna know everything
asking questions is op 💯
glass lichen
$0.\overline{9}=x \ 9.\overline{9}=10x \ 9+x=10x \ x=1$
ember ether
asking questions is op 💯
i swear my brain is going to kill it self
ocean sealBOT
Mosh
ember ether
thanks
sleek elbow
Thats confusing @glass lichen , how can adding 9's to the end ever make it to 1? that seems very weird
ember ether
idk
glass lichen
Yeah math isnt suppose to be intuitive
ember ether
i guess it's a thing called uncertainty
glass lichen
no
ember ether
oh
sleek elbow
How is it not impossible to get to 1? If I imagine myself writing 9's at the end forever, how will I get to 1
ember ether
not nine
but
0,999999999.....
to infinity
you are just getting closer to one
but not touching it
sleek elbow
yes
glass lichen
yes, a decimal expansion with infinitely many 9's = 1
ember ether
so saying its equal to one its kinda of confusing
sleek elbow
is it just defined as such?
sleek elbow
Cause it doesnt make sense that if I write infinite decimal 9's I will get to 1
ember ether
yeah because a number represents a certain amount of stuff
glass lichen
yeah it doesnt make sense, but by the constructions of R they are the same number
sleek elbow
yeah it doesnt make sense, but by the constructions of R they are the same numbe...
R?
ember ether
Real numbers
sleek elbow
oh ye
ember ether
and it's just gets to me
like when you are tracing a function you need those two axes
x and y
glass lichen
graphing*
ember ether
my bad i study math in french so it's kinda hard to tell what i'm talking about in english
crisp sleet
my bad i study math in french so it's kinda hard to tell what i'm talking about ...
samee lol
ember ether
uh so
crisp sleet
I study math in french too
ember ether
oh
crisp sleet
in my country
ember ether
i'm not french too
ember ether
me too
crisp sleet
I'm from morocco
ember ether
me too
crisp sleet
wait fr?
ember ether
yeah
sleek elbow
2x -3 = 1/2 * (x/3)
flat tundra
Cause it doesnt make sense that if I write infinite decimal 9's I will get to 1
Maybe it may seem counterintuitive, but that's because we can't actually comprehend infinity, but it makes sense that if something goes closer and closer to 1 for infinity it equals to 1 itself. It's counterintuitive because infinity doesn't have an end from our point of view , but asking what does 0.99999... equals to , is like asking what it equals to with a "complete" infinity of 9s , so it actually becomes intuitive that it is 1
sleek elbow
Maybe it may seem counterintuitive, but that's because we can't actually compreh...
it would make sense that it gets infinitely closer, but how is that 1
sullen nova
help
The histogram on the left shows the number of hours students in a British Literature class read last week, rounded to the nearest hour. Which of the following statements offers the best description of the median number of hours students in the class read last week?
flat tundra
it would make sense that it gets infinitely closer, but how is that 1
If we see math as counterintuitive it is because it can rappresent things that we would never understand with our own logic , as i said it is 1 because we consider infinity as a whole , so """"after""""" infinity, or when infinity is reached, it equals to 1
sleek elbow
If we see math as counterintuitive it is because it can rappresent things that w...
I see where that comes from, but its really counterintuitive
@sullen nova it tells you that b is right, no?
noble sinew
the easiest way to convince yourself imo is what would 1-0.999.... be equal to if not 0
and if you agree it is equal to 0 then they are in fact the same number
sleek elbow
the easiest way to convince yourself imo is what would 1-0.999.... be equal to i...
0.00...01 I guess
noble sinew
you can't have inf 0's then something after
sullen nova
<@!267283055520120832> it tells you that b is right, no?
eyah
noble sinew
so 0.0...1 doesn't make sense
sleek elbow
hmmm ye
flat tundra
0.00...01 I guess
The problem is that you are treating infinity as something finite
sleek elbow
thats true didnt think of that
vale ridge
three times one number added to another is 14. Twice the first number, minus the other number is 1. What are the numbers?
options are: 9 and 5, 10 and 4, 8 and 6, 3 and 5
noble sinew
it is just count how many is in each interval, then use definition of median
noble sinew
it is just count how many is in each interval, then use definition of median
namely for odd amount of observations the median is the (n+1)/2th number
sullen nova
how to do
noble sinew
20 is between 0-4
add them all together
then calculate (n+1)/2
and see which interval that corresponds to
flat tundra
three times one number added to another is 14. Twice the first number, minus the...
3 and 5
noble sinew
you tell me
noble sinew
if first 20 are in 0-4
then next 22 is in 5-9
so clearly 32 is in the interval 5-9
{21,22,23,...,42} is in 5-9
flat tundra
three times one number added to another is 14. Twice the first number, minus the...
Because 3x+y=14
2x-y =1 , now to eliminate the y terms you multiplicate the second one by -1 , and you get
3x+y=14
-2x+y=-1
You subtract the second equation from the first and you get that x=3
sullen nova
OMG
vale ridge
do parallel lines have the same x-intercept
glass lichen
do parallel lines have the same x-intercept
no
coral cosmos
do parallel lines have the same x-intercept
no
vale ridge
okay thanks
coral cosmos
well because suppose y = log N (to the base b)
which signifies b^y = N
so now if you take b any negative integer for example -2, and you take y as 1/2
you get sqrt(-2) which leads us to complex numbers and then it becomes to difficult to comprehend [giving wierd irrational values]
vale wigeon
because logs to base 1 are nonsensical, as are logs to bases that are zero or negative
glass lichen
yes, exponentials with base 1 or negatives dont make sense as exponentials
coral cosmos
I mean I know one would argue that (-2)^3 = 8 and it does makes sense I agree... but then you can't calculate things like sqrt(-2) etc. which leads to many many exceptions, so we avoid the negative values along with 1 and 0 altogether
glass lichen
it's 4/9
noble crypt
you can always approximate a recurring decimal to a fraction
ember ether
well yeah
glass lichen
but no, .4444.... is just that, 4/9
noble crypt
yeah that'll be the case for any recurring non terminating decimal number
it'll always have a fraction
thin wolf
i made 1 + 2cosx = 0 (x-axis) to show x-cords for A is 2pi/3 already, how do i find x-coordinate for B? Is it by cosine graph or can i use cos x = cos (360 - x)
rigid smelt
cos(x)=-1/2 has many many solutions, but there are two general solutions
you can find B from the other general solution
smoky relic
6 × 14/8
Am i could simplify 6 and 8 become 3 and 4?
If yes, why?
rigid smelt
and well you can use the identity that cos(x)=cos(2pi-x) but it might not give you B
rigid smelt
6 × 14/8
Am i could simplify 6 and 8 become 3 and 4?
If yes, why?
channel is busy and yes, because 6 and 8 both share a factor of 2
smoky relic
channel is busy and yes, because 6 and 8 both share a factor of 2
And i Don't need to change 14 become 7 that have factor of 2?
rigid smelt
lets move to another channel
smoky relic
Okay
thin wolf
and well you can use the identity that cos(x)=cos(2pi-x) but it might not give y...
sry for ping 🙏 but whats the other general solution? I solved with cos(2pi-x) and i got the answer shown on the paper
rigid smelt
cos(x)=a for -1<=a<=1 have two sets of solutions:
x=a + 2kpi
or
x=-a + 2kpi
for integers k
vague coral
cos(x)=a for -1<=a<=1 have two sets of solutions:
x=a + 2kpi
or
x=-a + 2kpi
for...
wow wow nope
rigid smelt
?
vague coral
cos(x) = y (-1<= y <= 1) implies there exists -pi< a < pi such as : cos(x) = cos(a) = y and then x = a + 2kpi or x= -a + 2kpi for k integers
rigid smelt
oh right, i forgot the arccos(a)
noble crypt
it's factorial
6! factorial means you need to multiply all natural numbers till 6
so 6! means 1 * 2 * 3 * 4 * 5 * 6
vagrant rover
got you
vale sapphire
ehh
that's not the biggest problem
if 0 were included, the factorial would be a dull function
noble crypt
lol yeah
vale sapphire
always being equal to 0
noble crypt
it would always result in 0
vale sapphire
for the record here the natural numbers include 0
noble crypt
wdym
vagrant rover
How do you evaluate that
noble crypt
Here, as it's taught, ℕ = {0,1,2,3,...}
wow ok
vagrant rover
for the record here the natural numbers include 0
Yeah on google it says sometimes natural numbers include 0
ancient creek
that's from the topic of combinatorics, you read it as "8 choose 6". Here is the formula:
noble crypt
then why are whole numbers there
vale ridge
can someone help me for my last question
vale sapphire
If we want to exclude it we write ℕ*
vagrant rover
that's from the topic of combinatorics, you read it as "8 choose 6". Here is the...
what does choose mean here?
ancient creek
noble crypt
yeah see @vagrant rover here there are ! marks which means factorial
vagrant rover
ahh alright
vagrant rover
so 8 substituted for n and 6 for k?
ancient creek
what does choose mean here?
It's quite a hard topic to explain, I would suggest watching these videos: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:combinations/v/introduction-to-combinations
vale sapphire
Horrible formula alert!!! Jokes aside, this doesn't explain what this is
vagrant rover
ty
vale sapphire
"n choose k" is the number of ways to pick k things from a set with n elements
ancient creek
so 8 substituted for n and 6 for k?
yea
vale sapphire
Where you just care about the elements and not their order
vagrant rover
Where you just care about the elements and not their order
oh
hazy dome
?
Use your intuition and common sense by looking at the time stamps of the most recent messages
vale ridge
mb
vagrant rover
What do you mean the number of ways to pick? @vale sapphire
You knw what, I'll just watch the vid
Watched the video, makes sense now. Thanks guys!
valid bone
Is there a way to rewrite absolute value x
hazy dome
Is there a way to rewrite absolute value x
Piecewise
noble crypt
,rccw
ocean sealBOT
valid bone
No
hazy dome
It looks like this
valid bone
-(x) and x for absolute value x?
valid bone
So I should rewrite this equation as piecewise
hazy dome
Absolutely
Because imma tell you, in Calculus, absolute value is SO ANNOYING
We just want piecewise to make everything easier
I don’t understand where this +1 is coming from
It’s just x and -x, like you said
valid bone
Yes
vagrant rover
Would the third term here be 21a^5 b^2 ?
shrewd otter
Would the third term here be `21a^5 b^2` ?
Yes.
vagrant rover
ty
so the coefficent of the third term is 21 and the coefficient of the second term is -7, right? @shrewd otter
shrewd otter
I'm not sure. It depends on whether the binomial is a sum or difference.
I guess it's true since you can express both as a sum.
vagrant rover
Okay thanks 😄
coral cosmos
hey can someone explain this to me?****
Take (3x - 2)^4 common
Which gives
(3x-2)^4 [ 4(3x-2) + 60x ]
Now the rest is easy to figure out, I suppose
glass lichen
common factor
coral cosmos
Yea
coral cosmos
oh wait i think im getting it now
I'll give you an example, to make things easier
5 + 10 = 15
Now take 5 common, it becomes
5(1+2) = 15
rustic mango
yup i see now
where i live they dont use perfect english so ive never used the actual term "common"
coral cosmos
Ooh I see
alpine sable
glossy tendon
I think you can use this rule
sage jacinth
actually you can just do this
glossy tendon
oh wait b^(logb(x)) = x right
sage jacinth
$x^{\textmd{log}_{x}(n)} = n$
ocean sealBOT
(バカ) baka
alpine sable
My friend ane me both couldn't solve this, we are ||morons||
sage jacinth
i got the answer with that rule
glossy tendon
My friend ane me both couldn't solve this, we are ||morons||
I mean, the thing @ (バカ) baka sent is not obvious if you dont know that
alpine sable
Still confused
glossy tendon
$10^{\log_{10} 8x-3} = 8x-3$
ocean sealBOT
robin
glossy tendon
also note that $log_e(x) = ln(x)$
ocean sealBOT
robin
minor heath
first, factor 6x-49
lone wraith
How tho
minor heath
$x^2-y^2=(x+y)(x-y)$
ocean sealBOT
G3oG0dly
lone wraith
What do i do next?
ocean sealBOT
G3oG0dly
lone wraith
without touching 6?
ember ether
ok
lone wraith
I got 7root(6x) - 12/3 = 6
minor heath
I got 7root(6x) - 12/3 = 6
um
lone wraith
Did i mess up some where?
ocean sealBOT
G3oG0dly
lone wraith
ye
minor heath
multiply both sides by 3
lone wraith
why?
minor heath
to get rid of the denominator
lone wraith
oo
wait i think i found where i messed in previous step
i think i got it
Now if i square both sides i can get 6
minor heath
wait whats the equation you are now on?
minor heath
yea
lone wraith
Thanks
minor heath
i guess, even tho you made me skip more than half of the steps
lone wraith
i guess, even tho you made me skip more than half of the steps
haha i would fail without u
oblique pulsar
Hi I have a quick question is there any one that made a multi-use conversion and scale equation? I want to know if I just spent about 2 hours of my life creating a easier method or just stumbled into a worse / equal version of one that is already available.
here are the equations made in notepad
alpine sable
If you spent only 2 hours of your life most likely you did nothing significant
oblique pulsar
I am not saying it is best of the best. I know it won't change much maybe stream line something but nothing else.
vagrant rover
(2a + 1)13
This has 14 terms, right?
slender thorn
is my answer correct?
tawny condor
so what was it
slate agate
Seemed legit to me
alpine sable
nobody would randomly give out nitro that expires in 361 hrs? I mean people could but thats like hella rare
tawny condor
I clicked it and it brought me to the discord nitro place
alpine sable
and nitro gifts usually have a lifetime of 48 hrs
slate agate
Anyways, can someone explain this? Wouldn't 5/3 make the fraction bigger?
glass lichen
Anyways, can someone explain this? Wouldn't 5/3 make the fraction bigger?
it would
the values in the sequence get bigger
vague coral
The best you can do is to see for x = 1
alpine sable
The best you can do is to see for x = 1
for x=1 it will be f(1)+f(0)=6
glossy tendon
$$
\begin{align*}
\frac{\frac{x-1}{x}-1}{\frac{x-1}{x}} &= \frac{1}{1-x} \
\frac{\frac{1}{1-x}-1}{\frac{1}{1-x}} &= x \
\end{align*}
$$
ocean sealBOT
robin
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
glossy tendon
not sure if anything useful...
teal epoch
How do I solve this?
this may not be helpful but I think you should determine what its highest degree of this function
probably it makes things easier
vague coral
this equation is tricky for real
alpine sable
hmm
strong furnace
consider this 1/(1-x)=x/(x-1)+1
alpine sable
Ah, my bad, I did my calculations wrong
alpine sable
This guy got you ^
strong furnace
inverse function
f(x)+g(x)=1
x+f(g(x))=2x
this does not solve anything yet
but might be a step
I am just thinking out loud here
vague coral
since f and g are inverse, you can use that to find a function that respects the equation
strong furnace
there's no way to use that and avoid 1/x so its still useless
alpine sable
so we just need to sub x with x-1/x
hollow kite
gilded kiln
Is this channel being used?
vague coral
yes
alpine sable
Is this channel being used?
ye
hollow kite
a
alpine sable
<@&268886789983436800>
tame falcon
@terse oracle Do you have anything meaningful to ask/contribute?
strong furnace
x = h(x)
(x-1)/x= d(x)
f(d(x))=x
f(x)+g(d(x))=1
g(x)+d(x)=1
why am I overcomplicating this lol
1/(1-x) was inerse
vague coral
xd
strong furnace
but we got 1/x
but if we take the linear
x
we get x+1-1/x
which cancels out the 1/x and gives us a linear function
the problem after taking the inverse turned into a linear functional equation
and we are still missing 2 constant terms
so x+1/x+1/(1-x)+1 should suffice
alpine sable
not sure if this is where I should be asking this question but, any idea what software is used to draw these?
I want to embed such graphs in my latex document
strong furnace
@alpine sable #latex-help
alpine sable
Thank you and sorry for the inconvenience
warped phoenix
can someone help walk me through this?
restive glacier
sorry
spring harbor
hm?
warped phoenix
well
glass lichen
yeah
warped phoenix
so how would 3pi or 4pi be possible
warped phoenix
oh wait is 3pi = 2pi and 4pi = 2pi?
glass lichen
no
spring harbor
no
glass lichen
clearly not
warped phoenix
but it's just another rotation
glass lichen
0 and 2pi are coterminal angles
pi and 2pi likewise
$\theta +2\pi n, n\in\mathbb{Z}$ will be coterminal with $\theta $
ocean sealBOT
Mosh
glass lichen
no
warped phoenix
😦
glass lichen
cause a full rotation isnt pi
warped phoenix
a full rotation is 2pi
glass lichen
yes
glass lichen
yes..
warped phoenix
and 4pi would be what i drew 3pi as
glass lichen
yes
alpine sable
Hello Guys. How can I resolve a fractional equation?
glass lichen
Hello Guys. How can I resolve a fractional equation?
in use clearly
warped phoenix
Hello Guys. How can I resolve a fractional equation?
channel in use
ok so they said to sketch it on the interval, -pi, 4pi
so i get why its sectioned off there
but what do they mean by "partition the interval 0, 2pi into 4 equal parts?
glass lichen
split it into 4 equal parts
alpine sable
No, in the next year, we need this again, but I forgetten this, how I make this.
warped phoenix
No, in the next year, we need this again, but I forgetten this, how I make this.
...?
glass lichen
No, in the next year, we need this again, but I forgetten this, how I make this.
didnt ask
channel is still in use.
warped phoenix
Why, what's the matter?
dude read #❓how-to-get-help
we're using this channel
you need to move to an empty one
alpine sable
Oh, now I unterstand. Sorry, my mistake.
warped phoenix
Oh, now I unterstand. Sorry, my mistake.
no worries
warped phoenix
split it into 4 equal parts
ok so i see the interval in question
how do i...split it
glass lichen
into 4 equal parts
glass lichen
sure if you feel the need to physically partition
warped phoenix
(pi/2, 0)
(pi, -3)
(3pi/2, 0)
glass lichen
but the important values in graphing sines and cosines are the multiples of pi/2
warped phoenix
(pi/2, 0)
(pi, -3)
(3pi/2, 0)
that's cut into four parts right
glass lichen
3
warped phoenix
since that's where the points are labeled
oh
well i could use either 0, 3 or 2pi, 3 for my fourth right?
since it's on the period
i think thats the right term
period
glass lichen
yes..
shell heron
hello
glass lichen
@shell heron dont be a pain in the ass.
warped phoenix
LOL
glass lichen
There is no need for reaction spam, find something productive to do with your life.
warped phoenix
:0
glass lichen
Im clearly helping Mane, thought you were reading.
warped phoenix
anyway, i see then, the reason we find 5 points is to plug the x value into that little table
shell heron
say what
glass lichen
yes
warped phoenix
which finds us our y value??? helping us complete the graph???? :000000
glass lichen
yes
warped phoenix
YAY
glass lichen
since then you can just repeat the shape
rigid ocean
How would you move the y's to the left? Would it just be -3y+y/2^2 = -x+1 ?
I want to move the y's to the left because they want you to put it in a(x-h)^2+k form
scenic flame
is this free?
rigid ocean
What
alpine sable
How would you move the y's to the left? Would it just be -3y+y/2^2 = -x+1 ?
So, what I decided to try and do was complete the square while y is still on the right side. I believe they want you to complete the square while y is in the quadratic, not x.
rigid ocean
So, what I decided to try and do was complete the square while *y* is still on t...
oh
alpine sable
"Complete the square on the right side"
Obviously this is an inverse equation considering x and y are switched. If you attempted to get x alone, it would be impossible to complete the square
Try completing the square with y instead of x
rigid ocean
<#486841085210132490> is available
wet frigate
quick question
does this mean tat the output of Q should have the same shape as A
or same number of components basiclly
vagrant rover
Use the following data set to answer questions
14, 12, 12, 16, 10, 16, 10, 12, 14, 12, 12, 16, 16, 10, 12, 16
What is the mean rounded to the nearest tenth?
Can someone help me with this?
glossy tendon
do you know how to get the mean/average?
vagrant rover
No
glossy tendon
(sum of all the data)/(number of data)
vagrant rover
Ah okay, and when do I have to order it?
Like order the data?
From least to greatest
glossy tendon
To find the median or something?
yeah it is need for the median
but for getting the mode it is optional, but it is easier to get it if it is ordered
vagrant rover
And rounding to the nearest tenth is would make 13.125 become 13.1?
@glossy tendon
vagrant rover
ty!
😄
10, 10, 10, 12, 12, 12, 12, 12, 12, 14, 14, 16, 16, 16, 16, 16
Would 12 be the median?
sleek elbow
Would 12 be the median?
I think so
vagrant rover
{5, 7, 8, 4, 5, 6, 3, 8, 2, 1, 0, 6, 8, 9, 4, 0}
And how do I find the interquartile range of the above data?
sleek elbow
no idea what "interquartile range" is, sorry. I would consider googling, but I have no idea how complicated or simple it is so do whatever you think fits @vagrant rover
vagrant rover
Okay thank you : D
sleek elbow
You're welcome : ) @vagrant rover
sleek elbow
yup khanacadeemy always good 🙏
fair sentinel
i recently had a maths exam wanted to check if one of may answers was correct
im only in year nine so it should be easy
red phoenix
What are you trying to work out here?
fair sentinel
perimeter of the square
red phoenix
You rounded, but it looks good
fair sentinel
thanks you worked that out fast!
red phoenix
np 🙂
vagrant rover
Can someone help me with this? What population are they talking about, but most importantly what is a standard deviation of the mean mean?
red phoenix
It means how many scores are within (mean + or - one standard deviation)
vagrant rover
It means how many scores are within (mean + or - one standard deviation)
But what is a standard deviation?
vagrant rover
oh
warped phoenix
hey guys
whats the name of that one math concept
i hear the word but idk how to spell it because writing it out gives me no results on google
i hear "conn exceptions" or "connexections" or something like that
it has to do with directrix and focus if that helps?
wooden harness
what is 1.5+y2
y=6
the y2 is y to the second power
obtuse root
37.5?
vagrant rover
what is 1.5+y2
y=6
the y2 is y to the second power
y^2 is how you write y squared
wooden harness
alr
vagrant rover
^ means to the power of
fair sentinel
$1.5+y^2$
ocean sealBOT
beanz
warped phoenix
Hey guys how would I simplify "sin $x$ tan $x$ + cos $x$"
vernal dragon
warped phoenix
wait
why did you do cos^2(x)/cos(x) and not just cancel out cos(x) from the numerator and denominator? @vernal dragon
oh wait you're not multiplying all the terms
vernal dragon
ok
warped phoenix
how does cos(x) + cos(x) equal cos(x)?
glass lichen
how does cos(x) + cos(x) equal cos(x)?
adding fractions..
vernal dragon
yea adding fractions
glass lichen
you dont add the denominators
warped phoenix
wait how does $\frac{\sin ^2\left(x\right)+\cos ^2\left(x\right)}{\cos \left(x\right)}=\frac{1}{\cos \left(x\right)}$
ocean sealBOT
TheMane3
warped phoenix
moreover how does sin^2(x) + cos^2(x) = 1?
fair sentinel
$ sin^2(x) + cos^2(x) = 1$
warped phoenix
you added a space
ocean sealBOT
beanz
fair sentinel
we don't know what x equals so we can possibly have an answer without x right?
vague coral
how does that equal 1
We can prove it by using Pythagorean theorem
alpine sable
Well yes
But its just like every other Diophantine equation, plus Ig you can construct a right-angled triangle based off of the pythagorean theorem
here's a proof using a right angled triangle and the trigonometric ratios
warped phoenix
We can prove it by using Pythagorean theorem
sure...so sin^2 + cos^2 = 1^2
then what
amber urchin
sure...so sin^2 + cos^2 = 1^2
Damn, that is correct but looks wrong
warped phoenix
?
clear chasm
guys, im in an argument with someone
nova shard
are there any possible solutions for a and b?
warped phoenix
are there any possible solutions for a and b?
channel in use
sleek elbow
guys, im in an argument with someone
ok
nova shard
channel in use
ok
clear chasm
whats, a^2 + b^2
warped phoenix
whats, a^2 + b^2
channel in use, delete your message and crosspost elsewhere please
sleek elbow
whats, a^2 + b^2
a^2 + b^2 is a^2 + b^2, also dont post here
vague coral
sure...so sin^2 + cos^2 = 1^2
if you consider the unit circle, take the sinus and cosinus of an angle x, you will have a right triangle
it's the easiest proof
vague coral
only in the unit circle, since sinx and cos x are coordinates
vague coral
hell no
warped phoenix
😭
vague coral
sin²x + cos²x =1
bleak vapor
