Available help channel!
#help-19
odd edgeBOT
Available help channel!
prime root
odd edgeBOT
spare hornet
can you flip it
prime root
can you flip it
i flipped it
prime root
ok so you have y = -1/2 x + 4
yes
prime root
multiply everything by 2
do we do that to get rid of the fraction?
runic swift
yes
jolly latch
In this question where is distance for the centre mass?
jolly latch
<@&286206848099549185>
zinc glacier
!status
odd edgeBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@jolly latch Has your question been resolved?
odd edgeBOT
@jolly latch Has your question been resolved?
tough galleon
!status
odd edgeBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
scenic shore
Have a question about continuous probability distributions
scenic shore
So lets say I have 2 continuous r.v.s, $A$, $B$ and I combine them to produce random variable $C = mA + nB$ for constants m and n. Now how would I express the cdf $P(A \leq a | C = c)$?
clever fjordBOT
Methylfluorophosphonylcholine
scenic shore
I can think of a way to do this easily in the case of discrete variables because I can use Bayes rule to break it up into $P(A = a | C = c) = P(A=a, C=c) / P(C = c)$ and from there I can just consider the discrete cases where A and B take on different values to satisfy C=c
clever fjordBOT
Methylfluorophosphonylcholine
scenic shore
But the same thing is difficult for me to see with continuous r.v.s
odd edgeBOT
@scenic shore Has your question been resolved?
obtuse roost
I am trying to figure out why:
odd edgeBOT
I am trying to figure out why:
obtuse roost
for c)
why is it a bijection
I thought that:
- It had to have unique pairs ex. 2^3 and -2^3 both result in 8 so I thought that meant it could not be injective
and if it cant be one to one than it cannot be bijective?
yet I find this
and I have abosoluetly no idea how they even did any of that
odd edgeBOT
@obtuse roost Has your question been resolved?
boreal thistle
1) It had to have unique pairs ex. 2^3 and -2^3 both result in 8 so I thought th...
2^3 = 8
(-2)^3 = -8
obtuse roost
... did my brain just do that
boreal thistle
happens
obtuse roost
thankyou
odd edgeBOT
Image
2/3 * n * sqrt(n) + sqrt(n + 1)
autumn turtle
.close
mystic saffron
<@&268886789983436800>
odd edgeBOT
<@&268886789983436800>
fresh shard
Please DM modmail if you have a question for mods
And not at all for math questions
Read #❓how-to-get-help
wooden python
<@&268886789983436800>
it is not moderators' job to help you with math.
you're thinking of Helpers,
but even then you have to post your question first.
odd edgeBOT
@mystic saffron Has your question been resolved?
smoky marten
can anyone
odd edgeBOT
can anyone
smoky marten
shoot any help tryna dissect this problem
currently I am trying to see what the algorithm does
im super new with graphs
wooden python
your drawing and writing contradict each other.
according to the picture $e_1$ is $v_1v_3$ but you write that it is $v_1v_2$.
clever fjordBOT
AnnGhost
wooden python
did you mean you pick e_1 or did you mean to pick e_2 = v_1v_2? make up your mind.
(also the way you're writing the empty set symbol is wrong)
@smoky marten
wooden python
E' will have all edges incident with either endpoint of e1 removed from it.
do you see what those are
smoky marten
like for the first interation right?
wooden python
you are looking at the first iteration here, yes.
can you tell me, looking at your picture, which edges are incident to e1?
smoky marten
can you define what edges incident mean, I havent heard of the term so im struggling a bit
wooden python
which edges share an endpoint with e1?
smoky marten
would that be e2?
wooden python
e2 and ONLY e2?
smoky marten
im tempted to say e3 too
wooden python
e2, e3, and NOTHING ELSE?
i am asking you for all the edges which share an endpoint with e1.
i.e. ALL edges which have either v1 or v3 as an endpoint.
wooden python
yes...
those edges, along with e1 itself, get removed from E'.
what is left in E'?
smoky marten
e6
wooden python
yes
wooden python
bad notation right before the "end"
wooden python
confused ∅ with {∅} by the looks of it
wooden python
you should not be mimicking it you should be understanding the notation and be able to translate this into words
"We remove the following edges from E': (u,v) itself, as well as all edges incident to either endpoint thereof."
odd edgeBOT
@smoky marten Has your question been resolved?
lucid stirrup
odd edgeBOT
lucid stirrup
Is this the correct way to start this
clever fjordBOT
odd edgeBOT
@lucid stirrup Has your question been resolved?
lucid stirrup
<@&286206848099549185>
upper onyx
is it $|(2-x)(1-x)|>2, x \in \mathbb {R}$?
clever fjordBOT
ThM
lucid stirrup
is it $|(2-x)(1-x)|>2, x \in \mathbb {R}$?
Yes
upper onyx
make 3 cases: a) x > 2, b) x<1 and c) x between 1 and 2
upper onyx
looks ok
upper onyx
Cuz theres no case with >2
why?
upper onyx
sorry, you asled if the written things on paper are right. and they are. you do not asked if they are useful. lets talk about this. what do you want to do with the written things?
lucid stirrup
You write the cases and solve per case
upper onyx
you have to brackets. the terms in the brackets can be positive or negative. if you combine this possibilities you get 3 cases. the 3 i mentioned above.
if x > 2, both brackets are negative. with x < 1 both are positive, in between one is positive and one is negative.
lucid stirrup
Why would it be >2
Its positive if the whole things is >0
If you put the whole thing >0 you get x<2
upper onyx
you look at the whole thing. i look at each bracket-term.
upper onyx
If you put the whole thing >0 you get x<2
no.
lucid stirrup
2-x>0
upper onyx
just try it. x = 4 ->(2-x)(1-x)=(-2)(-3)=6 > 0
lucid stirrup
X=4?
upper onyx
thats what i said.
lucid stirrup
Why x=4
upper onyx
just any value you like. take 23457654 ore something else. just an example to show you, that your statement "f you put the whole thing >0 you get x<2" is wrong.
if x > 2 then (2-x) is negative and (1-x) is negative, so (2-x)(1-x) is positive.
if x <1 then (2-x) is positive and (1-x) is postive, so (2-x)(1-x) is positive.
if 2 > x >1 then (2-x) is postive and (1-x) is negative, so (2-x)(1-x) is negative.
lucid stirrup
Then what bro
upper onyx
what is your question?
upper onyx
the written thing was ok before, and its ok now.
lucid stirrup
.close
ruby nacelle
i dont know how to continue
odd edgeBOT
i dont know how to continue
ruby nacelle
<@&286206848099549185>
odd edgeBOT
@ruby nacelle Has your question been resolved?
ruby nacelle
Oh
mystic widget
maybe it is a trigonometric identity
odd edgeBOT
@ruby nacelle Has your question been resolved?
odd edgeBOT
@ruby nacelle Has your question been resolved?
ember harness
Plugged in all the numbers given and don’t know how to continue
odd edgeBOT
@ember harness Has your question been resolved?
hasty yoke
odd edgeBOT
upbeat trench
Pls help me
hasty yoke
What am I doing wrong here?
upbeat trench
Oh
hasty yoke
bro
hasty yoke
get out of this channel lmao
upbeat trench
Sorry
odd edgeBOT
mystic saffron
please dont ping helpers just to close the channel and open a new one-
odd edgeBOT
Available help channel!
mystic saffron
odd edgeBOT
mystic saffron
Please help and tell me where I went wrong
glass wedge
@mystic saffron you wrote 1.2π instead of 1.2 in several places
mystic saffron
yeah because the theta is 1.2Pi?
glass wedge
The theta is 1.2 rad
Not 1.2π rad
If you know the circle has 2π rad, 1.2π rad would be a little over a half of the circle
You also saw that with 1.2π rad you get a negative sine and therefore a negative triangle area
Which isnt really possible
mystic saffron
I see. Im just a bit confused because im wondering how the calculator would know that 1.2 is actually 1.2 if i didnt write Pi right after it
glass wedge
It knows
If you don't set it to degrees
1.2 is as much of a number as 1.2π
Around 3 times smaller 🤣
When you calculate the area of the triangle with sin(1.2) you get 6.3
38.4-6.3=32.1
As in the solution
mystic saffron
Okay i see. Thanks - i mustve not been in class for this.
Really appreciate it
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
help with B please
odd edgeBOT
help with B please
stark heart
mystic saffron
yeah
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
<@&286206848099549185>
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
fluid pelican
odd edgeBOT
fluid pelican
How can i get the correct answer to this? i used chatgpt for help but the answer is wrong
manic sleet
1st issue: you're using ChatGPT
and 2nd, this appears to be more of an economic question
as far as I know elasticity is defined as: $E(p)=\frac{%\Delta Q}{%\Delta P}$
clever fjordBOT
PajamaMamaLlama
manic sleet
at least since the last time I've taken an economics class
reef sandal
Price elasticity of demand is $\dv{Q}{P} \cdot \frac{P}{Q}$
clever fjordBOT
Umbraleviathan
reef sandal
Which is the differential way of writing it
I prefer this one
If you think about it, it's kinda a 3D function
Eh
Not really
You can think Q as D(p)
So it's some kind of differential equation
manic sleet
oh wow ok this is much different than the economics I'm used to 
reef sandal
It's the same thing
This is just more accurate
I mean if you're a big fan of midpoint formula like me you're familiar with $\frac{Q_2 - Q_1}{P_2 - P_1} \cdot \frac{P_1 + P_2}{Q_1 + Q_2}$
clever fjordBOT
Umbraleviathan
reef sandal
But suppose the change is infinitemsal then you get the differential shown above
fluid pelican
So which method would be the easiest and how would I go about it
reef sandal
If you're using calculus, the differential works nicely
real sail
odd edgeBOT
real sail
its saying it isnt right
1 * 1/5 * 4/5
chance of them ending up in the same slot is 1/5 since theres 5 slots, then leaves 4/5 chance for the last one to be in a different one
I also tried 1/5 * 1/5 * 4/5
but it isnt right either
odd edgeBOT
@real sail Has your question been resolved?
real sail
.close
crisp ridge
Hey everyone!
I need some help with this question on differentiation under integral sign
I don't know how to integrate this further
crisp ridge
My friend solved it this way but I don't understand this, how can the derivative of sinxt/t be tcosxt/t
My bad, this should be in the university channel
I'll close this
.close
elder vault
why probability mass function being named as probability mass function??
elder vault
is there any property of it involves the concept of mass?
odd edgeBOT
@elder vault Has your question been resolved?
pliant latch
is there any property of it involves the concept of mass?
Not that I’m aware of. Though discrete probabilities were often referred to as “weighted biases” in the past, so perhaps that might explain the use of the word mass.
forest sky
probably by analogy to the probability density function?
elder vault
probably by analogy to the probability density function?
what kind of analogy?
forest sky
to find the probability of a variable lying in some range for a continuous random variable you take the integral of the probability density function. On the other hand to find the probability of a discrete random variable is at a specific point you take the probability mass function. Similarly, to find mass, you integrate over density
elder vault
.close
graceful shore
Hello, can someone give me some advice for resolving this one?
wooden python
well, photomath suggests l'hôpital.
graceful shore
i need something else
wooden python
this suggestion is kind of questionable yeah
graceful shore
It's too hard, and I haven't learned
wooden python
i'd begin by substituting t := x-3 (or equivalently, x = 3+t) to turn this into a limit at 0, maybe things will be easier from there.
wooden python
i want to turn this into lim[something -> 0]
what better something to pick than x-3
you'll get $\lim_{t\to 0} \frac{\ln(-2-2(3+t)+(3+t)^2)}{6-5(3+t)+(3+t)^2}$ before any simplification
clever fjordBOT
AnnGhost
unborn smelt
How do I solve for a b c d using simultaneous equations
tawny phoenix
help me out with the answer please!!!!
"Two similar triangles are formed by two differemt ladders of length 10m and 18m that are leaning against a wall, such that they make the same angle with the ground. The 10m ladder reaches 8m up the wall. How much further up the wall does the 18m ladder reach?
odd edgeBOT
help me out with the answer please!!!!
tawny phoenix
nope, unfortunately.
seems like a chill guy though
how do i get in contact with the so called tales ? 
fervent pewter
have you read congruence and similarity?
tawny phoenix
nope
fervent pewter
won't be able to solve if you don't know those concepts of a triangle in geometry
odd edgeBOT
@tawny phoenix Has your question been resolved?
shy moth
Alright ill tell u what sir Tales said
So basically you have two intersecting lines
And then you have two paralel lines that intersect with those lines making a triangle
Or rather heres it more simppe
Lets say you have a triangle and a Line paralel to one of its sides
Which is essentially what you have now
The stairs are paralel
Thisd be much easier if i had a pen and paper now but lets demote the distance from the bottom to the first stair (upwards) with a, and the distance from first to second stair with b, which is what youre looking for btw
Actually heres this image, it should make everything clear
The red lines are your stairs
Feel free to pm if you dont manage to grasp it
odd edgeBOT
@tawny phoenix Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
How do I show that $\abs{\R} = \abs{\C}$
odd edgeBOT
How do I show that $\abs{\R} = \abs{\C}$
clever fjordBOT
mystic saffron
or, translated, how do i show that the set of the real numbers has the same cardinality as that of the complex numbers
clever fjordBOT
AnnGhost
wooden python
and then using that, $\bR^2 \to (2^{\bN})^2 \to 2^{\bN} \to \bR$
clever fjordBOT
AnnGhost
mystic saffron
oh that works?
wooden python
basically construct bijections for each of these arrows
mystic saffron
wooden python
it might take some tinkering to make this work nicely
mystic saffron
okay one sec i will think of something
@wooden python
so this was actually the previous question which i didnt understand either haha
but can you explain to me their hint?
wooden python
do you know what schröder-bernstein says
mystic saffron
if there exist injective functions f: A → B and g: B → A between the sets A and B, then there exists a bijective function h: A → B?
wooden python
if there's injections both ways between two sets, then the sets have the same cardinality
yes
mystic saffron
yes ok
wooden python
right
(0,1) to (0,1)^2 is obvious
the challenge is to make one the other way
they suggest $(0.a_1a_2a_3 \dots, 0.b_1b_2b_3 \dots) \mapsto 0.a_1b_1a_2b_2a_3b_3 \dots$
clever fjordBOT
AnnGhost
wooden python
where a_i and b_i are decimal digits
wooden python
you need to take care that neither decimal expansion ends with a tail of nines
mystic saffron
curious as to why that restriction is there btw?
wooden python
which is only ever an issue for terminating decimals
wooden python
curious as to why that restriction is there btw?
disambiguation
mystic saffron
i see okay
okay
lets start by defining a function $f:\R \longrightarrow \R\cross \R, a\mapsto (a,a)$
clever fjordBOT
mystic saffron
we can prove that the above function is injective by showing
$\abs{\R \cross \R} \le \abs{\R}$
clever fjordBOT
iron bear
a -> (a, a) is showing |R| <= |RxR|
iron bear
and injectivity hopefully you can prove directly from the definition of f
wooden python
we can prove that the above function is injective by showing
you have some shit backward
wooden python
lets start by defining a function $f:\R \longrightarrow \R\cross \R, a\mapsto (a...
this function's injectivity is obvious, but it is a witness to |R| ≤ |R^2| not the other way around.
mystic saffron
yes that was my mistake sorry
okay so uhhh
we want to define a one-to-one function $g: (0,1) \cross (0,1) \longrightarrow (0,1)$
clever fjordBOT
mystic saffron
if we dont allow successive 9's then every number has a unique decimal rep.
wait brb im dehydrated as fuck i need water
ok back
lets say $\m g{a,b} \in (0,1)$ where [
a = 0.a_1a_2a_3\hdots \
b = 0.b_1b_2b_3\hdots
]
Then [
\m g{a,b} =0.a_1b_1a_2b_2\hdots
]
clever fjordBOT
mystic saffron
okay wait
ill reopen this channel because this is a freaking mess
newly coming helpers would be confused
.close
mystic saffron
odd edgeBOT
mystic saffron
Please someone help me
polar aurora
need help with the definition of ordered sets
mystic saffron
need help with the definition of ordered sets
Open your own channel
polar aurora
where do i post it?
mystic saffron
where do i post it?
Go to the "math help (avalable)" channel and post your problem in one of the open channels
polar aurora
thanks
keen acorn
hi, this question seems quite 'floaty' to me, Ive defined all probabilites, but cannot really get how to show it. p0 and r0 are arbitary number values that are to be calculated (which has been done alr so I only need help for part 1)
odd edgeBOT
@keen acorn Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
smoky atlas
hi
wooden python
do you know anything about logarithms
smoky atlas
Yes
wooden python
ok
smoky atlas
I actually know how to solve this but idk one step
wooden python
...
smoky atlas
so I can also look at it as log base e 1 =x right
then I bring e^x=1
and i know x has to equal 0 to become one
but how do I prove it mathematically
all I wrote was anything when x^y=1 has a y=0 exponent
leaden karma
for any $x>0, e^x > 1$ and for any $x<0, 0<e^x < 1$
clever fjordBOT
kheerii
leaden karma
but by definition, $\log_a(1) = 0 (a>0, a\ne 1)$
clever fjordBOT
kheerii
lime fog
yes
smoky atlas
oh thanks guys
odd edgeBOT
@smoky atlas Has your question been resolved?
smoky atlas
I have another question
guys
we have this right here, so I know this has an asymptote right a horizontal one at least, bc 1/4^x, how do I know which has higher degree? @lime fog
odd edgeBOT
odd edgeBOT
Available help channel!
toxic sentinel
How would I write the system of equations in matrix form for Case 3
toxic sentinel
All I was given was the first line in the matrix
sleek crag
**"Two similar triangles are formed by two differemt ladders of length 10m and 1...
i think its 72/5 by similarity , or u can solve by it using trigonometry .
odd edgeBOT
@toxic sentinel Has your question been resolved?
ancient lagoon
Question 3
odd edgeBOT
Question 3
toxic rose
Find by subbing x=each option one by one
stable glacier
How would you be able to take the magnitude of the following?
stable glacier
j is i
odd edgeBOT
@stable glacier Has your question been resolved?
leaden karma
I am assuming omega, mu, sigma and epsilon are arbitrary constants?
stable glacier
I am assuming omega, mu, sigma and epsilon are arbitrary constants?
yes that is right
leaden karma
then you need to get rid of the denominator first
by "rationalising" (multiplying by the conjugate)
odd edgeBOT
@stable glacier Has your question been resolved?
sleek crag
Question 3
A) because u get a complex no if u put 3 as its value .
urban smelt
soit p un polynome dont le reste de la division eucl par X-2 est 3 et par X+3 est 4 . quelle est le reste de la div euc de p par (X²+X+6)
urban smelt
let p be a polynomial whose remainder of the division eucl by X-2 is 3 and by X+3 is 4. what is the remainder of the div euc of p by (X²+X+6)
any help
chrome lynx
-6 or +6?
urban smelt
i found out that (X-2) x (X+3) = (X+X²-6)
chrome lynx
yeah
urban smelt
thats the exercice
chrome lynx
let p be a polynomial whose remainder of the division eucl by X-2 is 3 and by X+...
mathematically
translate the first sentence
of this
into maths
quotient and remainder
an equation
chrome lynx
i cant know
you didnt show anything you did
so im starting with the basics
people often ask questions without even knowing the definitions
but you know them
urban smelt
yes i do
i asked here because i already tried everything i know
and couldn't find an answer
so i need you help
soo?
chrome lynx
maybe write the euclidean division of q by x+3 and incorporate into the equaiton
same with k and x-2
p = q1 (X+3)(X-2) + r1(X-2) +3 something like this
and we have that defree of r1(x-2) +3 = 1 and is smaller than the degree of (X+3)(X-2)
so r1(X-2)+3 is the remainder
do you see where i'm going?
urban smelt
i didnt get it
chrome lynx
write the euclidean division
of q by (X+3)
and k by (X-2)
with some unknown quotients and remainder
chose names for them
odd edgeBOT
@urban smelt Has your question been resolved?
woeful orchid
need some help understanding what this is asking
odd edgeBOT
need some help understanding what this is asking
mystic saffron
need some help understanding what this is asking
yeah they might want you to calculate by using root 3 as 1.73
woeful orchid
yeah im assuming they want irrational numbers?
woeful orchid
Do you know some trigonometric identities?
a little bit, we just started learning this
woeful orchid
You've lost me😅
i know pi/2 is associated with something but cant remember with what
clever fjordBOT
Nel
woeful orchid
so sin(90- theta)
woeful orchid
alright
late dust
So sin(90º - theta) = ?
woeful orchid
how am i supposed to answer if we dont know theta?
late dust
You're not supposed to give an actual value
woeful orchid
Oh
late dust
woeful orchid
Yeah sin 90 is 1 ,so 1 - sin (theta)?
late dust
No
woeful orchid
I'm lost
mystic saffron
how this gonna help ?
late dust
Here's the same arrow, reflected about the blue line (45º)
Hint hint
Reminder, we're looking for sin(90º - theta) aka sin(angle of red arrow)
woeful orchid
so 45?
woeful orchid
okay
late dust
You don't know theta, so presumably the solution is something with theta in it
woeful orchid
1- sin theta/1 ??
late dust
No
You understand that the green and purple lines in the first picture are the representations of sin(theta) and cos(theta) right?
woeful orchid
yea
late dust
You see the other green and purple lines in that last picture?
woeful orchid
yes?
late dust
What do they represent?
woeful orchid
sin and cos?
late dust
of what?
woeful orchid
theta?
woeful orchid
I honestly have no clue, thought it was showing like half of 45 since the blue one is sitting in the middle of the 90 degree angle but im not sure
late dust
Here's the same arrow, reflected about the blue line (45º)
.
It's the reflection of the black line, the first one, which represents theta
woeful orchid
Alright
late dust
So can you find the angle it represents? I basically gave the answer already
late dust
The red arrow makes an angle of 90º - theta
.
This is just for an identity that you should know already so if you want to go back to the original question here's the answer:
||sin(90º - theta) = cos(theta)||
woeful orchid
If you wouldn't mind can you eleborate on that since I am still confused. I apologize for this.
late dust
The sin of an angle is the y coordinate of the corresponding point on the unit circle
That's what the green line is on the first picture
Same for cos, it's the x coordinate, and the purple line
If you reflect everything about the 45º line (blue), then the new angle still connects with the green and purple lines except now the green is for the x coordinate and the purple is for the y
woeful orchid
so they switched?
late dust
Yes, for the new angle
woeful orchid
oooh alright
So basically trying to tell me on the unit circle (sin theta, cos theta) right?
but took that and applied it to the homework and said my answers were correct so thank you.
late dust
Well haven't you learned the unit circle with trigonometry?
woeful orchid
So basically trying to tell me on the unit circle (sin theta, cos theta) right?
sorry other away around
late dust
That's how I learned it
woeful orchid
Well haven't you learned the unit circle with trigonometry?
My teacher didnt want us using the unit circle
woeful orchid
yeah, imagine my confustion
We only had two classes with her teaching stuff too and already have a test soon on it
late dust
I guess they want you to memorize the identities without proving them first?
woeful orchid
I assume?
late dust
Well, now you know
woeful orchid
Yes, Thank you
late dust
You're welcome
woeful orchid
.close
undone swift
Someone help pls?
odd edgeBOT
Someone help pls?
tight crescent
Someone help pls?
What does it mean if a triangle is equilateral?
undone swift
What does it mean if a triangle is equilateral?
That it has all sides or?
tight crescent
That it has all sides or?
Well, every triangle has all sides 😅
undone swift
Well, every triangle has all sides 😅
Loll
tight crescent
All sides are of equal length
undone swift
Yep
tight crescent
for like 3x+2
2y-x
y+3
So what does that tell us about these three sides?
undone swift
So what does that tell us about these three sides?
Idk 😭
undone swift
Oh-
tight crescent
One side is (3x + 2), the other (2y - x), the third (y + 3)
In math
a = a
So in a equilateral triangle, a = b = c, or a = a = a
tight crescent
One side is (3x + 2), the other (2y - x), the third (y + 3)
What does this tell us about these sides then
undone swift
Ye ight 
undone swift
What does this tell us about these sides then
3x+x = 4x?
undone swift
2+3 = 5
2y+y = 3y?
undone swift
How'd you get this?
I don't know I thought they need to be additional or multiply
tight crescent
c = (y + 3)
We just learned that a = b = c
So substitute the letters for the expressions there
tight crescent
I don't know I thought they need to be additional or multiply
No, they are equal.
undone swift
No, they are equal.
O
undone swift
We bring them all together? 3x + 2 = 2y - x = y + 3 ?
clever fjordBOT
USS-Enterprise
undone swift
Thx
quaint abyss
tight crescent
!occupied
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
quaint abyss
Wrong channel I’m so sorry
undone swift
Wrong channel I’m so sorry
No worries
tight crescent
Thx <:catthumbsup:614540188747563008>
So how do we solve this now?
undone swift
So how do we solve this now?
Oof idk
quaint abyss
Oh my I need domaine like Miguel imma wait in line for him
undone swift
Lol
tight crescent
Well, if a = b = c then, logically, a = b and a = c, right?
undone swift
Well, if a = b = c then, logically, a = b and a = c, right?
Ight ye
tight crescent
The transitive property
undone swift
The transitive property
I fr don't know sadly
tight crescent
Okay, so what do we get
tight crescent
**USS\-Enterprise**
This is in the form a = b = c
Take two and two
And you end up with a system of two equations with two unknowns
undone swift
3x + 2 = 2y - x = y + 3 ?
undone swift
Why we only need two tho?
tight crescent
Well that's how you solve this
You get a system of two equations with two unknowns
tight crescent
So 3x + 2 = 2y - x ?
You picked this right
3x + 2 is one side and 2y - x is another
undone swift
You picked this right
Thx lol
undone swift
3x+2
2y-x
?
tight crescent
I mean that's the same as before
undone swift
Yeah
tight crescent
Take one of the sides out and take the one you haven't used yet
undone swift
it's y+3?
undone swift
I don't understand sorry
clever fjordBOT
USS-Enterprise
tight crescent
We have this, right?
undone swift
Yup
tight crescent
Think of it as $a = b = c$
clever fjordBOT
USS-Enterprise
tight crescent
To solve this, form a system of two equations
Take two and two
So for example, take a = b and a = c
undone swift
3x+2=2y-x
2x+2=y+3
?
tight crescent
Where'd you get 2x + 2
undone swift
Wait
tight crescent
You mean 3x + 2 ?
undone swift
3x+2 sorry
clever fjordBOT
USS-Enterprise
undone swift
Yeah
undone swift
Hm I'm thinking
Can we do for example like this?
2(3x+2) or?
cuz of 2y and there's y
tight crescent
That's not how you solve a system of two equations with two unknowns
Have you learned how to solve this by the way?
undone swift
Have you learned how to solve this by the way?
Sadly no we don't have a good teacher this year
tight crescent
Ah
Well
You'll first learn two main ways to solve it: by elimination and by substitution
Solving by substitution means isolating a variable (for example x), and substituting it into the other equation and solving for the other variable
undone swift
Ye and my friend even though she gets A she's still struggling she does helps me but she's also got stuck in this
tight crescent
Solving by elimination means getting rid of one variable and getting the other that way
Let's do it both ways 🙂
Let's do by substitution first.
First thing we do, we pick one of the equations and isolate a variable in it
Doesn't matter which equation and doesn't matter which variable
undone swift
Thank you 🙂 👍
clever fjordBOT
USS-Enterprise
tight crescent
Try simplifying this by getting all terms with variables on one side and constants on the other
undone swift
4x+2=2y?
tight crescent
That's half the work
undone swift
Oof lol-
tight crescent
Constants are still alongside variables
So we move 2y to the left
And 2 to the right
We end up with $4x - 2y = -2$
clever fjordBOT
USS-Enterprise
undone swift
Omg thanks 🙂
tight crescent
So that's the first equation, do the same for the other
undone swift
👍
tight crescent
$3x + 2 = y + 3$
clever fjordBOT
USS-Enterprise
tight crescent
What do we get
undone swift
3x-y= 3+2?
undone swift
I forgott
clever fjordBOT
USS-Enterprise
clever fjordBOT
USS-Enterprise
tight crescent
we can simplify this even further
(this is the first equation)*
What can we do
We see coefficients 4, 2, 2
undone swift
Just min
tight crescent
👍
undone swift
We see coefficients 4, 2, 2
-2y = -2 - 4x?
clever fjordBOT
USS-Enterprise
tight crescent
How would you solve this?
undone swift
Ohh I thought we had to change or smth lol
clever fjordBOT
USS-Enterprise
tight crescent
We can do the same here
Because all coefficients are a multiple of 2
So dividing both sides by 2
We get $2x - y = -1$
clever fjordBOT
USS-Enterprise
tight crescent
This is the most simplified we can do
So, anyway. We've simplified everything we could
$2x - y = -1 \ 3x - y = 1$
clever fjordBOT
USS-Enterprise
tight crescent
This is our system of equations
tight crescent
**USS\-Enterprise**
This is exactly the same as this! We just simplified the equations
undone swift
Hey back sorry my brother came
tight crescent
No problem
undone swift
**USS\-Enterprise**
Lol interesting
tight crescent
Sorry, I don't accept friends. I have DMs open though 🙂
Okay
Now
Let's solve by substitution
This means isolating one variable in one of the equations and plugging it in the other
undone swift
Sorry, I don't accept friends. I have DMs open though 🙂
That's ok 🙂 I just wanted to be friends cuz you've helped 🙂
tight crescent
Which equation do you want to pick?
tight crescent
Yes, this is a system of two equations with two unknowns
Notice there are two equations
2x - y = -1, and 3x - y = 1
undone swift
hm
tight crescent
We have to isolate a variable in one of them
undone swift
maybe 3x-y=1?
undone swift
Thanks! 🙂
tight crescent
This is where you have to have a bit of skills
undone swift
This is where you have to have a bit of skills
Fr!
tight crescent
If we decide to isolate x we'll eventually have to divide by 3 etc.
So it's better to pick y
undone swift
divide is necessarily?
tight crescent
Well you'll eventually end up with 3x = something
And you solve this by dividing by 3 right
undone swift
Yeah
tight crescent
You need to isolate a variable (solve for a variable)
undone swift
So these are necessarily to always divide?
clever fjordBOT
USS-Enterprise
tight crescent
Let's try to isolate y
This means only having y on one side and everything else on the other
undone swift
This means only having y on one side and everything else on the other
Yeah
tight crescent
So that means it would depend what the question would ask u-
No, it's a matter of the equation. If we have like x + 3 = 9, we only move 3 to the right and get x = 6, but if we have like 2x - 1 = 3, then we move -1, we get 2x = 4 and then divide by 2 to get x = 2
Anyway
What do we do to get y alone?
tight crescent
No worries, take your time!
It's better to take your time than rush
We make mistakes when rushing
undone swift
y=3x+1..?
undone swift
We make mistakes when rushing
Yeah true
tight crescent
Almost
undone swift
No worries, take your time!
Thanks!
clever fjordBOT
USS-Enterprise
undone swift
That always needs to be moved?
tight crescent
Yes, you need to get y alone
nothing can be on the left side except y
We still have -y
So we multiply by (-1)
We get $y = -1 + 3x$
clever fjordBOT
USS-Enterprise
tight crescent
Or, to look more nicely, $y = 3x - 1$
clever fjordBOT
USS-Enterprise
tight crescent
It's 1 at the start
undone swift
Lol
undone swift
Yeah ight
undone swift
Yup- Lol
tight crescent
$2x - y = -1$
clever fjordBOT
USS-Enterprise
clever fjordBOT
USS-Enterprise
tight crescent
**USS\-Enterprise**
So we just substitute y into this
undone swift
Yeah
tight crescent
We get $2x -(3x - 1) = -1$
clever fjordBOT
USS-Enterprise
undone swift
Ur right!
clever fjordBOT
USS-Enterprise
tight crescent
$-x = -2$
clever fjordBOT
USS-Enterprise
tight crescent
$x = 2$
clever fjordBOT
USS-Enterprise
tight crescent
And we've got x!
And now we go into any of the equations which have both x and y in them
undone swift
cuz - and - becomes +
clever fjordBOT
USS-Enterprise
clever fjordBOT
USS-Enterprise
tight crescent
$6 - y = 1$
clever fjordBOT
USS-Enterprise
tight crescent
$- y = -5$
clever fjordBOT
USS-Enterprise
tight crescent
$y = 5$
clever fjordBOT
USS-Enterprise
tight crescent
And we've got both x and y!
undone swift
Thank you! You're awesome 🙂
undone swift
I forgot we still have the b) for perimeter
tight crescent
We have this system
tight crescent
I forgot we still have the b) for perimeter
We'll get to that
undone swift
We'll get to that
Thank you 🙂
tight crescent
$2x - y = -1 \ 3x - y = 1$
clever fjordBOT
USS-Enterprise
tight crescent
Solving by elimination means eliminating one of the variables
Now
With systems there are cool tricks you can do with them
undone swift
Solving by elimination means eliminating one of the variables
Yeah
tight crescent
Like adding both equations, or substracting both equations
undone swift
Like adding both equations, or substracting both equations
Yeah it would depend
tight crescent
Exactly
Notice how we have -y and -y in both
If we were to substract both equations, we'd get -y -(-y) or -y + y or 0
undone swift
True! Yeah
tight crescent
And we've eliminated a variable!
So let's try substracting the equations
Notice again why simplfying was necessary
You have to have the same terms under each other,
So 3x is under 2x, -y under -y, 1 under -1
Makes substracting easier
undone swift
Yeah- you're right
tight crescent
Okay so let's substract the second equation from the first