Available help channel!
#help-10
obtuse pebbleBOT
Available help channel!
zinc stump
Hey guys, any help with the following? Set theory question
I think the answer for 2 should be $\aleph$ but not sure how to show it. It's smaller than RxR which is $\aleph$ but has an $\aleph$ intervals that we could write as (0, a) where a > 1 belong to R.
Would appreicate any help for each of the rest
obtuse pebbleBOT
Hey guys, any help with the following? Set theory question
I think the answer fo...
warm shaleBOT
meitar5674
zenith raft
2 is smaller than RxR?
idts
i think it’s much larger than thay
isn’t it isomorphic to the power set of R\(0,1)?
zinc stump
2 is smaller than RxR?
🙈
Maybe I got it wrong I don’t know. Ain’t each is of the form (a,b) such that a,b in R but a < 0, b> 1? Which subsets RxR?
zenith raft
it just says subsets of R, not subsets of R that are intervals
so there is also e.g. (-1,2) union {100}
zinc stump
Oh right
So yeah your answer might be right
Cuz we do the Union of the interval with some set of the power set
zenith raft
yea
obtuse pebbleBOT
@zinc stump Has your question been resolved?
hollow comet
I've been trying to understand the integral test but every time I try I get even more confused. Here's an example question I got wrong.
obtuse pebbleBOT
I've been trying to understand the integral test but every time I try I get even...
hollow comet
a_n = 1/sqrt(n+3)
Find the limit that determines whether a_n converges or diverges.
It implied that it passed the integral test, so I integrated it.
I ended up doing it improperly by forgetting the reverse power rule.
For every corner I step with this topic, I mess up on one thing or another.
obtuse pebbleBOT
@hollow comet Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
Is the answer for this question 2/3?
timid silo
where does 2/3 come from?
Out of the Group A members, 40 are over the age of 10
or at least
and there is a total of 60 members'
so 40/60 = 2/3
plain stag
that's the probability that the randomly selected person is in group A and is at least 10 years old
the question asks for the person being selected from group A given that they're at least 10 years old
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
slate agate
Ok so question about basic ODE's
obtuse pebbleBOT
Ok so question about basic ODE's
slate agate
Im using pauls online notes and...
Does this not directly violate the following
Since tan(x) is not a continuous function? Neither is sec(x)?
zenith raft
they are continuous
brisk matrix
did you discuss the existence and uniqueness theorem?
slate agate
did you discuss the existence and uniqueness theorem?
first of all nice pfp and im a year removed from graduation so im reviewing a bunch of mathematics. we probably did but quite frankly it is not ringing a bell
zenith raft
and btw the procedural questions at "basic ODE" level are not going to pay any attention to that stuff, even though you're asking a good question
slate agate
hmm i see
zenith raft
like even this is not really a precise statement
brisk matrix
first of all nice pfp and im a year removed from graduation so im reviewing a bu...
the handwavy answer is that we just care about solutions on the domain were the coefficients are defined
if we restrict ourselves to those domains, each of those functions are continuous
slate agate
if we restrict ourselves to those domains, each of those functions are continuou...
oooooh
youre right
yep
zenith raft
well this is a simpler answer
brisk matrix
didnt even notice that
zenith raft
i think paul's online notes probably calls tan etc not a continuous function
which is stupid
unreal nexus
Could anyone help me with integral?
obtuse pebbleBOT
Could anyone help me with integral?
violet sentinel
feel free to post it
unreal nexus
Int^2_1 ( dx/x^3 )
I've tried to rewrite it like (1/x^3) * dx
(4/x^4) * dx, right?
violet sentinel
not quite
gleaming ridge
Int^2_1 ( dx/x^3 )
int^2 ??
violet sentinel
if it helps, re-write it as : $\int_0^2x^{-3} dx$
warm shaleBOT
MellowDramaLlama
gleaming ridge
as in $\int_{1}^{2} \frac{dx}{x^3}$
warm shaleBOT
numbpy (anti-glomed)
unreal nexus
**MellowDramaLlama**
Oh, ty, insightful
unreal nexus
**numbpy (anti-glomed)**
Yes
violet sentinel
Oh, ty, insightful
obv my lower bound I put 0 instead of 1 but the structure of the integral is the same
just use the power rule here
unreal nexus
obv my lower bound I put 0 instead of 1 but the structure of the integral is the...
Yes, it doesn't matter, you helped me to solve, thank you )
uneven otter
Can P = F?
obtuse pebbleBOT
Can P = F?
uneven otter
Im kind of lost like how should I approach this question
and also for R3
lets say i) and ii) end up being true then does that mean x not in F?
also wait wth in the definition it says
wild swallow
no that doesnt make sense, P is a subset of F
wild swallow
people use the notation $\subset$ to just mean subset as well
warm shaleBOT
wild swallow
lets say i) and ii) end up being true then does that mean x not in F?
this just cant happen for any element in F
wild swallow
are you sure that $\subset$ is being used to mean proper subset though
warm shaleBOT
wild swallow
because this is not a universal convention
uneven otter
are you sure that $\subset$ is being used to mean proper subset though
i thought $\subset$ means proper subset and $\subseteq$ is subset
warm shaleBOT
Calc II Victim
uneven otter
iirc thats what we learnt in class
wild swallow
not to everyone
uneven otter
so is that incorrect?
wild swallow
i wouldnt rely on that being part of the definition
especially since it doesnt need to be in the definition
wild swallow
it wouldnt be a very good question to ask if P can equal F if by definition it couldnt
uneven otter
true
wild swallow
im saying that relying on $\subset$ meaning proper subset is possibly dubious, since it is not always the case that people interpret that to be a proper subset
warm shaleBOT
uneven otter
wait so should I confirm wit my prof
if in this course $\subset$ implies proper subset
warm shaleBOT
Calc II Victim
uneven otter
also j curious but do some people treat $\subset$ it the same as $\subseteq$ ?
warm shaleBOT
Calc II Victim
wild swallow
yes
limpid widget
What's the difference between subset and subseteq?
wild swallow
you can prove it without assuming P is a proper subset
uneven otter
you can prove it without assuming P is a proper subset
wait fr?
wild swallow
well yes
uneven otter
mhm is it with the help of R3?
wild swallow
think about it
wild swallow
why?
uneven otter
0 isnt positive?
uneven otter
wait wymmmmmmm
how is it positive
whenever we talk abt positives in class we always do > 0
uneven otter
no?
wild swallow
justify
uneven otter
wait firsttly
does positive set imply that
all elements in that set
are positives
wild swallow
the definition of a positive element is something that is in the positive set P
uneven otter
ye so thats why all elements of P should b > 0 no?
wild swallow
why?
uneven otter
because P consists of positive elements only
wild swallow
a priori, there is no concept of "positive"
positive is by definition something in P
wild swallow
you cannot claim that everything in P is >0 without additional reasoning
wild swallow
stare at R3
wild swallow
okay so is x = 0 in P?
uneven otter
im so confused
wild swallow
exactly one of (i), (ii), (iii) can be true
uneven otter
ye and i) is true
wild swallow
when x = 0, (iii) is true
uneven otter
when x = 0 then i) and iii) are true no?
wild swallow
that is not possible
royal basin
Can P = F?
is this a bad time to say that a ≤ b should be a < b instead
uneven otter
because (iii) is true
oh so ur saying
if one of them is true I can ignore the rest 2?
wild swallow
no, im saying (iii) is true => (i) and (ii) are false
wild swallow
no elements in your screenshot are not in F
0 (the additive identity of F) is certainly in F
but it is not in P
uneven otter
shit
now im even
more confused
one second let me re read all of the messages from top
i asked my prof they said
that $\subset$ refers to proper subset
warm shaleBOT
Calc II Victim
uneven otter
But I searched up the definition of field orders I think its a typo in the definition
uneven otter
but it is not in P
oh its not in P because iii) is true thus i) cant be true
wild swallow
yes exactly
wild swallow
so 0 is never in P
royal basin
But I searched up the definition of field orders I think its a typo in the defin...
ordered field
youre in that part of math where exact words kind of matter
uneven otter
right my fault
would this much be sufficient?
i meant cant be true instead of cant both be true
wild swallow
writing something like "Then by R3, because (iii) is true then ..." flows better logically to me
wild swallow
yeah great
uneven otter
.close
cerulean stump
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/486841106298961930/1114299561515700224/im...
@cerulean stump Has your question been resolved?
pulsar breach
obtuse pebbleBOT
pulsar breach
how to integrate it to find v?
high lily
integrating accelaration gives velocity
use the given info to determine the constant of integration
power law would be appliacble here
pulsar breach
so v = -9/2 (x^2) + C
high lily
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hoary mirage
Number of ways of distributing 'n' identical objects among 'r' groups if n<r and any group can have empty objects.
obtuse pebbleBOT
Number of ways of distributing 'n' identical objects among 'r' groups if n<r and...
royal basin
n identical objects?
then it's not r^n
if the n objects were distinct then you could view this as assigning to each object a number from 1 to r (designating which group it goes in), thus you have r choices for each object and you multiply them
ruby path
What you're referring to is $\binom{n - r - 1}{r - 1}$
warm shaleBOT
NEONPerseus
hoary mirage
if the n objects were _distinct_ then you could view this as assigning to each o...
Sorry I just realised it was stupid. It's C(n+r-1,r-1). I proved it dumbly. Thanx.
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
glacial compass
Hi, good day. We were given a practice exercises for our upcoming exam. Our topic is about multiple integration. I have here a triple integral. Can someone check my work for this? Huhuhuhu I am not really sure about my process
obtuse pebbleBOT
Hi, good day. We were given a practice exercises for our upcoming exam. Our topi...
glacial compass
I just want to ask help to check my process of converting the equation into much simple form using polar coordinates
obtuse pebbleBOT
@glacial compass Has your question been resolved?
obtuse pebbleBOT
@glacial compass Has your question been resolved?
fallen needle
can someone explain why this statement means that it is irrational
obtuse pebbleBOT
can someone explain why this statement means that it is irrational
royal basin
Suppose log_2(7) is rational.
we arrived at a contradiction, therefore our last assumption was false.
@fallen needle
fallen needle
> Suppose log_2(7) is rational.
oh so both the lhs and the rhs have to equal for the statement to be rational
royal basin
wow yeah what a shocker right
when we say two things are equal it means they are equal
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
silver owl
Is this even solveable? For context, I have no working out beside the fact ive written the information down
obtuse pebbleBOT
Is this even solveable? For context, I have no working out beside the fact ive w...
silver owl
there is no linear equation for me to use Expected value formula
hi
im not sure
this is help section so i assume not
maybe in another section
unless you need help
no im just a member
yes
candid oracle
" .close " without quotes NVM I thought you were the OP
obtuse pebbleBOT
@silver owl Has your question been resolved?
long plinth
there is no linear equation for me to use Expected value formula
There is:
weight of full bag = 10 g + weight of first orange + weight of secon orange + weight of third orange + ... + weight of tenth orange.
royal basin
but tropo that's got WORDS!!! 😱
long plinth
Hush.
jagged kernel
obtuse pebbleBOT
jagged kernel
the answer in the pic is wrong
where did I mess up?
also the question asked to use cylindrical shell method, but I wanted to try the normal one because I saw that it's possible
jagged kernel
oh yeah that one
old isle
do you understand how the washer method works?
if you were trying to use that you’re missing a component
jagged kernel
yes i practiced before
jagged kernel
yes, i've done it before
like my understanding is not super in depth but I think I know how it works
sonic anchor
you only calculated for the inner radius
jagged kernel
I see
old isle
yeah
jagged kernel
so 2 - something
old isle
you have to subtract the inner radius from the outer radius
old isle
it’s not 2
jagged kernel
oh it's 4
old isle
yea
jagged kernel
aight ill try it out
sonic anchor
also the outer radius dont need to be an integral
cause its constant
its just a cylinder
they already did the correct work for rotation the inner body
sonic anchor
now you are rotating this
you still want to rotate x=y^2 like you did in your picture
jagged kernel
this not adding up
sonic anchor
ofcourse not
you changed the object entirely
this is the blue part you rotated before
you get the part you actually want to rotate
by finding the volume of entire cylinder and subtracting that part
jagged kernel
im using disc washer method
sonic anchor
thats also what im saying
jagged kernel
I don't think this is wrong
the disc washer method calculate the volume of the shape "attached" to the y axis
by using x = 4-y^2
the area of the shape from 0 to 4 is equivalent
what are you trying to fix actually?
can you just point out my mistake?
@sonic anchor
sonic anchor
the area is equivalent but the volumes after rotating are obviously not
just think of how the shapes would look
jagged kernel
the shape would be different but since it's the same area rotated it's going to be the same volume?
I don't get what I got wrong here
one would be a solid-disc shaped
the other one would be a cylinder with it's middle pushed in
sonic anchor
yes so two different 3d shapes with different volumes
this is what ive been asking from the beginning
you add the volume rotation the OUTER radius
and subtract the volume rotattion the INNER radius
you already calculated the inner radius rotation
jagged kernel
can you just give me the number? I get your idea but the equation would help me understand faster
jagged kernel
can you write it down?
jagged kernel
what would the outer and inner equation be?
sonic anchor
they are radius
so outer radius for the green are i just drew
would be 4 right
the inner radius for the blue part i drew
jagged kernel
4-y^2?
sonic anchor
is not constant it is determined by y^2
jagged kernel
so it is 4-y^2
sonic anchor
no
sonic anchor
what is 4-y^2
jagged kernel
y^2 is to get the x value
sonic anchor
pi * R^2 * h - pi * r^2 * h
jagged kernel
why is there h?
sonic anchor
its the height
jagged kernel
also the question asked to use cylindrical shell method, but I wanted to try the...
this one
my god
u missing everything
sonic anchor
thats the formula for a disc
jagged kernel
there would be no height
sonic anchor
pi * r^2 * h is the volume of a disc
jagged kernel
what?
with h, it's the cylindrical shell method
the rotating disc doesn't have h
sonic anchor
do you know what integration means?
like inutitively what it can represent in this case
jagged kernel
you see
sonic anchor
you are adding up infinitely small cross sections
jagged kernel
you integrate the curve
you get the area under the curve
then u rotate it to get the volune
sonic anchor
thats not very constructive here
jagged kernel
pi * R^2 * h - pi * r^2 * h
why r u giving me this formula?
sonic anchor
because thats literally the disc washer method
i feel klike youre here to argue
instead of trying to learn
i cant even continue down one path
jagged kernel
sorry can you just write everything down?
along with the equation and stuff
this is really going nowhere lol
it doesn't click
sonic anchor
pi * R^2 * h - pi * r^2 * h
outer radius is R=4
h= 2
so pi * 4^2 * 2 - pi * r^2 * h
so far we good no?
then the inner radius
is y^2
height is y
so because the inner radius is not constant you need to integrate
for the inner part
and its exactly what you did before
you are adding up infinitely small cross sections from y=0 to 2
jagged kernel
i know
sonic anchor
youre summing up infinitely many h's
really small heights
the reason this is needed is because the radius changes
as the height changes
at h=1 the radius is 1^2=1 but at h=2 the radius is 2^2=4
so you sum up all these cross sections
broken minnow
what does the black dots mean
mental wyvern
numbers included to range
broken minnow
ok
mental wyvern
while white dot is there
-2 isnt included
to range
while 4 is included
what grade are you
obtuse pebbleBOT
@broken minnow Has your question been resolved?
chilly crater
obtuse pebbleBOT
rich plume
find area of sector
rich plume
,w calculate (40/360)pi7*7
warm shaleBOT
rich plume
,rccw
warm shaleBOT
rich plume
oh that's the answer
autumn spade
obtuse pebbleBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
timid silo
either row reduce, or examine the linear dependence of the rows
autumn spade
either row reduce, or examine the linear dependence of the rows
R2 = tR1 - sR3/r?
tardy epoch
R2 = tR1 - sR3/r?
What does that tell you
autumn spade
What does that tell you
idk
tardy epoch
either row reduce, or examine the linear dependence of the rows
Do you know what this means
"Linear independence"
autumn spade
idk what that means either
gleaming ridge
R2 = tR1 - sR3/r?
maybe rewriting it as R2 - tR1 - s/r R3 = 0 where t,s,r are non-zero
does this ring a bell
autumn spade
does this ring a bell
nope
i dont get it
im kinda new to matrices and determinants
tardy epoch
im kinda new to matrices and determinants
Do you know what the determinant of a matrix with a zero row equals
autumn spade
Do you know what the determinant of a matrix with a zero row equals
0?
autumn spade
Yes. Do you know why
cus when computing the determinant the normal way when we multiply by 0 everything becomes 0
tardy epoch
Sure
autumn spade
i think i get the idea here
if i make the second row 0
the determinant would be 0
R2 -> R2 + s/r R3?
that would make R2 = [ta11, ta12, ta13]
now R2-> R2 - tR1
that would make R2 = [0, 0, 0]
that would make the determinant 0
is this correct?
@tardy epoch sorry to ping you
but can you please verify if my thinking is correct?
oh?
<@&268886789983436800>
this guy was trolling and now he deleted his msgs
obtuse pebbleBOT
@autumn spade Has your question been resolved?
autumn spade
<@&286206848099549185>
timid silo
is this correct?
yes
restive kestrel
can anyone help me
obtuse pebbleBOT
can anyone help me
ivory trout
restive kestrel
severe dune
theres not much to help here right i guess just tilt your head
cloud berry
seems quiz or exam
restive kestrel
so like i need help
cloud berry
a quiz in which no calculator is allowed
cloud berry
it called help
no its called cheating
restive kestrel
am out
cloud berry
.close
quaint helm
im basically thinking of doing a multivariable optimisation investigation involving space. I'm trying to fill a square warehouse with 2 types of boxes, trying to occupy the most space obviously, and im gonna assume the height of the 2 boxes the same so i can simplify it down to the 2d surface
so then i'll be trying to fill a square with 2 types of squares (assuming boxes r squares), and i'll call them box a and box b; but a constraint will be applied, so like there must be 5 box a and 10 box b
i know theres like the intuition solve of "first put all the large boxes down and then just fill the rest of the space with small boxes", so im just planning to make the dimensions really awkward
to simplify things again for the "awkward dimensions", imagine one side is 1.5m, and box a is 0.7m, and box b is 0.5m, with the constraint being i must use at least 1 box a; so then the solution will be 2 box a instead of 1 box a and fill the rest with box b
obtuse pebbleBOT
im basically thinking of doing a multivariable optimisation investigation involv...
quaint helm
and im planning to use the kuhn tucker optimisation, and that should produce me a 3d parabola where i can find the minimum and find the values of box a and b for that area of square (warehouse)
but can someone just confirm whether that will probably work or not; and what are some alternative methods that i can use (to either find the number of each box or the model the actual square with the number of boxes out); or how to find the dimensions that I should use
for the controlled variables, it'll be the dimension of the square and dimension of the boxes
obtuse pebbleBOT
@quaint helm Has your question been resolved?
obtuse pebbleBOT
@quaint helm Has your question been resolved?
prime pebble
unless you drop the idea that the boxes are of fixed size and there can be multiple of them, this is not a problem to which KKT can be applied
everything has to be continuous and differentiable, function that counts the number of boxes is certainly not one of them
quaint helm
unless you drop the idea that the boxes are of fixed size and there can be multi...
yeah they are, im just keeping the size of box a and b the same, so the space occupied should be xa+yb
quaint helm
everything has to be continuous and differentiable, function that counts the num...
oh-
but does it not work though
like having a 3d graph where its z=x+y but f(a,b)=xa+yb where x and y r constants
prime pebble
what does not work
quaint helm
like u said it has to be continuous and differentiable
prime pebble
yes
quaint helm
oh wait so do u mean like if im counting the numebr of boxes as a whole number
its not continuous
prime pebble
yes
quaint helm
oh 😭
i guess i cant really chop up the boxes can i
do u know another optimistion model that might work?
prime pebble
only if you try to find the largest box that fits
quaint helm
but then what will be the constant variables though
cause i mean i cant just have 1 box or a set number of boxes
prime pebble
you tell me, I don't know what you want to do exactly
as far as I understand you want to fit boxes into some area, how you describe that area I have no clue
quaint helm
hmm
but except KKT do u know if theres any other model that would work for my original area
a model for a non-continuous function
prime pebble
you can write any model you want using math
the question is whether an efficient way to solve the problem exists or not
quaint helm
ok
prime pebble
KKT exists for continuous differentiable problems, the rest can be analyzed only in specific cases (KKT is not a model)
quaint helm
ahhhh
hmm ok i think i need to think abt this a bit more then
so right now my idea isnt continuous and just barely differentiable right
i have to try to get a continuous one with at least a square so i can get a min/max point
prime pebble
if it's not continuous it's automatically non-differentiable
prime pebble
no
quaint helm
ok
so the original idea is still viable, just not with KKT and for the actual solution for that, it has to be analysed individually and theres no way of knowing whether there exists an efficient way to solve it
prime pebble
who knows whether it is viable or not
quaint helm
prime pebble
the solution might easily not exist, like trying to cover a circle with squares
quaint helm
ohhh
prime pebble
the maximum covered area doesn't exist
quaint helm
the maximum covered area doesn't exist
and this is definite right
prime pebble
you can just take smaller and smaller squares and fill more area
prime pebble
well maybe, but it's difficult in the context of optimization, you should probably look for space tiling math instead because this is where people prove that some shapes can cover some area fully
prime pebble
some parts of it can be understood by anybody, some are so complicated there's not a known answer to this day
toxic gorge
i'm trying to find the median in a frequency table, the total of the frequency is 88 and for the median location i have to do +1 then divided by 2, but it comes in a decimal number, should it be like this?
obtuse pebbleBOT
i'm trying to find the median in a frequency table, the total of the frequency i...
fathom flicker
can you send the original problem please
toxic gorge
can you send the original problem please
the table
or is the table just wrong?
from where i got it?
probably that
so if the total of frequency was 87, the median would be 3, correct?
.close
neat folio
obtuse pebbleBOT
neat folio
where does the 10 degrees come from
knotty crow
neat folio
oh i was too focused on the depressed angle to think about the triangle being addedup to 180
okay thanks!
.close
jaunty bear
can someone please explain this to me, i don't understand this
obtuse pebbleBOT
can someone please explain this to me, i don't understand this
jaunty bear
scarlet gale
@jaunty bear What have you done so far?
jaunty bear
<@665305426887311360> What have you done so far?
it's not about what i have and haven't done.
i simply do not understand a thing
scarlet gale
Oh, OK. Do you know what a slope is?
scarlet gale
it's not about what i have and haven't done.
i simply do not understand a thing
If you don't know what a slope is, I can show you, but I need to know where you're at to help.
jaunty bear
i know all the basics
but i have no idea how to solve this question
and the explaination in the book just fucked me up even more
scarlet gale
OK, so let's look at problem a.
jaunty bear
mhm
scarlet gale
You have two points: (2, 7) and (5, 13).
What's the slope of the line that goes through them if you know?
jaunty bear
i need to calculate that right?
scarlet gale
Yes, that's right.
jaunty bear
i got 6/1
scarlet gale
What way did you get that?
jaunty bear
scarlet gale
OK, so we do $m = \frac{y_2 - y_1}{x_2 - x_1}$.
warm shaleBOT
Chai T. Rex
jaunty bear
What is y₂?
isn't it coordinates?
scarlet gale
Yes, it's one of the coordinates.
The y coordinate in the second point.
So, point 1 is (2, 7) and point 2 is (5, 13).
And with coordinates, they go in alphabetical order, so it's (x, y).
So to get y₂, you look at point 2, which is (5, 13). Then, you look at the y coordinate, which is 13.
Does that make sense how I got that?
scarlet gale
OK, so what does the top of your fraction look like when you fill in the y values it asks for?
jaunty bear
5-13
scarlet gale
Not exactly. Let's go over that a bit.
We need y₂ - y₁.
y₂ uses the 2nd point.
And the y comes after the x, so (5, 13).
So, y₂ is 13.
What is the y coordinate of the first point (2, 7)?
scarlet gale
Almost, you have 13 - 7 because it wants y₂ first, so 13 goes first.
Let's go over the yₙ stuff.
jaunty bear
alr
scarlet gale
You have (2, 7) and (5, 13).
We know that x comes before y.
So, x for the first point is 2, then y comes after it as 7.
What is the x and y for the second point?
jaunty bear
5-2
scarlet gale
No, I want to step away from question a on your homework for a minute.
You have (2, 7). x comes first, so that's 2. y comes second, so that's 7.
Does that make sense so far?
jaunty bear
yes
scarlet gale
What are the x and y for (5, 13)?
jaunty bear
x:5
y:13
scarlet gale
Good.
Now, we write it like this.
We put x with a little number by it.
The little number tells which point we're talking about. 1 for the first point. 2 for the second point.
So, I had x = 2 and y = 7 for the first point.
So, I would write that as x₁ = 2 and y₁ = 7.
Does that make sense why I wrote the little number there?
jaunty bear
yes
scarlet gale
OK, so the second point is (5, 13), and you said that x was 5 and y was 13.
So, since it's the second point, you would write a little 2 after the variables.
x₂ = 5 and y₂ = 13.
So, when you start a problem like this, write down the different coordinates like that.
x₁ = 2, y₁ = 7, x₂ = 5, y₂ = 13
Then, it's easier to fill them into the formula.
Does that make sense so far?
jaunty bear
yup
scarlet gale
OK, so the top of the slope formula is y₂ - y₁. What do you get after filling those in?
If you're stuck, please let me know.
jaunty bear
OK, so the top of the slope formula is y₂ - y₁. What do you get after filling th...
13-7
scarlet gale
Good. What do you get for x₂ - x₁ on the bottom?
jaunty bear
5-2
warm shaleBOT
Chai T. Rex
jaunty bear
6/3
scarlet gale
OK, and what does that simplify to when you reduce it to lowest terms?
jaunty bear
2
scarlet gale
Good, so we know now that m = 2.
Now, we want to get the slope-intercept form.
The way that we do that is that we pick a point we were given. It doesn't matter which one.
So, let's do point 1.
x₁ = 2, y₁ = 7
We want to write it like this:
(y - y₁) = m(x - x₁)
Basically we have the variable without a little number minus the variable with a little number.
So, y - y₁ on the left.
x - x₁ on the right.
Does that make sense?
jaunty bear
yea
scarlet gale
And then we have m multiplied by the x side.
m is usually on the x side in these things.
So, we know three of those variables.
We know what m is.
We know what y₁ is.
We know what x₁ is.
So, what do you get after you fill those in to this:
(y - y₁) = m(x - x₁)
jaunty bear
(y - 7) = 2(x-2)
scarlet gale
Good.
Now, that's called the slope-point form.
Because all you need for it is the slope and the point's coordinates.
You just fill them in and you're done with the slope-point form.
It's asking for the slope-intercept form, though.
That looks like y = mx + b.
b is the y intercept, which means where does it hit the y axis?
jaunty bear
2?
scarlet gale
No, we're not there yet.
Sorry, that was a rhetorical question.
So, let's say the line goes across the y axis and it hits the y axis at (0, 10).
The y intercept (when x is 0 is where the y axis is on a graph) is 10 there, so b = 10.
Does that make sense?
jaunty bear
yup
scarlet gale
Like this has b = 10:
You can look at the graph and see that it crosses the y axis when y is 10.
So, if you know the slope and where it crosses the y axis, you can easily just fill those two things in to y = mx + b and you're done.
Does that make sense?
scarlet gale
No, you never change y to a number when you're getting the equation to a line.
Because the line will have lots of different y values, one for each point on the line.
So, we leave y as a variable so that someone can fill that in for a specific point.
Like if y was 25 and they wanted to know what x was, they'd go:
(y - 7) = 2(x - 2)
(25 - 7) = 2(x - 2)
And then they could solve for x.
But we're not trying to solve for an exact point on the line, we want it to work for every point on the line.
So we have to leave x and y as variables because each point will have a different x and y value.
Does that make sense?
jaunty bear
yea
scarlet gale
What I was trying to show was that if you have y = 5x + 10, b is 10, and so it hits the y axis at y = 10.
Let's go back to our problem.
We have (y - 7) = 2(x - 2).
That's in point-slope form because we got to it from a point and the slope.
Slope-intercept form looks like y = mx + b.
So, we want to use algebra to get it to look like that.
y should be alone on the left.
We should have mx + b on the right.
We know m. It's 2.
So, it'll be y = 2x + something.
That's how we want it to look when we're done.
Does that make sense?
jaunty bear
yea
jaunty bear
=7 on both sides, removing the 7 from the y side
scarlet gale
OK, what does the equation look like after you do that?
scarlet gale
=7 on both sides, removing the 7 from the y side
Let me know if you're stuck or if you went ahead and got the final answer.
jaunty bear
OK, what does the equation look like after you do that?
y = -5(x-2)
scarlet gale
Oh, no, it works a bit differently.
y - 7 = 2(x - 2)
y - 7 + 7 = 2(x - 2) + 7
y = 2(x - 2) + 7
You add 7 to both sides, but you can't change a multiplier by adding something.
Like if you were adding 2 to 5 times 7, you'd write 5·7 + 2
That becomes 35 + 2.
So, the answer is 37.
But if you do something with the multiplier, like 7·7, where you add two to the multiplier, you get 49, which is different from 37.
Does that make sense?
When you add, it sort of stays separate from any multiplications.
jaunty bear
oooh ok
scarlet gale
OK, so we have y = 2(x - 2) + 7.
That's almost there.
But we have y = mx + b, which has x by itself and not in parentheses.
So, we want to get rid of the parentheses.
How do we do that?
jaunty bear
2 times x-2?
scarlet gale
Right. How do we do the multiplication?
jaunty bear
2x -4
scarlet gale
Good, you expand or distribute it, however you want to call it.
So, we have y = 2x - 4 + 7.
We're almost there.
How can you simplify that?
jaunty bear
y=2x -3
scarlet gale
Almost.
Notice that the + part is higher than the - part.
So, the + part should win.
And the answer should have + in it.
jaunty bear
oh ok so it becomes
y=2x+11?
scarlet gale
Not exactly.
The minus part is in the other direction from the plus part.
So, it should pull it towards the negative direction.
But the bigger number will win.
So, -4 + 7 should be positive.
But it should be closer to the negative numbers than 7.
But 11 is farther from the negative numbers
jaunty bear
so y=2x + 3?
scarlet gale
Yes.
Now that's an answer that might be right.
We could have made a mistake.
So, we want to check it.
We have two points.
(2, 7) and (5, 13).
So, we want to see if our line equation works for those points.
So, I'll do the first one so that you can see how.
For the first point, x = 2 and y = 7.
So, we have y = 2x + 3, and we fill those in.
(7) = 2(2) + 3
Now we do the arithmetic and see that we get:
(7) = 2(2) + 3
7 = 4 + 3
7 = 7
So, since 7 does equal 7, the first point is part of our equation's line.
So, that's good. We wanted the line that goes through that point, and it goes through that point.
Does that make sense how I did that, or do you have any questions?
scarlet gale
OK. Now, you do it with the second point (5, 13).
Make sure it goes through both points.
You're welcome.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
copper spire
isn't this a counter example of the 4 colors theorem?
obtuse pebbleBOT
isn't this a counter example of the 4 colors theorem?
kind hawk
probably not a good idea to try to find a counterexample to a theorem
copper spire
probably not a good idea to try to find a counterexample to a theorem
yes but it is fun
copper spire
this IS the colors theorem
yes i just was stupid
untold garnet
obtuse pebbleBOT
untold garnet
for question a)
why is it both quadrant 2 and 3 shouldnt it be just 2?
or is it cause cos is neg in quads 2 and 3?
native inlet
cos = adj/hyp do you think you can construct a right triangle with that leg and hypotensure measure on the xy plane? 🤔
untold garnet
whats a hypotensure
native inlet
the longest side on a right triangle
or the side opposite of the 90deg angle (thats the better definition)
native inlet
so if cos(x)=adj/hyp
can you construct that right triangle in the coordinate plane?
obtuse pebbleBOT
@untold garnet Has your question been resolved?
edgy saffron
Help😭
obtuse pebbleBOT
Help😭
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
fervent flint
Hi again
fervent flint
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
Where are you here?
edgy saffron
1
I’m having way too much trouble
With this unit
Yeah
Fortunately 💀
It seems like it
There are vertical angles
fervent flint
Same, I think i can explain but im not sure the words
edgy saffron
If that means anything
Holy shag
You’re right
Because it’s a pareelelegram
Botched that
So hard
🤯
Angles e and g?
We know angle b is angle b
So e and g for AA proof?
Ahh
Thanks
Wait
What’re the alternate angles supposed to be?
Rgb and gbc?
Wait
I’m confused
Confuzzled
Well so
It would be corresponding angles then
Right?
Angles a
?
Wdym positive
I havent gotten to alpha yet
Oh shoot
My fault
WAIT
Bpe
And gre
Are simular
Because
Of the corresponding angles
Maybe
Right?
Damn
So
Oh my god
Are they all similar?
Oh
Whew
Alpha and beta are in all three triangles?
Bro
Ebony
Egr
Ebp
Yeah
There are three
It’s so annoying
Yeah
So
Aren’t they all similar?
Damn
To me
They’re all similar
I guess it just wants you to do b and c
A is just
Silly
Yeah
It seems so
Obvious
Now that I look at it
So
I think i got parts one and two down
Yeah
Yeah
So that makes part c easier
I guess
👍
Thanks
Is there a way to do part 3
Without it sounding like I’m pulling the math from out of my ass
Like
Ik how to do it
But
Yknow
But
400 doesn’t represent
The legnth of GE
And