manic flax
not 1
#help-17
zinc hornet
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abstract walrus
Simple question here regarding matrix linear transformations:
I have to find a rotation matrix and then reflect that matrix in the x axis.
Do I multiply the rotation matrix with the reflection matrix, or the other way around?
That is:
Rotation Matrix x Reflection Matrix
or
Reflection Matrix x Rotation Matrix?
I was thinking that it was the first option, but some google searches suggest otherwise. If not, why is this not the case seeing as reflection occurs AFTER rotation?
vocal sleetBOT
Simple question here regarding matrix linear transformations:
I have to find a r...
ashen remnant
think about what happens when the transformation gets applied to a vector
in the first case you would get
Rotation matrix x Reflection matrix x vector
so the vector actually gets reflected and then rotated
abstract walrus
you're saying it's the second option?
quick crag
Think of it this way. Let M and N be matrices, and v be a vector.
M N v is the vector meaning M (N v), which is "do N, then do M"
heavy yoke
matrices are like functions in that they apply "right to left". so for example sin(cos(x)) applies cos first and then sin
abstract walrus
ah those explanations are understandable
second option it is
cheers all.
.close
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versed pelican
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versed pelican
Can someone explain the jump from first to second step
Shouldnt the 7 be in the denominator?
Bc isnt 7^n+1 just 7^n times 7?
autumn idol
what does / mean there ?
versed pelican
And flipping the fractions would put 7^n+1 in the denominator
Divided by
Fraction
Top is a_n+1 bottom is a_n
autumn idol
maybe 7^n isn't included in the fraction
versed pelican
They make it seem like it is
autumn idol
There should be parentheses there tho
But if it isn’t like that then 7 should be in the denominator
versed pelican
Huh yeah i think they must have just made a typo or something
autumn idol
yeah porbably
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versed pelican
There we go
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atomic hill
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atomic hill
hello i am trying to show that it isnt surjective how would i go about doiong that
i need a hint to push me in the right direction
heavy yoke
try a few examples of elements of N × N and try to find their preimages
and if you can't, try to show that they don't have a preimage
atomic hill
try a few examples of elements of N × N and try to find their preimages
welll i mean i could just brute force it
bu like i feel like that would do no good
icy ocean
i need a hint to push me in the right direction
think of the elements in the codomain whose first entry is prime
atomic hill
think of the elements in the codomain whose first entry is prime
ok well you have 1, which is gotten by 1, 1
oh shit wrong question again
ok wait lemme pull out a scrap pape
@icy ocean its always gonna create a distinct element in teh co domain
but im still confused on how i am supposed to show that it isnt surjective
there has to be an element that isnt mapped
in the co domain
icy ocean
if p is prime and p = nm, what can you say about m and n?
icy ocean
m has to be p
icy ocean
so, is there a preimage to (7,2), for example?
atomic hill
ok so i just do a direct counter example
icy ocean
you simple must show an element of the codomain which does not have a preimage under f
and justify why so
icy ocean
on the first line of the argument, it should be "its only divisors"
to simplify it, you could just that there does not exist an integer m such that 2m = 7
atomic hill
oh ok alr thanks
atomic hill
how do i show that this is surjective, showing surjectivity seems confusing
heavy yoke
given any k, try to come up with some formula (doesn't have to be the only possible formula)] for n and m which gives f(n, m) = k
atomic hill
given any k, try to come up with some formula (doesn't have to be the only possi...
do i show that more than one thing can map to it or smth like that
more than one m and n
i am a bit confused on how id go about doiong that
heavy yoke
that isn't really relevant to surjectivity, just injectivity
for surjectivity, just show that at least one (m,n) is mapped to each k
atomic hill
well we are trying to shw surjectivity here tho
i mean like im a bit confused
how tf are you supposed to do that
plus like if there is an element in the codomain that isnt mapped then its intantly not surjective
heavy yoke
we would like to show that each element in the codomain is mapped to at least once
atomic hill
we would like to show that each element in the codomain is mapped to at least on...
how would you go about doing that tho
heavy yoke
we don't care if it happens more than once, just showing that it gets mapped to once is enough
so we would like to come up with a formula which associates each element in the codomain with one preimage int he domain, if possible
atomic hill
oh ok
ok
so lets say f(n.m) = k
and k = m + n -1
given this since its (m,n) in N^2
we know that it is mapped to every number
@heavy yoke is this corret
heavy yoke
well we would like to show that assuming k is a natural number, you can give a solution for m and n in N
so can you give me a formula which takes in k, and gives me positive integers m,n?
atomic hill
a formula that takes in K and gives you positive m, n
m = k - n + 1
and n = k - m + 1
@heavy yoke im confused
how does this work
heavy yoke
well you can see that at the moment we have a bit more freedom than we know what to do with
atomic hill
yea math is hard man
heavy yoke
it might help if you arbitrarily fixed one of the two variables (m or n) and solved for the other one in terms of k and the fixed variable
atomic hill
it might help if you arbitrarily fixed one of the two variables (m or n) and sol...
😭 this sounds way too complicated
heavy yoke
not really
just choose a very simple value for either m or n
then you have less to work with
heavy yoke
well we can't fix both of them
but for example let's fix m to be 1. can you then find a formula for n in terms of k?
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languid tree
Hi, I'm having trouble with an algoritm tion
vocal sleetBOT
Hi, I'm having trouble with an algoritm tion
languid tree
Im just confused where to even begin. We've learned about the Dijkstra algorithm, max flow, and max matching but I'm not sure how to apply those concepts to this problem
I think I should be using the max matching technique. It's just a weird problem because it says describe the algorithm you would use
Would I just say maximal matching where each square is a vertex and there are edges between each square next to each other?
ashen remnant
if you learned about an algorithm to find the max matching then you can probably cite that
ashen remnant
i would say something like
- check whether there are the same number of squares of each color (if there aren't, then it's impossible)
- apply the max matching algorithm on the graph you described
- if the size of the max matching = half the number of squares, then it's possible, otherwise it's impossible
this would be an "algorithm"
languid tree
ok thanks so much! this was very helpful and I really appreciate it
ashen remnant
no problem
languid tree
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versed knoll
hi can i have some help for precalculus
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hi can i have some help for precalculus
rugged orchid
!da2a
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versed knoll
why would you plug in arcsin(0.3052) instead of arcsin(-.3052)?
rugged orchid
,w arcsin(-0.3052)
twin meteorBOT
rugged orchid
that does not look like x is in 0 to 2π
versed knoll
what if u +2pi
rugged orchid
,w arcsin(0.3052)
twin meteorBOT
rugged orchid
it makes more sense looking at a graph i think
versed knoll
what abt unit circle diagram
rugged orchid
rugged orchid
what if u +2pi
this is the right intuition
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fringe cairn
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paper depot
fringe cairn
uh
nothing much
i just dont understand it
i thought it would be 118
since central angles are equal to its arc
but ig not
paper depot
since central angles are equal to its arc
these are not central
paper depot
when you have two intersecting chords like this there's a theorem which says that angles SRT and LRU are each equal to half the sum of arcs ST and UL
fringe cairn
sorry
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humble temple
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@humble temple Has your question been resolved?
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@humble temple Has your question been resolved?
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@humble temple Has your question been resolved?
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@humble temple Has your question been resolved?
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@humble temple Has your question been resolved?
random wave
You might not have any answer because some of the notations in the statements are not standardized.
Personally I can't see what is this m thing, as well as what is this K(97). But the E, I'm pretty sure it stands for the mean value, since it is normalized but ... That's pretty much it
So as a consequence, you would need to clarify it, then create a new post
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true juniper
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true juniper
Can someone explain why I would +13 first
PEMDAS would have me do otherwise no? Or since im only face with what I have, I have to do that first
outer warren
+13 to both sides isn't the first thing that you "must" do
but in many cases its more convenient to work towards first isolating -9x or 9x
and not introduce fractions until the end / when required
true juniper
So always isolate the variable first?
outer warren
not an "always" / "must" situtation
its just more convenient if you do
true juniper
ive noticed when I do them in different orders I get different answers
outer warren
if done properly, the end result will always be the same
outer warren
if you're getting something different, you messed up somewhere
true juniper
So for example I can divide by 8 or subtract 7 from both sides and will get the same result
let me test
ah well no because sometimes ill get a deicmal right
outer warren
if dividing by 8 first, make sure you're dividing the whole side by 8,
not just whatever term happens to appear first
leave expressions as fractions
don't round / use a calculator to get decimal approximations
e.g. leave 31/8 as 31/8 and work with that
true juniper
Yes I did notice when I get decimals it cant be that so I usually backstep and add or subtract first
These two steps are extremely simple but you gotta know the rules
thanks
outer warren
wdym it can't be that
true juniper
It cant be a decimal it has to be a whole number
so I correct myself and do the other thing first
I.E not the nunber with the variable
outer warren
is that stated in the question / a restriction of the problem?
outer warren
solutions to equations aren't always nice, and won't necessarily be integers
and intermediate values don't necessarily need to be integers either
dividing both sides by 8 is perfectly legal,
and 31/8 can be represented as a terminating decimal,
that in no way means this process is invalid
outer warren
as mentioned, as long as the steps are valid,
the end result will be the same
outer warren
your manipulation was invalid
true juniper
oh
paper flume
$\frac{n+5}{-16} \neq \frac{n}{-16} + 5$
twin meteorBOT
Charky
paper flume
hint: we have to times by something both sides of equal sign
true juniper
so we multiply x -16 to both sides
outer warren
just -16
paper flume
so they cancel out
outer warren
(don't use x for multiplication)
true juniper
yea I should use parenthesis
outer warren
and you already used the word multiply
paper flume
$\times$
twin meteorBOT
Charky
paper flume
yea I should use parenthesis
now what do u get
true juniper
W BOYS W
paper flume
good job
outer warren
if you wanted to do subtraction/addition first,
you'd wan't to first split the fraction
$$\frac{n}{-16} - \frac{5}{16} = -1$$
so the value you'd want to add to both sides would actually be $\frac{5}{16}$ \
$$\frac{n}{-16} = -\frac{11}{16}$$
and multiplying both sides by -16 will give you the same result of $n = 11$
twin meteorBOT
ℝαμOmeganato5
true juniper
woah
outer warren
like i won't call it a hard rule, just convenience to do multiplication first there
one of the basic principles of equation manipulation is applying the same operations to both sides,
just do what you feel will help work towards isolating your variable
vocal sleetBOT
outer warren
also helps to explicitly state your intention when still new to this
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summer carbon
Need help with this question, losing my mind
vocal sleetBOT
Need help with this question, losing my mind
summer carbon
I determined the critical points were x^2=0, x-3=0, (x+5)^3=0 to get x= 0,3,-5. I'm just not entirely sure where to go from her e
paper flume
yes
easiest way is to literally test points between those values
u have the following boundaries to test, x < -5, -5 < x < 0, 0 < x < 3, x > 3
heady vine
check where the inequality doesn't hold
for x^2>0 hold for R-{0} but then a value like x=2 wouldn't hold in the original inequality
summer carbon
by testing them am i just plugging them into the formula as a whole to see if it's greater than 0?
so -5^2(-5-3)(-5+5)^3>0?
paper flume
yeah, but not the boundary points, cuz its greater than
at the boundary points the equatin is equal to 0 not > 0
so u could test like, x = -10, x = -1, x = 1, x = 10
note that x^2 > 0 for x not 0, so u can look at the other two only
summer carbon
wait explain that last part for me
paper flume
for example at x = -10, (-10 - 3)(-10 + 5)^3 = (-13) * (-5)^3 > 0
paper flume
wait explain that last part for me
doesnt matter what x value for x^2, it will always be positive for x not 0
therefore x^2 > 0 no matter what
its just a shortcut
summer carbon
so i really only have to worry about the latter part of the equation?
paper flume
yep
summer carbon
rah one sec
rugged orchid
There’s a much easier way to do this
summer carbon
so the neg 13 x neg 5cubed is -1625 which is less than zero, so that doesn't work right?
rugged orchid
You’re given the inequality in the factorised form of a polynomial
The sign of the highest power tells you the general shape
Each factor tells you the roots
And the power of that root gives its multiplicity
You can easily sketch the polynomial
paper flume
so the neg 13 x neg 5cubed is -1625 which is less than zero, so that doesn't wor...
its pusitive
do yk how to graph it
it is alot easier if yk
rugged orchid
Graphing is a lot easier
paper flume
yeah ur right
summer carbon
@rugged orchid i think the way that charky is doing it is the way we were taught, which is how the prof wants us to work it out
we haven't learned about graphing it
rugged orchid
<@244390699431100416> i think the way that charky is doing it is the way we wer...
Perhaps, but it’s good to be wary of other possibly better techniques
paper flume
we haven't learned about graphing it
ah
rugged orchid
Ah I see
paper flume
i was taught to do that too at first
rugged orchid
My curriculum spent a lot of time teaching us curve sketching
summer carbon
this is math for business and economics, idek if we'll cover that. plus i switched to nursing to this won't really be applicable in my future lmao
rugged orchid
They don’t teach math because of specific math concepts, it’s more generally applicable as a way of thinking and solving problems
summer carbon
well i was a finance major which is why the advisor suggested this class over different math course
rugged orchid
Testing points vs curve sketching is an example of 2 pretty different methods for solving this problem, but one is much easier and faster, so it’s about picking the right tool for the job
summer carbon
understood
so i got that -10 and 10 fit the equation, but -1 and 1 do not. so its (-oo,-5)U(3,oo)?
rugged orchid
Yes
summer carbon
i couldn't guess that even if i was drunk with a pencil man LOL
rugged orchid
When you learn curve sketching it makes a lot of sense
winter hawk
in general cauchy condensation test is good for weird logs
but do u know how condensation works
condensation says 2^nf(2^n) is our comparison candidate. i suggest trying to find the same candidate another way
typo mb
they probably found a different comparison candidate and used p series test on it
ig they saw $1/(\log n)^{\log n}\le1/n^p$ for some $p$ and for all large enough $n$
twin meteorBOT
ロケットジャンプ
winter hawk
it sounds reasonable but im gonna leave the details to u since i have a movie to catch
austere tulip
vocal sleetBOT
austere tulip
Can someone help on part c
@math helper
I don’t get the marking point
Why do u set it as 512b and -144a
<@&286206848099549185>
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little yoke
Teacher hasn't returned my lectures, is this correct? Law of cosines, solving for angle A
vocal sleetBOT
Teacher hasn't returned my lectures, is this correct? Law of cosines, solving fo...
kind light
no
edgy gulch
2(10)(18.06) is not 36.12
steep crater
Ok, I'm supposed to do inverse cosine but my calc keeps saying math error
Is the value you are inverse cosining more than 1
edgy gulch
i think you messed up your decimal placement
little yoke
Ok, I'll redo it in a sec
edgy gulch
,w 21018.06
twin meteorBOT
edgy gulch
¯_(ツ)_/¯
little yoke
a=10 b=12 you accidentally swapped them
Nope, the example problem my teacher gave me is that
little yoke
Ok I'm definitely blind, thanks vro😭
kind light
Nope, the example problem my teacher gave me is that
is it the problem above with finding c?
little yoke
is it the problem above with finding c?
Yeah
edgy gulch
Ok I'm definitely blind, thanks vro😭
also what he said
the side on the left should be the side that is opposite with angle A
kind light
yeah that is swapped, but it didnt matter as the answer will be the same, if you continued what you were doing then you would be finding angle B instead of angle A
edgy gulch
in this case its 10
little yoke
Wym?
kind light
it should look like this, see a=10 and b=12
edgy gulch
i mean you could continue with what you had
but you have to subtract 180 with the two angles that you have
to get A
little yoke
Excuse my penmanship 👽
edgy gulch
yeah somewhere about that
though you should avoid rounding in the middle of calculations
to get the most accurate calculations possible
little yoke
Alr
But it should alr if I rounded off the c value before using it in finding angle A right?
raven bough
The author tried explaining the difference between the two questions but I am still not able to see it , can someone explain it to me
vocal sleetBOT
The author tried explaining the difference between the two questions but I am st...
raven bough
only the ques
vocal sleetBOT
@raven bough Has your question been resolved?
drifting whale
The author tried explaining the difference between the two questions but I am st...
So the best way to do this is to draw trees of intersection I think
If you want to visualize it
But basically conditional probabilities have so “symmetry” its like
Pr (A|B) = 0.5
Which wouldnt mean that Pr (A’|B) = 0.5 but it does not denote that
Pr(B|A) = 0.5
If you took a complement
I think thats what you were asking
raven bough
I think thats what you were asking
i didn't understand a word you said 😭
dumb it down a little
I didn't get what you mean by "symmetry" over here , even the author talks about it but i didn't quite understand it
drifting whale
So like
You know compliment theory
I think thats what they mean
For conditional probability you cannot just subtract to get another different condition. Like 1 - Pr(A|B) is not equal to Pr(B|A)
raven bough
but don't both the ques mean "atleast one child is girl?"
drifting whale
I think thats because of how the question is written
raven bough
so is it right or is it wrong ?
raven bough
💀
drifting whale
Just not the same context for each problem
raven bough
the more i think about it the more i get confused
raven bough
what whom how where when
raven bough
The statistics discord
ah wait lemme find it
drifting whale
I mean the question is kinda funky but its basically the same concept no? You know one of them is a girl and given this information what is the probability that the other is a girl
raven bough
The statistics discord
I couldn't find any 💀
can you share the link
drifting whale
raven bough
I mean the question is kinda funky but its basically the same concept no? You kn...
according to me both ques are asking whats the probability that atleast one is a girl
raven bough
https://discord.gg/statistics-554277759405260822
ayo vibe stats 💀
don't tell me people be using AI models to explain stats stuff
drifting whale
according to me both ques are asking whats the probability that atleast one is a...
Well you fulfilled knowing that atleast 1 of them is a girl
drifting whale
don't tell me people be using AI models to explain stats stuff
Nah its more like some dude named normality is a lie going off and explaining everything
drifting whale
Well you fulfilled knowing that atleast 1 of them is a girl
But its still a conditional probability
Since its asked you what is the probability that both are girls given you know atleast 1 of them are
raven bough
complicated sh*t
raven bough
Since its asked you what is the probability that both are girls given you know a...
exactly , so why aren't the ans to both the ques same ?
scenic ravine
vocal sleetBOT
twin meteorBOT
What a wonderful world !
scenic ravine
we thus have
sudden relic
!occupied
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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).
sudden relic
!occupied
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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).
scenic ravine
I mean, let me send my working first
paper depot
!occupied
that is not how you use this factoid
that's for when someone else barges into a channel that's not their own, but with a different question entirely than OP
sudden relic
that is not how you use this factoid
whats a factoid
scenic ravine
$2x= \lambda y
\
2y =\lambda x$
\
$\lambda = \pm 2$.
\
We thus have $x=y$.
\
We thus substitute that into the constraint to obtain $x =y= \pm 1$
\
Thus the maximum , subject to the constraints is $2$
twin meteorBOT
What a wonderful world !
paper depot
whats a factoid
our bot has a bunch of canned messages for common scenarios so that helpers don't have to retype the same thing a million times, and instead can just type a factoid name beginning with ! and have her say it
sudden relic
our bot has a bunch of canned messages for common scenarios so that helpers don'...
gotcha, thanks
paper depot
hold on, didn't we do this some days ago
or are you going over the exact same problem for the (n+1)st time
sudden relic
(n+1)st time
so wouldnt n just be the number of times that the question has been asked
and then the plus one is like the current time
and then st is like 1st kinda 'st'
i solved the problemm
scenic ravine
or are you going over the exact same problem for the (n+1)st time
Just revising some basic problems for my quiz tomorrow
paper depot
@sudden relic ... if you just want to goof around, may i please direct you to #discussion or #chill for that?
help channels are not the place for this.
sudden relic
help channels are not the place for this.
okay
i was just trying to help
but i will leave
scenic ravine
Does this work fine?
scenic ravine
thanks
signal pendant
**What a wonderful world !**
Are you sure that the maximum is 2?
Let x = 2 and y = 1/2 then x^2+y^2 = 17/4 >2
paper depot
it should make sense geometrically that there is no max
f(x,y) is the squared distance from (x,y) to the origin -- and the curve xy=1 goes off to infinity
vocal sleetBOT
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peak cloak
Heyy, could someone explain to me how im supposed to prove something is a generating set?
vocal sleetBOT
Heyy, could someone explain to me how im supposed to prove something is a genera...
peak cloak
I know a generating set can generate the entire span of a verctor space
But how do i show that???
real idol
But how do i show that???
take an arbitrary element of the vector space and show that it can be expressed using the elements of the generating set
paper depot
Heyy, could someone explain to me how im supposed to prove something is a genera...
missing info
you're doing linear algebra, yes?
so you have some (presumably finite) vector set S, and some vector space V containing S, and your goal is to show that span(S) = V right?
vocal sleetBOT
@peak cloak Has your question been resolved?
peak cloak
so you have some (presumably finite) vector set S, and some vector space V conta...
Yea, that's what im trying to dk
In R4
vocal sleetBOT
paper depot
.reopen
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✅
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@peak cloak Has your question been resolved?
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@peak cloak Has your question been resolved?
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hazy urchin
Hey o
hazy urchin
I tried doing the intercept theorum
Oh yeah the translation is
- The figure below shows two rulers, A and B, graduated linearly, with different units and positioned parallel to each other.
The figure also shows where the x-values (horizontal positions) of three points on both rulers coincide.
The value y on ruler B, which coincides with 27 on ruler A, is:
a) 54
b) 55
c) 56
d) 57
e) 58
Basically find out what Y is
hazy urchin
I don’t see one 😭
pearl wadi
not long lol
pearl wadi
no usually when u get stuck at a question u try finding a pattern instead of sticking with the regular method
hazy urchin
I tried
pearl wadi
trust me there are way smarter people here than me
vocal sleetBOT
@hazy urchin Has your question been resolved?
hazy urchin
did you get it now?
Yeah thank you
I’m doing thr other questions so
Just waiting to see if I get stuck again
The figure representa a profile of a reservation of water with side AB parallel to CD.
If a is smallest and b is 50% bigger than a, than the value of X is
I think I figured it out
Smallest cousin is 2
vocal sleetBOT
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lone linden
,w x=3/2 (x-2)
twin meteorBOT
hazy urchin
,w x=3/2 (x-2)
How do u input those white boards
lone linden
How do u input those white boards
What do you mean by "white boards"?
pearl wadi
x = 3/2(x-2)
2x = 3x - 6
-x = -6
x = 6
grim escarp
What do you mean by "white boards"?
i think they mean the wolfram solutions
hazy urchin
The commands for bots
A group of people was divided into two halves. In the first half, the ratio of the number of men to women is 1 to 2, and in the second half, the ratio of the number of women to men is 2 to 3. In the entire group, what is the ratio of the number of women to the number of men?
I have no clue
My guess was to add up both ratios
But it doesn’t seem right
Yeah I’m lost
<@&286206848099549185>
vocal sentinel
# A group of people was divided into two halves. In the first half, the ratio of...
U write both team man:woman
tranquil charm
write ratio for both
vocal sentinel
Men:women
team1 1:2
team2 3:2
vocal sentinel
LCM?
tranquil charm
eh
hazy urchin
What’s LCM
vocal sentinel
Lowest common multiple
hazy urchin
VERY carefully
There’s more woman in first and less woman in 2nd
hazy urchin
Lowest common multiple
15
tranquil charm
Example: LCM of 3 and 4 is 12
hazy urchin
Example: LCM of 3 and 4 is 12
Yeah I live in Brazil rn so I learned it in Portuguese
grim escarp
there's 2 ways id go about doing this
either 1. assigning a value to the total myself and working backwards with actual values
or 2. using 2x as the total and working in terms of x to get a final man/woman ratio in terms of x so that theyd cancel out and i'd be left with just the ratio
peak flower
there's 2 ways id go about doing this
either 1. assigning a value to the total m...
yeah, should we just let one half have x men and 2x woman, group 2 have 2y women and 3y man and solve
hazy urchin
So I didn’t know the abbreviation
hazy urchin
there's 2 ways id go about doing this
either 1. assigning a value to the total m...
Uh
hazy urchin
there's 2 ways id go about doing this
either 1. assigning a value to the total m...
Can u show an example pls
grim escarp
Can u show an example pls
which method
hazy urchin
1
grim escarp
alright so first id write down the ratios
hazy urchin
Mhm
tranquil charm
How many women
hazy urchin
But there’s more men in the 2nd
tranquil charm
He is talking about first
grim escarp
1:2 men to women in the first
we're only talking about the first ratio rn
we'll get to the second dont worry
hazy urchin
Why u putting it in 1:3 rn then
grim escarp
1/3 men and ___ women
answer this
grim escarp
Why u putting it in 1:3 rn then
it's 1:2
do you know what 1:2 means
let's say we have 3 apples
hazy urchin
do you know what 1:2 means
Yeah but u said 1/3
grim escarp
I want you to divide them in the ratio 1:2 between me and you
hazy urchin
1/3 men and ___ women
Look
grim escarp
how many apples will you get and how many will I
hazy urchin
how many apples will you get and how many will I
I will get 1 u will get 2
grim escarp
exactly! so to put this as a fraction, you got 1/3 of the total while I got 2/3
hazy urchin
Or ill get half what u get
hazy urchin
nope you were right the first time
Ok
hazy urchin
exactly! so to put this as a fraction, you got 1/3 of the total while I got 2/3
That makes sense
hazy urchin
if there's 1/3 men
2/3
grim escarp
perfect
hazy urchin
U have to finish the rest right
grim escarp
so let's say for example we had an original total
of 300
now let's see your question
"A group of people was divided into two halves."
hazy urchin
A group of people was divided into two halves. In the first half, the ratio of the number of men to women is 1 to 2, and in the second half, the ratio of the number of women to men is 2 to 3. In the entire group, what is the ratio of the number of women to the number of men?
hazy urchin
150
grim escarp
perfect, now on the first half apply the ratio 1:2 and tell me how many women and men are there
in the first half
hazy urchin
50 men 100 women
grim escarp
PERFECT!
hazy urchin
grim escarp
can you do the same for the second group now?
be careful though the ratio is the other way round this time
hazy urchin
can you do the same for the second group now?
60 women 90 men
hazy urchin
140 men 160 women then we simplify right
grim escarp
and now find the ratio of women to men!
hazy urchin
7:8
grim escarp
# A group of people was divided into two halves. In the first half, the ratio of...
last line ", what is the ratio of the number of women to the number of men?"
grim escarp
perfecto
the other method is more generalized
you'd take 2x as a total
so that each half would have x
right
hazy urchin
So u just have to put a placeholder number
hazy urchin
you'd take 2x as a total
Ok
grim escarp
So u just have to put a placeholder number
yes that or im explaining with x too
hazy urchin
so that each half would have x
Right
grim escarp
right
then youd apply the ratio on x
meaning in the first group youd have 1/3 x men and 2/3 x women
hazy urchin
then youd apply the ratio on x
Ok
hazy urchin
Oh right
grim escarp
important to specify
then
youd total them up
and then you'd find the ratio!
,w (16/15 x)/(14/15 x)
twin meteorBOT
hazy urchin
I don’t get it we did them separately
hazy urchin
Oh ok
grim escarp
I don’t get it we did them separately
it's the same as using a placeholder
just instead of a placeholder
you use x
because what if we took 100 instead of 300
then dividing 50 in 1:2 involves decimals
which can give rounding errors
this is foolproof
hazy urchin
Mhm
grim escarp
i hope this helped
hazy urchin
I just don’t get how u do this
How did u get from that fraction to the other one 8/7
Wait can u do the inverting thing to make it multiplication
grim escarp
yep
grim escarp
(it's called taking the reciprocal just fyi)
hazy urchin
I live in Brazil so idk the names in English
hazy urchin
I left Canada after 5th grade
tranquil charm
sam
hazy urchin
Sometimes I don’t understand well
tranquil charm
you can use latex to help them understand
grim escarp
you can use latex to help them understand
im in the process of learning latex
i just write it on a calc and ss for now
tex is hard 😭
grim escarp
18
hazy urchin
Damn
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
hazy urchin
I wonder if I’ll know as much as you when I turn 18
Let dev mask finish typing then I’ll type it
tranquil charm
$\frac{16/15}{14/15}$ can be written as $\frac{16}{15} \cdot \frac{15}{14}$
hazy urchin
What
twin meteorBOT
devthemasked
hazy urchin
U just swap the denominators
grim escarp
$\frac{16/15}{14/15}$ can be written as $\frac{16}{15} \cdot \frac{15}{14}$
as I said im in the process of learning tex rn
tranquil charm
U just swap the denominators
u multiply with reciprocal
hazy urchin
Mhm yeah
grim escarp
(if im being honest i havent even started learning tex 😭 im gonna after my exams in june)
tranquil charm
just check my code and u will understand a lot
hazy urchin
Imma go write this down now cause I have to present these questions tomorrow to my teacher
tranquil charm
ok
hazy urchin
Tysm
tranquil charm
!done
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
hazy urchin
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
median thistle
In the adjacent figure, the triangle OBM is isosceles.
a) Prove that the coordinates of M are (-√3, 1)
b) Calculate the trigonometric numbers of the 150° angle.
Can someone explain to me how to solve this?
The image in the book doesn't have that A line but the version of the problem i found online had it
sweet phoenix
In the adjacent figure, the triangle OBM is isosceles.
a) Prove that the coordi...
if MO is 2 would u agree that MB is also 2
so MA is basically cutting the triangle in half, forming 2 right triangles
lets first find the length MA, remember we're involving the hypotenise and opposite side of the 30 degree angle here
sin theta equals opposite over hypotenuse
we know that theta is 30 and the hypotenuse is 2
median thistle
so MA is basically cutting the triangle in half, forming 2 right triangles
why do we split the triangle in 2
sweet phoenix
why do we split the triangle in 2
so we have right angles to work with
much easier
so the opposite side should be 2 sin 30
which if u input it in ur calculator, is 1
so would u agree M has a y coordinate of 1
sweet phoenix
ok
median thistle
which if u input it in ur calculator, is 1
this doesn't make sense
30+2 is 32
oh wait
sweet phoenix
30+2 is 32
u input sin 30 first
then multiply the whole thing by 2
so basically 2 lots of sin30
median thistle
u see it on ur calculator right?
yea?
median thistle
my calculator shows sin cos
sweet phoenix
my calculator shows sin cos
in all 1 button?
median thistle
in all 1 button?
yes
sweet phoenix
ah its alright
sweet phoenix
do u have the sin function displayed
median thistle
yes
median thistle
ok
sweet phoenix
and u would get something like 0.5
median thistle
0.9
sweet phoenix
0.9?
median thistle
0.988
sweet phoenix
maybe ur calculator is in radians not degrees
twin meteorBOT
sweet phoenix
basically how the sin function works
median thistle
ok what about the √3
sweet phoenix
A lies on the x axis, so its y coordinate is 0, so does it make sense that M's y coordinate is 1?
median thistle
A lies on the x axis, so its y coordinate is 0, so does it make sense that M's y...
i mean why not
it lies on the x axis tho
A
not y
sweet phoenix
now lets find the x coordinate for M
do u recall the pythagorean theorem
or pythagoras for short
sweet phoenix
mhm
whats our c in this case?
the hypotenuse
and our a?
the new length we just found, 1
so 4=1+b^2
because 2 squared is 4, 1 squared is just 1
so b^2 is 3
take the square root of both sides
b is square root of 3
that make sense?
median thistle
I'm so fucking lost I'm so sorry
i need to go on after school classes
math is not for me
i got a 14 the last semester
out 20
sweet phoenix
I'm so fucking lost I'm so sorry
where in my statement did u start to go off track
median thistle
where in my statement did u start to go off track
the pythagoras thingy
sweet phoenix
ok
do u have an issue with why it exists, or how to apply it to this situation?
do u have trouble knowing what is a b and c?
median thistle
how i use it
median thistle
do u have trouble knowing what is a b and c?
yes
median thistle
yes
sweet phoenix
and there is a very long one
longer than the 2 of them
which is the hypotenuse
like this side
u can see its the longest side of them all, but not by a lot
median thistle
i know the hypotenuse is the opposite side from the 90
sweet phoenix
i'll have to derive the pythag hold on a sec
so ur average right triangle
with a square attached to each side
lets call each side a letter
cuz it could be 10 could be 10000 we could make up anything
but for simplicitys sake lets call the shortest side a, the second shortest b, and the longest (hypotenuse) c
something like this
median thistle
do we choose what to name the sides
sweet phoenix
do we choose what to name the sides
we can, but lets stick to a b and c for now
convenience
median thistle
we can, but lets stick to a b and c for now
no i mean
can c become a
a become b
median thistle
ok ok continue
sweet phoenix
so we got a few squares
how do we find the area of them?
we know that the area of a square is length x length
aka length squared
so would it make sense for a square with length "a" to have the area "a^2" and "b" "b^2"?
median thistle
yes
median thistle
i don't mind
median thistle
ab²
sweet phoenix
should be equal to the big square, c^2
median thistle
i guess
sweet phoenix
that is defined for every right triangle
so apply this to our problem
lets make a square on each side of our "triangle"
our "question" here
we previously showed that the side is 1
remember i said the area of the 2 small squares add up to be the big square
so what should the area of our square equal
median thistle
? = 1 + 4
sweet phoenix
so rearrange the equation
and u would get ? = 4-1
which is 3
now
if the area of a square is 3
what is the length
sweet phoenix
mhm
so in our original question
we're moving sqrt3 spaces to the left
and 1 space up to get to M
bold star
vocal sleetBOT
vocal sleetBOT
@bold star Has your question been resolved?
onyx sapphire
Basically i want to find the slope for 30 min to 45 min but idk how to do change of y over change of x properly
vocal sleetBOT
Basically i want to find the slope for 30 min to 45 min but idk how to do change...
onyx sapphire
Basically which order the points should go
heavy yoke
you can pick any two points provided it's easy to read their coordinates
manic bay
Basically i want to find the slope for 30 min to 45 min but idk how to do change...
Y2-Y1 / X2- X1
Formula to find slope