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i seem to have something different
oops one moment
nvm, still different
what did you do?
4.88m?
80 something
That can't be right
,w integrate (1.2sqrt(x))
seems so
Alright thanks
I just get confused on how to integrate for these type questions
So if it asks "How far did the object travel in it's 8 seconds of motion" I would find the integral from 0 to 8 of v(t) right?
And if it asks "How far did the object travel in it's 8th second of motion" I would have to find the integral from 7 to 8 of v(t) right?
yeah
also yeah
๐
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Original qn is: f: R->R
f(xf(x)+f(y)) = (f(x))ยฒ+y
||P(c,x) ; c any constant => f is surjective
P(k,x) ; f(k) = 0 => ff(x)=x
P(f(x),y) =>( f(x) )ยฒ + y = xยฒ + y => f(x) ={+x,-x}||
||Now the point wise trap||
||let a,b such that f(a) = a and f(b) = -b; with a,b != 0. Then by P(a,b) we get:
f(aยฒ-b)=aยฒ+b
Case 1: f(aยฒ-b) = aยฒ-b
=> aยฒ-b = aยฒ+b => b = 0 (contradiction)
Case 2: f(aยฒ-b) = -aยฒ+b
=> -aยฒ+b = aยฒ+b => a = 0 (contradiction)||
Can smb check this soln
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How can I find a functions with images being f: R-> R ?
Anyone know what this even means lol?
f1 outputs all possible real numbers, f2 outputs just positive numbers, f3 inputs real non-integers, and f4 outputs only integers
[f1, f2 and f4 should be relatively easy to find examples of, f3 might need a bit of thinking for...]
@gritty pond Has your question been resolved?
So in that case, how are these functions?
i: f(x) = x
ii: f(x) = e^x
iii: attachment #1
iv: attachment #2
Because for each possible input, you have one and only one output
Hopefully plotting x and e^x should show why their images are all real numbers and strictly positive real numbers respectively
yes
What do u think about iii and iv? i feel like im cheesing it
Those work, f3 would have been the hardest of them all to think of an example, but yours is something that I would have thought of
[for f4, you could e.g. take the floor or ceiling of x]
Wdym?
floor rounds you down, ceiling rounds you up
Yep, $\floor{x}$ for the floor and $\ceil{x}$ for the ceiling
@pseudo ice
Well now you have 
So if x was replace by pi
for the floor function
it become 3?
and 4 for the ceiling?
Result:
4
,calc floor(pi)
Result:
3
What is this
can't remember, think that rounds you to the nearest integer if I recall properly, though I might be wrong on that one(!)
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is my first step correct
i dont think it is but idk how else to approach this question wihtout using integration?
umm what do i do
$g(x) = \exp[3f(x) \ln(f(x))]$, apply chain and product rules to get a formula for $g'(x)$.
Ann
what does exp mean
$\exp(z) = e^z$
Ann
i am using this notation for convenience
so g(x)=e^(3f(x)ln(f(x)) then?
yes that is what i said.
okk ty
umm how do i proceed since i dont know f(x) or ln(f(x))
or is this evem correct
this seems correct to me!
okk i thought so, but how do i proceed and find g'(0) since this equation has both f(x) and ln(f(x)) which i dont know?
hmmm but you do know what f(0) is
no, whats in the question is all i know
so f'(0)=3x+2
and i cant use antiderivatives cause its not been taught yet
No that's wrong
oh
you are misinterpreting
is this why ive been stuck bruh ๐
the equation of any line is $y = mx+b$, with $m$ being the slope of the line and $b$ being the $y$-intercept of that line
so like Include the tangent to it here
ok so f'(0) is 3 then?
yes
and f(0) is 3x+2?
no
that doesn't make sense even how are you evaluating at x = 0 but still getting an expression with x? ๐
๐
anyways like this is the tangent line of the function f(x) at x = 0
meaning the equation of the tangent line, y, and the function f(x) share a common point at x= 0
if you evaluate the tangent line at x = 0 you also find f(0)
umm so f(0)=2?
yeahh
yeppie
yeah just plug and chug ๐
omg yayy
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What do i do with the curve ontop of 2 and 4
What's the question
What's a
Also the x any y intercepts
Solving for a
What is a
I dont know how to describe a
What were you told the definition of a is
Lemme check my notes
Uh sry for wasting your time cause i cant even find what a is or its definition in my notes or the presentations provided by my school ;w;
are the instructions for your problem written down anywhere?
Nope
I think cher didnt put any instructions as he taught us last last week how to solve the problem ;w;
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question: where did the t+4 go? xD
0*(t+4)=0
multiply t+4 on both sides
o h
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find all X for which this holds true
does this have solution?
because i came to this
0=1 and that is vontradicuton
if you've got a contradiction then theres no solutions
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,rotate
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I'm having a problem with a question in my Mathematics class in computer science. Let me break it down.
We have a set A containing the following 5 sets:
{1}, {2, 3}, {2, 4}, {1, 5}, {5, 6}
We have a set B containing the following 3 sets:
{1, 2}, {2, 3, 4}, {5, 6}
Let R โ A ร B be the binary relation defined as
(X, Y ) โ R โโ X โ Y
How can I describe the relation R?
I first need to map it with arrows, something like this:
but connected by arrows
So far I've come to the conclusion that:
{1} --> {1,2}
{2,3} --> {2,3,4}
{2,4} --> {2,3,4}
{1,5} (not sure about this one)
{5,6} --> {5,6}
{1,5} is the only part I'm struggling with
Why do you think there should be a set S from B s.t. ({5, 6}, S) is in R?
If there's no such S, then just don't mention any pairs containing {5, 6}
I dont really know what you mean by this. Sorry
R is just {({1}, {1, 2}), ({2, 3}, {2, 3, 4}), ({2, 4}, {2, 3, 4}), ({5, 6}, {5, 6})}
That's it
So {1,5} and {2,4} map to nothing?
It's fixed now
Alright, {1,5} to nothing then
But {1, 5} still does not map to anything
I thought that to start but I wasnt sure because I then have to say if theyre total, single-valued, injective and surjective
And given {1,5} maps to nothing, it cannot be total, single-valued or injective
I'm still not sure if its surjective or not, the definitions I find are very unclear. I know that the broader definition states that every element in the co-domain must be mapped to however I'm not sure if every element in the domain needs to be used. Can you help with this definition?
Not every element from the domain needs to be used to prove surjectivity
Is surjectivity in your case defined only for functions or for relations in general?
Simply checking if the relation R satisfies it or not. No mention of functions.
"For each of the properties listed below state whether R satisfies it or not."
So I would say relations in general
In which case it would be surjective i guess
Alright, this R is indeed surjective then
Would I be right in saying R is not total, single-valued or injective?
I think it is single-valued though
Assuming by that you mean that if (x, y) and (x, z) are both in R, then y = z
Is that your definition?
The definition I've been working with is "To be single valued it must map each input to at most one image"
Yeah, that's the same
Oh I see how that could be seen as single-valued
This R is single-valued
becuase 0 is at most one isnt it
Right
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I need help with this riddle please.
47 21 63
27 48 95
16 35 ?
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ok
joke answer: 42, because the polynomial f(x) = -72 + (183013 x)/168 - (21180617 x^2)/10080 + (2430277 x^3)/1440 - (4024453 x^4)/5760 + (23257 x^5)/144 - (60533 x^6)/2880 + (14491 x^7)/10080 - (1619 x^8)/40320 has values f(1)=47, f(2)=21, ..., f(8)=35 and f(9)=42
No jokes! He's serious
the point is more that riddles of these form always have more than one solution because you can make up a solution
like I did
It has a pattern.
yes. the polynomial I gave
I am too dumb for that.
well, if you could provide any options, it would really narrow down possible solutions
It isn't 49
calculate the difference of each column
๐
I doubt it's 1364189472 either
the pattern is kinda obvious
Please tell me
Do it yoursel
27-21=6
Math hard
Yes
Why not?
Because it's hard
Reverse continuation from a, b times.
I would rather solve TDSE with a time dependant complex potential
a - b = a <- b times
could also be 113204/1689 because then the matrix is singular
What
jokes aside, I dont see the pattern
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substract 2 on both sides
operate so you only get one fraction
when is a fraction positive?
Yea it would seem so
But actually you have to times the top and the 2 by (x^2-4x-5)^2
To solve the quadratic inequality
@past gull Has your question been resolved?
Yo give me a second @past gull
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herro
,, \sum_{n=0}^{\infty}\frac{5+2n}{(1+n^2)^2}
HeccinTech
how in the fucc do i calculate the convergence of this
its literally my last question and im so stucc
what i have tried
i have tried breaking them up in to different equations like 5/((1+n^2)^2) + 2n/((1+n^2)^2)
and knowing 5 goes to zero ur left with
2n/((1+n^2)^2)
i know it converges to 1/4
but this doesnt proove it
im so stucc
i tried to also do limit testing
but that shiets its self because n goes to zero
and by limit comparison test n is supposed to start at 1
so
can someone with neurons that actually fire
take a shot at this
cuz my neurons have decicided to stop existing
@calm willow Has your question been resolved?
<@&286206848099549185>
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@calm willow Has your question been resolved?
help
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Yo
I need help again
I can't even make sense of this question
Anyone??
Can any of yall atleast explain what I should do
I am confused
Hello???
Maybe try describing the set they ask you about in words?
or you can try drawing a venn diagram
that always helps me when i thinkof set operations on two sets
Tf is Morgan's law
I am gonna do that wait
Okay so
How do I draw this in a Venn diagram
A minus B union B minus A ??
Kinda: I meant more like โstuff in A that isnโt in B, andโฆโ
The thing is, I don't know which one is greater
It just says both A and B are non empty sets
A-B is A intersect. ~B
@wraith gazelle Has your question been resolved?
I got it yall
@wraith gazelle Has your question been resolved?
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The characteristic polynomial of this system is $-(\lambda - 4)^{3}$. I'm confused on finding the general solution to this system since the solutions are repeating (multiplicity of 3). Any help is appreciated!
zoga
If I recall.... If $f(t)$ is a triple solution to your DQ, then your three homogenous solutions are $f(t)$, $t\cdot f(t)$, and $t^2\cdot f(t)$.
SWR
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A and b
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What do you know
close one of your channels
I think the quadratic function of the first graph is f(x) = -2(x-3 ) ^2
Ok
can't be -2
2(x-3)^2
yes
Yes because it's upwards
mhm
And the second one
Is that right
Thats how the form goes
Yep its correct
Plot it in desmos and check
You can just sub in x = -2, and -1 and see y value
That too
Funny question how did you get that?
Ok
@vague needle Has your question been resolved?
Yes
@vague needle Has your question been resolved?
Not yet
<@&286206848099549185>
I think this is wrong
And this too๐ฅฒ
Are u sure
?
.
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how can I rationalize this?
$\frac {1}{K \sqrt{K+1} + (K+1) \sqrt{K}}$
beautiful man
SWR
oh, so just the conjugate, i thought there was something more
i rushed and expanded the brackets
thanks
.close
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Anyone know why this is true?
x here is cartesian product apparently
How does the and symbol turn into cartesian product?
cookie2
@gritty pond Has your question been resolved?
Here, x denotes all the elements of A and C together (no reputation of common terms).
Same with y with the case of B and D.
As x and y are variables, think of them as sets containing all the elements of A and B ; C and D respectively ||(respectively means for the 1st variable takes the 1st value and 2nd variable takes 2nd value (always used to think why I need to give them respect...))||.
And a Cartesian product can be denoted by (x, y) for which both x and y are values.
And ร is another notation for when u want to use the name of the set.
So it's just teaching the notation, not anything complicated till this point.
@gritty pond Has your question been resolved?
So let me get this straight
If there's a x e.g. cartesian product symbol anywhere in the proof question, I make it (x, y) right?
If there is no x cartesian product symbol, i just make it x ?
Yes, but it depends on what the question wants you to do.
Please send the whole question if any
is a and b a subset of A? why or why not?
$$A\cap B \subseteq A$$
cookie2
Tell me what do u understand by AโฉB
Correct.
That means x is in A too.
Is (x is in A) the same as saying (x is a subset of A)?
So what is the problem with this question that u are facing.
$$\in=\subseteq$$?
cookie2
oh wait
What do u understand by subser.
Yes
subset of A means that this area is just part of A?
The selection of all those "x"s is a subset.
Subset means it's inside of the set.
?
cookie2
Yes.
Ok makes sense
now tell me is A U B will be a subset of A Or not.
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Hi i need help on #3 and #4 and im not sure if im doing this correctly
Okay are 1 and 2 correct?
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where did I mess up in this distribution with [1-cos^2x]? I multiplied it with sinx
sorry if it's very obvious
(1-cos^2)* sincos^2 = sincos^2 - sincos^4
oh so you multiply [1-cos^2x] with the entirety of sinxcos^2x?
I was distributing sinx
ye, have to distribute everything
$$(1-1)\cdot2\cdot3= 0 = 2\cdot3 - 2\cdot 3 \ne 2 - 2\cdot3 = -4$$
IV
sometimes constructing small sanity checks helps
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not sure how to do this, could anyone help?
i understand that
Yeah look up exponent rules
thats not the issue, its a negative exponent on the right tho
i have to express it as positive exponent
well, what happens when you subtract a negative number
^ forgot to mention this MB
anyone know this??
Educational institutions โ Suppose that someone can buy multiple licenses for Word Search Maker software (for making word puzzles) at a total cost of C(x)=24โ(20x^2+250) dollars for x software disks. Do not include the units in youir answer
a. Find the marginal cost function rounded to 4 decimal places at x=200
answer
b. Find C(201 ) -C(200) rounded to 4 decimal places
answer
c. Are the answers close? Type Y for yes and N for no.
answer
N
go into anotha thread dawg
thanks
im so stupid i overcomplicated it @high rapids
i tried flipping -1/4 to make it positive
and got 1/3 as my answer
its supposed to just = k
so
$k^{\frac{3}{4}}/k^{-\frac{1}{4}}=k^{\frac{3}{4}-(-\frac{1}{4})}$
also, you cant just flip the exponent, a negative exponent different
InfinityMango
This algebra math video tutorial explains how to simplify negative exponents in fractions with variables and parentheses. It discusses the basic properties of negative exponents and how they work. it provides a nice introduction into the topic. This video contains plenty of examples and practice problems for you to work on.
Access Full-Lengt...
Org chem is the goat
he has carried me since my freshman year of highschool, if you ever dont understand a concept he probably has a video on it
Bro's a wizarding genius
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no
i'm pretty certain this is arccsc
so like, inverse of csc
may be not obvious but can you see that csc^-1(x) = sin^-1(1/x)?
csc=1/sin
mhm
why doesnt csc^-1 = 1/sin^-1
why would it
cuz csc = 1/sin
but it doesn't work like that with inverse functions
look
csc(y)=x
solve for y
oh when u take arccsc of both sides you get x=arccsc(1/sinx)
y=arccsc(x)
ye
but csc(y)=1/sin(y)
in that case
1/sin(y)=x
solve for y
1/sin(y)=x
sin(y)=1/x
therefore, y=arcsin(1/x)
which is what i claimed
does that make sense?
oh ye
then what
then you get arcsin(3/2sqrt(3))
oh wow
magic, right?
ye lol
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Hello math expert. I know a lot about politics and I argue about politics a LOT. But one thing I'm not good at is MATH. I'm so bad at it. I'm currently faced with a math problem I cannot answer with 100% honesty and truthfulness. I am all about having the truth go out to the people
Here is the information I have
The first image is the graph of the demographic of people who rape animals
The second image is the demographic numbers of people who are apart of the furry community
What I am trying to find here is the correlation percentage of each statistic
Here are factors I'd like to contribute
- Gender
- Race
- Age range
first of all
I'd like to find how similar these groups of people are by percentage
those are random google statistics
random google stats are not credible
you cant use them to make good faith arguments
secondly
thats a weird ass question buddy
You're right by the images show the source and the source provides the info. But that's off topic
I know its a weird ass question and I'm sorry
I'm not a math guy, I'm just a political debater
the number I've gotten is 99.18%
clearly a bad one given you use questionable sources
But I'm not good at math again
The first image is from JAAPL
how'd you do that??
the other ones arent even from the sources themselves
THis is JAAPL
Correct but the google excerpt takes from the source which is "Furscience"
and the other source is
Furry Fandom Wiki
and your reason to believe something called "furscience" is credible is...?
you are joking...
Becaues it's the home of the furry community
Who better to ask of the demographic of furries than the furries themselves
if youre using freaking fandom wikis
next youre gonna tell me you went on 4chan to find info
the hell
Riddle me this. If you wanted to find info on the backrooms, the best person to ask is the backrooms wiki writers is it not?
but thats entirely fictional
its really not?
if youre using questionable statistics
you get questionable answers
Yes. All I'm trying to find is the numbers
and thats bad math
but they are bad numbers
and misleading
I have all the sources you'd like I'm not an anecdotal type of guy
They're not misleading. They're almost intertwined with each other and by my findings 99.18% intertwined
but I may be wrong
thats why I need your help to get the true number
you have 2 sources related to the demographics and they aren't credible
if you cite that shit people will laugh in your face
The JAAPL is not credible?
what exactly did you find are 99.18% intertwined?
you have 3 categories
which ones are intertwined with which?
because you are looking for statistics
statistics are very different from fictional info
for info that is not based in reality you can ask the people who believe in it
you don't have any actual informatino on the demographics because the fucking furry wiki isn't a credible source
its not political
youre doing bad stats
its mathematical
anyone who is an actual data scientist
who would have access to the resources necessary to perform a decent study
that is entirely false
and an assumption that comes from where?
for all you know they pulled them out of their asses
you cant do data analysis on data you don't know is accurate
yes but if youre part of the academic community its much more unlikely
and these people are...
not
so find me actual studies
and then you can do data analysis
you ARE the god damn misinformation
youre promoting fake stats
ok then
show me the methodology of the studies done to find them
show me the authors of the study
show me those author's careers
show me the institutions theyre associated with
hmmmmm
they do seem to be backed by some actual reu's
what do their statistics have to do with their skill in math
one is data collection
the other is analysis
hmm
alright
lets say i believe these stats
how'd you get 99.18%
Ok ok hold on
Explain why you are doing these
What
No
Explain why youโre doing the addition
Is that covariance or something
Why is that statistically relevant
The sum I mean
I do not care whether or not you do mental math
What relevance does the sum have
What is the significance of the sum of those percentages
What
No??
Why would it do this
What are you applying
What theorem or statistical use
Shouldnโt be
If youโve taken statistics
You should know the names
Then you arenโt qualified to do statistical analysis
??
Maybe instead
You should be focusing on statistics thatโs been done
The numbers you got arenโt really relevant to anything
Of course it didnโt you made up random formulas to use
Why do you think that
Do you even know the correlation function
No no
Like
Have you calculated correlation
Thereโsformulas for this
What if I told you thatโs because most crimes committed are by men and most nerds are men
Or most people with weirder hobbies are men
That doesnโt follow
At all
Your analysis is flawed
Dude
If you donโt know anything about statistics
Donโt do statistical analysis
You think you see patterns
They donโt work
Thereโs probably a correlation to be found
Iโm sure
But itโs not going to be as high as you think it is
At all
No
Lmao
Itโs probably around a quarter of that
Iโm just eyeballing
But like
No
Please just quote professional research
Until you know stats
You arenโt the right person to do that yet
Since you dint have information
Itโs a good goal tho
Nope
You kinda arenโt
No you donโt
Lmao
You havenโt taken stat
No but this server is for learning math not getting others to validate your weird dislike for furries
This server isnโt for validating your personal phobias for other people
Please go somewhere else fox this question
Well
You shouldnโt be
Not because of what you are trying to accomplish
But because you are unqualified
You canโt combat misinformation if you dint even have information
please chumchumlol for the love of god go learn some statistical analysis
im not an expert, but the fact that 86% of animal rapists are male and 84% of furries are male does not constitute evidence of a correlation between furries and animal rapists
where is that number coming from
THE SAMPLE SIZE IS 60
yes i could guess that
where was the study done
yes
are you serious
these are just people found randomly on omegle?
quizzes*
you did this?
you conducted this study?
YOU WHAT!?
yes I know and i'm just going to ignore the fact that that's really messed up right now
Yes. It's my opinion that it's wrong to deceive and manipulate people into trusting you with information they wouldn't have otherwise
YOU DON'T SEE A PROBLEM WITH THAT!?
YOU CAN'T JUST MAKE THAT GENERALIZATION
I agree, but this is not an example of that
especially because you went in not thinking that furries are raping animals
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You said you wanted to give these numbers to organizations. What analysis could you possibly do that would be better than the analysis of the phd statisticians those organizations already have
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How does the limit when b is infinity on 2arctanx = pie
arctan(infinity) = arctan(1/0) = pi/2
Thatโs why we say tan(pi/2) is undefined
Therefore 2arctan(1/0) = 2 * pi/2 = pi
@tranquil tulip
How does 1/0 get pi/2?
Ohhh ok, I understand that part now but how does the arctan(inf.) get to (1/0)
Why do we use pi/2 specifically
Range of arctan is (-pi/2, pi/2)
,w arcsine
There
Woah
Wolfram gives the ranges for all 3
And look at the last image
lim x-> infinity arctan x = pi/2
Ok thank you so much
Np
.close
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for this one, the sum is 1
so I thought it should converge
but my book says its divergent?
but I thought divergent was only for plus minus infinity and stuff that does not exist
$\sum_{n=1}^{\infty} 1 + \frac 1n= \sum_{n=1}^{\infty} 1 + \sum_{n=1}^{\infty} \frac 1n$
Stephen
Funny thing is even the last sum diverges
what does this mean ;-;
am i not suppose to take limits?
$\sum_{n=1}^{\infty} \frac 1n$
Nel
This one diverges
and since this one diverges the whole thing does i see
I mean Stephen showed you it gets split into this one plus another one that very obviously diverges
My point is, even if the individual terms converge to zero, the sum may still diverge
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You could go by contradiction maybe?
If thats the case
if A is invertible
what does that tell us
I recall the professor wanted us to stay away from determinants
Well if A was invertible, and A^2 = 0, what's the value of A?
the determinant way is the easy way :dismay:
assume A is invertablw... then A^2= 0...
AxAxA^(-1) = 0xA^(-1)
@humble oak does this first step in the contradiction proof help at all
do you see how to continue to finish the contradiction?
can you explain where you got this AxAxA^(-1) = 0xA^(-1)
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iโm supposed to identify similar triangles and find each measure
Do you see which triangles are similar
HGD and HGJ
because of angle angle
yes
Ok you can find another set of similar triangles. Think about what angle DJH must be
wdym
Since HGD and HGJ are similar, that means you know angle GHD and angle DJH are the same
Try drawing all the triangles side by side in the same orientation and see if you can find the ratio between any of them
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how do I show this on the complex plane?
e^ix
this is your standard e^ix format for a complex number
cosx + i*sinx
Which is a circle centred at the origin with radius 1
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waittt thatโs sus
?
because the ans shows a linear line graph
well yeah, Re(z) is the x coordinate and Im(z) is the y coordinate. Just plot x+y = 1
Yeah. Its easier to think of Re(z) and Im(z) as your x and ys on the cartesian plane. And yes, its just a linear line graph
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I have to solve this using Bayes Law/Theorem
indeed
I'm just kinda confused on breaking down the problem, I guess
I have P(A), P(A|B), and P(A|B')
what are A and B?
A is 0.94 and B is 0.06?
so P(A) = P(0.94) = ?
It has us doing tree diagrams for it like this
generally these questions are easier if you apply more natural letters to the events
so try using H and W for the event that the husband or wife respectively is employed
Yeah
Well so what I'm debating is how I would want to first write this out
In this example of "rains" and "does not rain" for the first tree
I was thinking "Husband employed" and "husband not employed"
but I feel like thats wrong
why do you think it's wrong?
I guess because I have no idea how I would solve for when the husband is unemployed
solve for what?
read the third sentence of the question again
Yeah, at least a husband or wife had to be employed
Which is also what confuses me
so if the husband isn't employed
Yes, the wife has to be
indeed
I just don't get how you would know.
because the question tells you directly
What that percentage would be for the wife
I know that, I meant how would you tell what the chance for the wife to be employed would be seperately from the husband?
if the wife has to be employed, what is the probability that the wife is employed? (conditioned on the husband being unemployed)
1?
1
So the other one would be 0
Then its
(0.96*0.72)
for the success
and (0.960.72)+(0.041) for all possible occurrances of the woman employed?
what's a "success"?
good branch, good result, good path, success
is used in another area
Basically just good results divided by possible results for what its asking for
Which is a employed woman with a husband
an employed woman with an employed husband would be preferable

