oh shit
#help-19
mystic saffron
Nice
spiral crane
and for the next 2 space?
n-3/n-1-?
for the one above?
i just wanted to confirm if im doing it correctly thats all
mystic saffron
Which one again ?
spiral crane
1
mystic saffron
And what's your answer
spiral crane
n-3/n-1 -?
mystic saffron
Yep!
mystic saffron
Yes
spiral crane
hm?
mystic saffron
Man probability always gets me confused
spiral crane
oh?
mystic saffron
You removed a non white ball from n-3 non white balls
How many are you left with?
(balls) XD
spiral crane
How many are you left with?
i mean
they are not being replaced
and you're picking up 2 right?
so
if previously in first ball
not white was n-3/n
OH
mystic saffron
Yes
mystic saffron
ā
odd edgeBOT
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south igloo
Why does it equal one? I tried using derivatives and got 0.31
quasi sparrow
why are you using derivatives anywhere
south igloo
It was suggested š¦
quasi sparrow
by?
south igloo
ah
quasi sparrow
,tex .FTC1
clever fjordBOT
riemann
meager sail
||sorry to bring this previous question into this, but the solution starts off like this, thanks for the help tho ||
Sorry above message is not related to this
quasi sparrow
||sorry to bring this previous question into this, but the solution starts off l...
next time open your own channel or post it somewhere else
south igloo
,tex \.FTC1
would it be to plug in pi/4 and 0 into the equation and then subtract them?
quasi sparrow
would it be to plug in pi/4 and 0 into the equation and then subtract them?
what equation are you referring to
south igloo
sec^2 x dx
quasi sparrow
no
quasi sparrow
**riemann**
if you don't know what antiderivative is, find that first
odd edgeBOT
@south igloo Has your question been resolved?
odd edgeBOT
@south igloo Has your question been resolved?
mystic saffron
odd edgeBOT
mystic saffron
the system is telling me one of these is incorrect, but i'm struggling to see which one it is
forest sky
for 10, consider the xy, yz, and xz coordinate planes
clever fjordBOT
AĻ
odd edgeBOT
@languid helm Has your question been resolved?
odd edgeBOT
@languid helm Has your question been resolved?
molten sparrow
odd edgeBOT
molten sparrow
are these right?
teacher didnāt provide an answer key so I kinda just gotta rawdog it
Iām stuck on 3
elfin zodiac
$x^2-4x+4-1$ is not $x^2-4x+4$
clever fjordBOT
Samuel
elfin zodiac
Unless i am not reading well ur writing
clear current
You're forgetting to subtract the 1
elfin zodiac
4-1 is not 4, is 3
golden marten
what happened to the -1 in q1
elfin zodiac
odd edgeBOT
@molten sparrow Has your question been resolved?
red blade
odd edgeBOT
red blade
Not exactly sure how to even startš
earnest nebula
do u know the that $sin^2theta+cos^2theta=1$?
clever fjordBOT
Bihandu
red blade
But isnāt that only for cos squared
earnest nebula
and u should know that in the 2nd quadrant
cos->(-)
tan->(-)```just square cos theta and u get cos squared theta
red blade
So is sin 3/5?
earnest nebula
Ok Iām gonna solve the rest can u stay lmk if theyāre right š
k
earnest nebula
um
red blade
Is that a no
earnest nebula
np
odd edgeBOT
@red blade Has your question been resolved?
mystic locust
hello, i need help with this please
odd edgeBOT
hello, i need help with this please
mystic locust
i dont know how to do any of this
odd edgeBOT
@mystic locust Has your question been resolved?
dire cosmos
by alternate angles theorem, 5 = 2 and since 2 = 7, that means 5 = 7.
7 and 8 add to 180. note that 8 and 6 also add to 180. thus 6 = 7.
since 5 = 7 and 6 = 7, 5 = 6
sterile blaze
odd edgeBOT
sterile blaze
sorry, the commutator subgroup? also how did they get that the order is 1 or 47?
odd edgeBOT
@sterile blaze Has your question been resolved?
sterile blaze
i was guessing its order is something with 35 but then i realised im not sure if i can even come to that conclusion
from a previous part, they used the notation with G' denoting the commutator subgroup so I am assuming that it is as such
.close
odd edgeBOT
dire cosmos
Yes, you can write my explanation with those statements. For example my first statement "by alternate angles theroem, 5 = 2" could be represented by the 4th line in your list "if lines parallel, alternate angles are congruent".
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reef ivy
odd edgeBOT
reef ivy
when only looking at the denomenator
how did the person go from the 1st to the 2nd part??
is it possible to use trig identities/ is it even correct??
reef ivy
yeah but is it even possible with b being there
golden marten
yeah but is it even possible with b being there
there's no b infront of cos^2p?
reef ivy
no
golden marten
it looks right to me
reef ivy
someone said that it wouldnt work tho
cuz it would have to be like the part in pencil
and then you csnt equal them to 1
golden marten
but we're just dealing with cos^2(p)?
there's no B involved
cos^2p=1-sin^2p
just imagine substituting that in instead
which is fine because they are equivalent
golden marten
so theyre not using sin^2(x)+cos^2(x)=1
they are
but rearranged
to cos^2(p)=1-sin^2(p)
pale atlas
wait so where does the (b^2-1) come from
bĀ²sinĀ²p+1-sinĀ²p
1+(bĀ²sinĀ²p-sinĀ²p)
Taking sinĀ²p common
1+sinĀ²p(bĀ²-1)```wdym common
pale atlas
wdym common
Well if you have something like
ab+ac ,you can factor out a and write as a(b+c)
That's what I meant by taking common out
odd edgeBOT
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somber skiff
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fervent hawk
if you just want your answers checked, yea, they are both correct
fervent hawk
for this is it 17.1428572 feet?
very close, it's better to represent as a fraction
pale atlas
is it 109.848 feet?
You should show your work, instead of asking if your answer is correct or not š
That way is easy to check
somber skiff
sorry lol i do my work on a whiteboard thats why i dont wanna type it
odd edgeBOT
@somber skiff Has your question been resolved?
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obsidian yarrow
how would I go about solving this integral in terms of k?
k is a constant between 0 and 1.
obsidian yarrow
apparently the answer is literally just k
night raven
You can split it into 2 integrals and solve both
obsidian yarrow
I am kind of scared because apparently e^x/x and e^x/x^2 are not solvable via. elementary functions
night raven
Yeah this doesnt work
wicked kestrel
No it does, there's a funny thing you can do
lyric dust
diff?
wicked kestrel
First, is this e^ln business your doing or can you just rewrite them as k^t?
dapper canyon
how would I go about solving this integral in terms of k?
k is a constant betwe...
try differentiating this wrt k or ln(k)
lyric dust
oh nvm it is much simpler
lyric dust
First, is this e^ln business your doing or can you just rewrite them as k^t?
i think it is helpful to see it as product rule no?
wicked kestrel
If that's the intention then sure
dapper canyon
what
obsidian yarrow
try differentiating this wrt k or ln(k)
k is a constant
dapper canyon
ok you can view the whole integral as a function of k
lyric dust
what
night raven
Yes but k is still a constant
dapper canyon
it's defined pretty much for all k>0
wicked kestrel
There's no reason to do that
lyric dust
you are just integrating a diff here
obsidian yarrow
First, is this e^ln business your doing or can you just rewrite them as k^t?
it was like that originally but I thought it would be simpler with e as the base
this is the original integral:
lyric dust
i feel like this is getting convoluted for no reason
dapper canyon
we are just discussing different approaches
wicked kestrel
This is slightly different
obsidian yarrow
I made the sub t=1/z
wicked kestrel
That's cool
wicked kestrel
how would I go about solving this integral in terms of k?
k is a constant betwe...
Something fun happens if you split this into 2 integrals and then do IBP for the k^t/t one
lyric dust
you can rewrite the integrand if you want to skip some workingout but i think steakanator's suggesition makes more sense
odd edgeBOT
@obsidian yarrow Has your question been resolved?
obsidian yarrow
Something fun happens if you split this into 2 integrals and then do IBP for the...
lol that is so nice
it cancels out
wicked kestrel
Indeed
lyric dust
can't believe all of that simplifies to k
u might also be able to recognise the integrand as a product rule
directly
obsidian yarrow
hmm
lyric dust
which could save you a lot of time
but ig some might not consider it formal working out
lyric dust
i mean im not clever either
just kinda intuition
since -1/t^2 is diff of 1/t
and lnk k^t is diff of k^t
the integrand can just be collapsed into d/dt( (1/t)k^t)
obsidian yarrow
but ig some might not consider it formal working out
oh yeah, that's genius
the integral just boils down to this:
btw, this is the problem that inspired this integral:
and since the answer is just k, it's a uniform distribution
so fascinating
the integral was basically calculating the volume bounded by the curve (xy)^z = k
and this is how I calculated it
anyway, thanks for the help solving the integral lol
obsidian yarrow
[found it](https://www.youtube.com/watch?v=ga9Qk38FaHM)
yep, sorry for not linking it!
like grant said, I have no intuition for why this is true lol
just some tedious calculations and it happens to work out
obsidian yarrow
yw!
eager kiln
odd edgeBOT
eager kiln
is there any way to solve this problem a bit fast?
the method I thought of would take a lot of steps
for example this is what i got for āĀ²z/āxĀ²
ocean torrent
Didn't you ask this yesterday?
ocean torrent
Did you not get a response?
eager kiln
i did get a reply from @quasi sparrow to show my working
but then he went somewhere ig
so yea my problem is still not solved
@ocean torrent do you know some better way to approach this question?
odd edgeBOT
@eager kiln Has your question been resolved?
ocean torrent
Sadly I don't, was trying to think about it yesterday, but I could only get the tedious way.
A bit hard to read your handwriting, but I, personally, can't think of a better way to do it than you, so I'd wait to see if someone else has a simpler method. Also, do you have an expected number of marks for the question? That method could very well be correct if it's something like a 5 mark question
I've seen many big mark questions that do want it to be really tedious
eager kiln
Sadly I don't, was trying to think about it yesterday, but I could only get the ...
My teacher gave me this question in the assignment
there were 10 questions and no question had any marking scheme/limit
I will try asking her the weightage of the question, if it was to come in our exam
ocean torrent
Then there may not even be a faster way. Again, many questions do require that much working. You can wait for someone else to respond, but I'm guessing that by the time someone else gives a faster solution you'll have already asked your teacher
If your teacher says it'd be worth anything less than 4 marks then there probably is a faster way
eager kiln
Then there may not even be a faster way. Again, many questions do require that m...
hmmm but I do think that there is a faster way because the xĀ² āĀ²z/āxĀ² term, came out to be very symmetric
like very clean
ocean torrent
Honestly, mark schemes can be really wack. I've seen 5 mark questions only require 3-4 lines of math, other times they can need over 10, you'd probs be best just sticking with what you have and asking your teacher later
eager kiln
Honestly, mark schemes can be really wack. I've seen 5 mark questions only requi...
yup I will. thankyou
she just replied and she is asking for my working
ocean torrent
np, hope you find the answer
eager kiln
eager kiln
@ocean torrent I tried re writing my solution (I hope this is a bit more readable). This is just the xĀ² āĀ²z/āxĀ² term
odd edgeBOT
@eager kiln Has your question been resolved?
eager kiln
no problem
odd edgeBOT
@eager kiln Has your question been resolved?
eager kiln
<@&286206848099549185>
eager kiln
<@&286206848099549185>
quasi sparrow
Yea very few people are gonna read 5 pages of work with poor photo quality and barely legible handwriting. I suggest writing more neatly and picking a specific part of the 5 pages you're least confident about.
odd edgeBOT
@eager kiln Has your question been resolved?
eager kiln
Yea very few people are gonna read 5 pages of work with poor photo quality and b...
its too much to write again :/
i tried my best to write it neatly
i can tell the result that i got, if that helps
this is what i got
eager kiln
Yea very few people are gonna read 5 pages of work with poor photo quality and b...
I am confident about my answer. I just want to know if there is any other way to solve it faster
odd edgeBOT
@eager kiln Has your question been resolved?
odd edgeBOT
@eager kiln Has your question been resolved?
eager kiln
.close
odd edgeBOT
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Available help channel!
mystic saffron
How can I find the range?
odd edgeBOT
How can I find the range?
deft kestrel
How can I find the range?
what have you tried so far?
mystic saffron
what have you tried so far?
I thought it was E
I tried putting it's lowest value
I tried forming a perfect squared?
deft kestrel
I thought it was E
what made you think that?
mystic saffron
what made you think that?
I tried putting it's lowest value for cscx
but I know that bc there is a -6 it makes it complicated
and I have no idea what to do now
deft kestrel
right
deft kestrel
I tried forming a perfect squared?
so you had the right idea
deft kestrel
but I know that bc there is a -6 it makes it complicated
not sure why you think this
mystic saffron
not sure why you think this
it makes the other value lower
and maybe there is a point when it balances the best
to maximize it
deft kestrel
why?
it'd be hard to analyse the range with two separate csc expressions. You can analyse the range easily if it were a simpler expression. completing the square here would allow you to end up with just one csc
mystic saffron
it'd be hard to analyse the range with two separate csc expressions. You can ana...
yes
mystic saffron
ok, I think I see that if cscx = 9, that would make -5 the lowest value instead
and it's indeed C
I didn't stop to analyze it
thanks
deft kestrel
ok, I think I see that if cscx = 9, that would make -5 the lowest value instead
yeah if you just analysed the range without completing the square. you wouldn't know when the two csc's interact with each other, the range of csc is -infinity to +infinity, the range of -6sqrt(csc) is -infinity to -6, and the range of 4 is 4. out of this it's impossible to tell that the lowest value was -5, so you had to complete the square to say something more useful about the range
odd edgeBOT
velvet badger
Can someone tell me where I went wrong?
velvet badger
fr?
echo ginkgo
yea
echo ginkgo
it's completely fine yes
echo ginkgo
it's quite obvious to see on the matrix here yes
odd edgeBOT
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Available help channel!
rapid schooner
im looking at the solution for this problem and it dosnt make sense
nimble blaze
which part doesn't make sense to you?
rapid schooner
how my teacher solves it
nimble blaze
which step do you have an issue with
rapid schooner
second one
nimble blaze
they're applying the limit identity for sin(t)/t as t approaches 0
$\lim_{t \to 0} \frac{\sin(t)}{t} =1$
clever fjordBOT
āĪ±Ī¼Omeganato5
rapid schooner
ok so i checked my notes for that identity and yeah i got it, i completly forgot about it
it dosnt make sense but its exists
thanks
.close
odd edgeBOT
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inland niche
What is an equation of the line that passes through the point left parenthesis, 3, comma, minus, 3, right parenthesis(3,ā3) and is parallel to the line 5, x, minus, 3, y, equals, 35xā3y=3?
inland niche
How can i solve this really quick
5xā3y=3 , another line is parrelel and it passes through the point 3,-3
what is the equation for the other line
The only quick way i know of solving this is solving for y and then using y = mx+b to find the equation
fair prism
5xā3y=3 , another line is parrelel and it passes through the point 3,-3
Any line with the same coefficients will be parallel. So you need to a number c such that 5x-3y=c passes through (3,-3)
inland niche
Any line with the same coefficients will be parallel. So you need to a number c ...
how can i solve it fast
i know how to solve it
i have to solve for y
fair prism
This is the fastest way
You do not need to solve for y with the way I showed
Just find c
inland niche
How do i solve for c
fair prism
I mean find what c should be
Not solve for it
You can find it by plugging in the point (3,-3)
inland niche
I know how to find the coeffiecient and stuff basically what im trying to say is
Is there anyway faster way to solve for the equation of the other line than this:
y = 5x
y = 5x+b
-3 = 5(3)+b - insert points
-3 = 15 + b
-18 = b
y = 5x-18
fair prism
Yes. With the process I showed above
I will restate it
-
Notice any line of the form 5x-3y=c is parallel to the given line
-
Plug in (3.-3) to find c
Then you are done
!occupied
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
inland niche
Go to another help
inland niche
Yes. With the process I showed above
I will restate it
1. Notice any line of t...
Can we do an example
fair prism
Yeah do you want to give another problem or should I make one up
inland niche
hmm
What about 2x + 3y = c
How can we find the equation of another parralel line with points 2,-3
fair prism
We know any line parallel to this can be written as 2x+3y=c a number c.
We want it to pass through (2,-3) so the c must be chosen such that 2(2)+3(-3)=c. Ok well then lets just choose c= 2(2)+3(-3)=-5
Thus 2x+3y=-5 is parallel and passes through (2,-3)
inland niche
so how can i make a y = mx +b equation using the -5
fair prism
You can just solve for y in the final equation if you need the equation to be in slope intercept form
2x+3y=-5 implies y=-(2/3)x-5/3
inland niche
so we basically just switched the steps
fair prism
2x+3y=-5 is a valid equation for a line though. With the wording of your original question this is a valid answer
inland niche
of this
y = 5x
y = 5x+b
-3 = 5(3)+b - insert points
-3 = 15 + b
-18 = b
y = 5x-18
fair prism
Yeah its pretty much the same thing except there is no need to use slope intercept form
Which takes an extra step
fair prism
np
inland niche
.close
odd edgeBOT
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velvet badger
If null(L) = 0 is L one-to-one?
odd edgeBOT
If null(L) = 0 is L one-to-one?
forest sky
what is L?
velvet badger
I have to prove this
and I let L be the following:
Since i'm constructing an isomorphism
I gotta show it's one-to-one
If we let L([a b c d]) = [ 0 0 0 0]
then [ a b c d ] ^T = [0 0 0 0]^ T
Hence, a=b=c=d=0, so the only element mapped to zero is the zero matrix, i.e., Null(L) = {0}. Therefore, L is one-to-one.
Would that make sense?
forest sky
as long as L is linear, then that arguments holds
velvet badger
I showed L to be linear like this:
forest sky
as long as L is linear, then that arguments holds
note that if L is linear then L(x) = L(y) implies L(x) - L(y) = L(x-y) = 0 which implies x - y = 0 only if the only vector mapped to 0 is 0
velvet badger
Hence, a=b=c=d=0, so the only element mapped to zero is the zero matrix, i.e., ...
So thus this holds right?
forest sky
yes
forest sky
seems fine
velvet badger
So I have shown that
It's linear
It's one-to-one
Do I also have to show it's onto to complete the isomorphism?
forest sky
yes
forest sky
if you have a basis of the codomain then you can show that the transformation can result in each of those basis vectors
velvet badger
Isn't that rlly easy?
Would this be right:
Well
We are trying to show that for every vector in R^4 , we can find a corresponding matrix in M_2x2(R) that maps to it.
right?
Would this be correct?
forest sky
seems fine
velvet badger
We are trying to show that for every vector in R^4 , we can find a corresponding...
so this is what u meant right?
.close
odd edgeBOT
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modest owl
how to get the area of each figures?
odd edgeBOT
how to get the area of each figures?
glad lake
How to prove that sin^2 O + cos^2 O = 1
O = theta
verbal sandal
How to prove that sin^2 O + cos^2 O = 1
O = theta
! occupied
odd edgeBOT
How to prove that sin^2 O + cos^2 O = 1
O = theta
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
quasi sparrow
how to get the area of each figures?
The two rectangles and circle are easy. The triangle interesting the circle is mpossible without more information
,tex .plane geom
clever fjordBOT
riemann
modest owl
.close
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quasi bluff
<@&286206848099549185>
odd edgeBOT
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quasi bluff
i dont understand why the answer is 9
sweet cloud
What's the command again
lyric dust
uh
sweet cloud
i dont understand why the answer is 9
Who said it's 9?
lyric dust
definitely not 9 tho if that makes u feel better
dont ping helpers immediately tho next time
quasi bluff
Who said it's 9?
apparently my friends said so š
lyric dust
your friend is wrong
quasi bluff
do you know what the answer is?
sonic nova
Roots are actually exponents
lyric dust
you can do this either
sqrt(3*12)=sqrt(36) = 6
near frigate
idk
sonic nova
So they get all the properties that exponents do
quasi bluff
you can do this either
sqrt(3*12)=sqrt(36) = 6
oh thanks alot!, could you explain why the answer is 6 tho???
sonic nova
That lets us say
Sqrt(a) * sqrt(b) = sqrt(ab)
lyric dust
^
quasi bluff
tysm you guys are a lot of help
sonic nova
That lets us say
Sqrt(a) * sqrt(b) = sqrt(ab)
Sqrt(3) Ć sqrt(12) = sqrt(3Ć12)
= sqrt(36) = 6
sweet cloud
apparently my friends said so š
Well they're wrong
quasi bluff
Well they're wrong
yeah i know
quasi bluff
No???
sweet cloud
Ok
quasi bluff
its just some leftover homework
sweet cloud
When you're done ,close this channel
haughty scaffold
soapeater
when you multiply two square roots you can use an identity that we know from power laws
sqrt(a) * sqrt(b) = sqrt(ab)
lyric dust
already went through above
quasi bluff
how do i close this channel š
haughty scaffold
you do .close
quasi bluff
.close
craggy anchor
why does f(1) equal ln1 and not ln3
odd edgeBOT
why does f(1) equal ln1 and not ln3
quasi sparrow
Should be ln (3) you're right
upper pasture
Should be ln (3) you're right
Help me
odd edgeBOT
Help me
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
odd edgeBOT
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ocean lantern
can someone explain how the second solution makes sense
ocean lantern
haughty scaffold
well there are 3 street lights, and we want at least one of them to be green. here are all the possibilities
A is green and B,C are red
A,B is green and C are red
A,B,C are green
A,B,C are red
we dont care about the order of the lights, i just arbitrarily named them A B and C to keep track
well 3 of those scenarios are suitable for us, the first three since they contain at least one green light
the first scenario has 2 red lights, which has a probability of 0.2
the second scenario has 1 red light, which has a probability of 0.1
the third scenario has 0 red lights, which has a probability of 0.4
ocean lantern
ohh
haughty scaffold
since all three of those scenarios are acceptable we can just add all those odds up to get the 0.7
ocean lantern
I see what u mean now
for the 3rd one is it because 0 and 2 are even numbers
so u take them out
haughty scaffold
yes exactly
odd edgeBOT
haughty scaffold
no worries
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Available help channel!
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forest sky
1 mol = 6.022 * 10^23 atoms
analog wind
correct
fast ivy
So thats good for this problem
analog wind
no, thats just the start, you still would have to find the element afterwards
but atleast you know how many mols you have, do you have a calculator on hand?
fast ivy
no
dusk flicker
Hey I'm a little confussed about this question
Calculate and show graphically the intersection between the 2 equations below.
-x = -10 - 2y
-3x - 5y = 25
fast ivy
i think i typed something wrong
analog wind
Hey I'm a little confussed about this question
Calculate and show graphically th...
please go to the avaliable channel section :) this one is taken up
dusk flicker
please go to the avaliable channel section :) this one is taken up
Oh shoot
analog wind
i think i typed something wrong
what did you type
analog wind
I did not see it was occupied
alg
analog wind
3.64x10^21 / 6.022^10^23
do you mean 6.02x10^23? or did you type 6.02^10^23
fast ivy
i take picture
analog wind
ok thank you
analog wind
all good, if you put the numbers into parenthese it should work
fast ivy
oh
ok
sry my calc died
so i went on an online one
i did parantheses with fraction
analog wind
all good
hmm, you are close but I think you may have mistyped one of the exponents this time, try double checking you put them to the right power
analog wind
there you go, so now you know the mols of your unknown element, do you know what the next step might be?
analog wind
yup thats the one š
fast ivy
ok perfect
analog wind
if you input your numbers you should get something pretty close to the molar mass of an element
but be careful and pay extra attention to units when plugging in here
analog wind
3.64x10^21 atoms times 1mol/6.022x10^23atoms
no, if you look back here, you can see the atoms units cancelling out, leaving mols behind
analog wind
i got confused becuz mol is here
is this apart of the same problem?
fast ivy
Oh
analog wind
it tells you how many grams you have in the picture you sent a few minutes ago
fast ivy
I clicked off
Ok
hm
Ok so M= /0.0060445036
ik that so far
the grams part
only thing i think of
537 mg to g?
analog wind
correct
fast ivy
oh ok prfct
analog wind
now its just plugging in and receiving answers
analog wind
yuppp
analog wind
thats what i got as well :)
analog wind
yea no problem man, gl with chemistry š \
odd edgeBOT
analog wind
all good
odd edgeBOT
Available help channel!
serene crown
can someone explain why we multiply the x-values for horizontal dilation by 2, rather than 1/2? i thought you have to multiply by its reciprocal
odd edgeBOT
can someone explain why we multiply the x-values for horizontal dilation by 2, r...
@serene crown Has your question been resolved?
serene crown
<@&286206848099549185>
serene crown
can someone explain why we multiply the x-values for horizontal dilation by 2, r...
also the answer is C
sinful grove
Just to make sure I understand the word, horizontal dilation is just stretching the appearance of the graph horizontally?
serene crown
Just to make sure I understand the word, horizontal dilation is just stretching ...
yeah
dilates the x-values
sinful grove
So youāre right in terms of what weād do to f, but youāre conflicting this with h.
That is h(x) can be defined as h(x) = 1/2f(x/2)
So the xās here really in some sense do behave the way we wanted
Notice that x = 8 from h corresponds to x = 4 for f
sinful grove
Ur welcome!
serene crown
.close
dreamy ravine
Hi guys not an actual math question but if anyone from Australia could help me, how should i study for my up coming hsc exams, i do maths advanced and i want to know what is the best way to study as i do still struggle with just doing past papers. if anyone else from other countires could help i just said Australia because they have the exact same syllabuses
dreamy ravine
please @ me when you respond :)
odd edgeBOT
@dreamy ravine Has your question been resolved?
odd edgeBOT
random bane
What is the question?
wanton bison
there is no question
random bane
Thatās just a function that is defined. Are you trying to solve something?
upper pasture
Uhhh
Are you serious?
Look at the exponent and the answers
You see a pattern?
Which is?
Letās break it down
For the first one
The exponents are what?
random bane
You have to solve it like a system of equations
upper pasture
1 right
And when the exponent is 2
Whatās the answer
What?
Where did 4 come from
quartz trellis
solve for x in first equation
swift rock
solve for x in first equation
that would get messy tbh , i think multiplying 2nd and 3rd equation would also work
quartz trellis
yep
upper pasture
Stop wasting peoples time
nocturne brook
alright this guy is just searching up hardest math problems
that was obvious from the first picture tbf
tacit wasp
And why?
upper pasture
<@&268886789983436800>
tacit wasp
What does he expect from you??
upper pasture
that was obvious from the first picture tbf
I honestly thought the answer was 5
Untill someone said it isnāt
Reverse searched it and itās the hardest problem apparently
nocturne brook
I honestly thought the answer was 5
that also wasn't the first picture
upper pasture
People are using their own time to help people out for free
Donāt waste their time
For stupidity
zealous mango
near wedge
compactness does not imply continuity right? If i have some compact operator can i think it as like the value the operator goes too is like a black hole and I cant get contunity out of it?
sinful grove
compactness does not imply continuity right? If i have some compact operator can...
Compact operator in what sense?
near wedge
i was just talking to my thesis supervsor and he said something along these lines
ive never had a funtional analysis course or anything
so im unsure, and i just wanted to make sure i understood what he said
he said something along the lines compactness doesnt imply contunity
so its different than boundedness implying contunity of an operator
sinful grove
So if youāve not had functional analysis are you asking about any type of function on compact sets?
Like are you asking if you had a function defined on compact sets, does it have to be continuous?
Itās a bit vague
odd edgeBOT
sinful grove
near wedge
<:catshrug:563818735085944843>
thank you for your time brudda! š
sinful grove
Oh no worries! Compactness in general isnāt specific to functional analysis btw
near wedge
Thats true, im just unaccustomed to it. its coming up soon in topology i think anyways š
odd edgeBOT
Available help channel!
pure ice
help
steady tide
is this a quiz?
pure ice
yup
steady tide
<@&268886789983436800>
pure ice
i have 1 hr to complete
steady tide
you are not allowed to ask questions about an ongoing exam/quiz
summer cradle
viscid flint
.close
next coyote
odd edgeBOT
next coyote
srry the image quality is a little bad
p(x) = 5x^2 - 14x - 3 and q(x) = 2x^2 -x + k contain a common factor of the form (x-a), where a is an integer. Find k
thats the question ^
man anyone?
cold sage
if they have that as a factor, then if you sub x=a, p and q=0
by finding a, you can find k
next coyote
if they have that as a factor, then if you sub x=a, p and q=0
by finding a, you ...
so i have a question here
if i find roots of p(x) and substitute those roots in q(x) = 0
will i find k
next coyote
just note a is an integer, so thats the common root
okay
@cold sage hey u still there?
š
my handwriting is cool right?
cold sage
more the image quality than the writing
next coyote
more the image quality than the writing
do i substitute x = 1 as p(1) = 7 and q(1) = -6
?
then find a linear eq in variables m and n and then solve them
bro died š
oh cmon bro someone
odd edgeBOT
@next coyote Has your question been resolved?
mystic saffron
Have you tried possibly using Vieta's theorem?
next coyote
Have you tried possibly using Vieta's theorem?
what is that
mystic saffron
Uhh
next coyote
bro this is a question from the chapter factor and remainder theorem š
mystic saffron
Its a way to find relations between the sum of roots
mystic saffron
bro this is a question from the chapter factor and remainder theorem š
Oh mb š
next coyote
high school
mystic saffron
What does the second last word say
next coyote
What does the second last word say
equation
only the image quality is bad
my handwriting is gorgeous
next coyote
What does the second last word say
btw
that "equation" is cancelled
its polynomial
i made a mistake there
hold on 1 s
mystic saffron
Oh okay np
next coyote
is this better now?
mystic saffron
Yeah
next coyote
kk
mystic saffron
10(x+2)(5xā1)(2x+1)=0
next coyote
howd u come up with that
mystic saffron
rational root theorem
I'm sure they didnt teach us this stuff in school where im from but its useful in competition maths
Wait i should check if its correct
next coyote
synthetic division?
mystic saffron
(x+2)(5xā1)(2x+1)=0
mystic saffron
synthetic division?
Some of it
mystic saffron
Yeah
mystic saffron
Do you know about rational root theorem?
next coyote
well ik synthetic division
mystic saffron
Idk they normally dont teach that kinda stuff
next coyote
thats what we're taught
mystic saffron
well ik synthetic division
Ok thats a start
The rational root theorem states that potential rational roots of a polynomial are given by the factors of the constant term divided by the factors of the leading coefficient
next coyote
um k
mystic saffron
Basically
in this question, the factors of -2 (which is the constant term) divided by 10 which is the leading
-2 has factors +- 1 and +- 2
10 has factors of +- 1 +- 2 +- 5 and +-10
so you can divided the factors of -2 by factors of 10 to find the possible roots
or you could just factorsie tbh
next coyote
is it possible to send an image of the working?
mystic saffron
Uh i did it in my head
next coyote
Uh i did it in my head
how th š
mystic saffron
also my mum took my phone š
next coyote
k ig
mystic saffron
Ā±1,Ā±2,Ā± 1/2 ,Ā± 1/5,Ā± 1/10,Ā±5,Ā±10
those are the possible roots
then you can go ahead and test them in the polynomial
and luckily
-2 is a root
If you're writing out working just mention that you found -2 as a root
mystic saffron
Oh maybe im overcomplicating things
next coyote
and we havent been taught that stuff yet so its a little problem to submit
mystic saffron
Sorry about that
next coyote
na there could be various methods
mystic saffron
How about you just say that after trial and error, you found that -2 is a root
then you can use synthetic division
next coyote
Ā±1,Ā±2,Ā± 1/2 ,Ā± 1/5,Ā± 1/10,Ā±5,Ā±10
ill write this
and also how did u find out +
mystic saffron
wdym
mystic saffron
Because the factors of -2 divided by the facotrs of 10
Tbh you can skip the whole rational theorem thing if its not needed
mystic saffron
you could just brute force found -2 as a root
mystic saffron
Its meant for longer a bigger polynomials but ig it works idk
They dont teach us this until Further Maths IGCSE š
next coyote
They dont teach us this until Further Maths IGCSE š
whats igcse
mystic saffron
British Exam
mystic saffron
ohhh your from britain?
Im from Malaysia
next coyote
Im from Malaysia
for that question i had used a weird method
mystic saffron
Show
next coyote
i substituted x as 0
got -2
then took it at first root
then did -2/4 which is -1/2
2nd root
lol
next coyote
pretty sure thats incorrect
mystic saffron
but theres only one case when you can substite 0 for x
next coyote
because -2 just so happens to be a root
well in every case its supposed to be a root right?
mystic saffron
and thats if there is NO constant term
mystic saffron
well in every case its supposed to be a root right?
Technically, if you substitue 0 for x, you end up with -2=0
mystic saffron
yeah
next coyote
it was just a coincidence
next coyote
its just sythetic divison all the way
oh i see
mystic saffron
After you find what possible roots there are, just test them
next coyote
After you find what possible roots there are, just test them
yea i already used microsoft calculator to find roots
mystic saffron
Genius
next coyote
the thing abt this chapter and another one is
i know the formulae
but when using them
comes the problem
the other chapter isnt of mathematics so ill have to deal with it somehow
mystic saffron
the other chapter isnt of mathematics so ill have to deal with it somehow
what
Now that I see it, its also possible to use vietas theroem
it would probably be a bit easier but its the same nonetheless
next coyote
what is vieta's theorem
next coyote
ohhh
mystic saffron
They teach us that in Middle school here
next coyote
-b/a and c/a?
mystic saffron
YES
mystic saffron
same lmao
next coyote
same lmao
also the question said to factorize the polynomial
what do they mean by factorizing here?
mystic saffron
They just mean putting them into brackets
next coyote
like?
mystic saffron
Like (x-1)(x+1) is the factorised version of x^-1
because now you have 2 "factors" of the eqations
because they multiply together to make the origional equation
next coyote
oh so (x+2)(x+1/2) ?
next coyote
ah okay
mystic saffron
oh so (x+2)(x+1/2) ?
ah be careful
that doesnt always work
you cant just say (x+1/2) because you know -1/2 is a root
next coyote
ah be careful
also after you got possible roots its all trial and error right?
mystic saffron
No, you shouldnt assume that (x+1/2) is right
mystic saffron
also after you got possible roots its all trial and error right?
yeah ... tbh thats the only way
next coyote
yeah ... tbh thats the only way
kk
odd edgeBOT
@next coyote Has your question been resolved?
mystic saffron
x,y,z belongs to (0,1)
odd edgeBOT
x,y,z belongs to (0,1)
mystic saffron
by the given info
we can say that x(1-z) + y(1-x) +z(1-y) = 1-2xyz
so we need minimum value of 1 -2xyz
we also know that x,y,z lies in the interval [0,1]
so the minimum value of 1-2xyz would be -1
what am i doing wrong ?
ik the AM > GM concept
š„ŗ
onyx cloak
we also know that x,y,z lies in the interval [0,1]
so the minimum value of 1-2x...
(0,1)*
mystic saffron
hmm alr lets consider (0,1)
in my book it says [0,1]
anyway
i think i made some progress
onyx cloak
in my book it says [0,1]
then your answer seems correct for that
mystic saffron
lets select terms as x(1-z) ,y(1-x) , z(1-y)
if we do AM>Gm x(1-z) + y(1-x) +z(1-y) > 3*(xyz)^2/3
and we know that x(1-z) + y(1-x) +z(1-y) = 1 -2xyz
so the inequality becomes
1 -2xyz > 3*(xyz)^2/3
mystic saffron
then your answer seems correct for that
answer according to the book is 3/4, i think book has typo