It just won't be easy
#help-41
lusty turret
knotty reef
It just won't be easy
Yup maybe u can contact a proff and ask them for help Or study from yt Or somewhere else
lusty turret
My prof from Uni doesn't know how to help sadly
Did ask him once a year ago about it, but I was too occupied to keep up with Uni math to learn on my own
knotty reef
dam u can try using yt and if ur stuck anywhere the server is always here for u
and me too
lusty turret
Thank you for that
Luckily as long as it's numbers I manage to do them with the correct tutorial
knotty reef
amber waspBOT
@split sail Has your question been resolved?
quartz crescent
is this solvable?
amber waspBOT
is this solvable?
dull pike
Yes
amber waspBOT
@quartz crescent Has your question been resolved?
amber waspBOT
@quartz crescent Has your question been resolved?
quartz crescent
can any1 help?
mint wraith
can any1 help?
Connect vertices with the midpoint
quartz crescent
like from the corner to the intersection?
quartz crescent
take your time
mint wraith
Yes
amber waspBOT
amber waspBOT
Available help channel!
rare hatch
amber waspBOT
rare hatch
let’s do this again
solar oyster
I thought the last guy did a good job lol 😨
rare hatch
what was bro even yappin about
did not help one bit he just started spewing words that I didn’t even understand what was going on
solar oyster
what was bro even yappin about
smth like complete the square
tiny latch
can anyone help me figure out what I'm doing wrong
weak zinc
can anyone help me figure out what I'm doing wrong
!occupied
amber waspBOT
can anyone help me figure out what I'm doing wrong
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).
rare hatch
smth like complete the square
yeah but the steps I just don’t get those
that’s literally all I’m asking
lusty pine
yeah but the steps I just don’t get those
what do you not get?
solar oyster
Sorry I forgot
solar oyster
I don’t understand the process
u want to change the original equation into a form like (x+a)^2 + b
amber waspBOT
@rare hatch Has your question been resolved?
solar oyster
Cause vertex form
rare hatch
Wow so helpful
solar oyster
my fault
amber waspBOT
@rare hatch Has your question been resolved?
rare hatch
.close
long yoke
$\mathcal{(L}_s)^{-1} (\frac{s^2 + s +1}{s^2 + 4s +5})$
amber waspBOT
$\mathcal{(L}_s)^{-1} (\frac{s^2 + s +1}{s^2 + 4s +5})$
grizzled pagodaBOT
Triaxyz
long yoke
I will explain my process but I got $\delta (t) -3e^{-2t}\cos(t) -4e^{-2t}\sin(t)$ which symbo says is wrong
grizzled pagodaBOT
Triaxyz
long yoke
convert $\frac{s^2 + s +1}{s^2 + 4s +5}$ into $\frac{s^2 + s +1+3s+4-3s-4}{(s+2)^2+1}$
grizzled pagodaBOT
Triaxyz
long yoke
which becomes $\frac{(s+2)^2+1}{(s+2)^2+1} - \frac{3s}{(s+2)^2+1} - \frac{4}{(s+2)^2+1}$
grizzled pagodaBOT
Triaxyz
cedar plaza
all s variables have to be replaced by s-a for you to use that
long yoke
so 3(s+2-2) which turns into +6 on that last term
and 6-4 = 2 which is the coefficient that symbo says
alright I got it
thank you
.close
amber waspBOT
amber waspBOT
Available help channel!
glad schooner
I’m not sure if I plugged In the number correctly. Can someone please tell me if I have or not? And if I’m going in the right direction?
split sail
clicky with the linky?
vernal surge
^ porn
glad schooner
pls I just want help with my hw
split sail
<@&268886789983436800> 18+ (nsfw)
(sorry for ping)
(i turned off reply ping to that message)
abstract canopy
<@&268886789983436800>
glad schooner
I’m not sure if I plugged In the number correctly. Can someone please tell me if...
So can anyone help me with this
I rewrote it bc I think the first time I wrote it wrong
<@&286206848099549185>
amber waspBOT
@glad schooner Has your question been resolved?
glad schooner
<@&286206848099549185>
bronze basalt
I rewrote it bc I think the first time I wrote it wrong
why are you using f(x)?
glad schooner
What am I supposed to plug in for y then 💔
glad schooner
why are you using f(x)?
because I thought f(x) and y is the same thing
bronze basalt
you don't plug anything in for y
bronze basalt
because I thought f(x) and y is the same thing
no, y = f(x) is very common notation, but you can't assume it here unless you're told to do so
glad schooner
no, y = f(x) is very common notation, but you can't assume it here unless you're...
So I just keep it as Y? Like this?
glad schooner
Oh okay thank you!
amber waspBOT
Available help channel!
gusty stream
Hello guys, quick question:
How can I write
$\dots + \frac{-7}{2} + \frac{-5}{2} + \frac{-3}{2} + \frac{-1}{2} + \frac{1}{2} + \frac{3}{2} + \frac{5}{2} + \frac{7}{2} + \dots$ as a series?
grizzled pagodaBOT
Akkaman
split sail
why do you want to write that as a series
gusty stream
Because I need it to solve a problem. 😄
I'm just unsure about how to write it as a series with the sigma symbol.
tropic wadi
**Akkaman**
bruh isn't it just 0
split sail
it is
pseudo crescent
Well...
vernal surge
bruh isn't it just 0
not really
gusty stream
Yeah it is, I am looking at the reciprocals of them, so $\frac{1}{\frac{-7}{2}}$ etc...
grizzled pagodaBOT
Akkaman
pseudo crescent
not really
sane answer dropped
gusty stream
It has something to do with another problem.
I really just need to know how to write it without the dots but rather with the sigma symbol. 🥲
pseudo crescent
It has something to do with another problem.
you better show the another problem then, this is not an expression you wanna play with
tropic wadi
not really
why though?
gusty stream
you better show the another problem then, this is not an expression you wanna pl...
Wait.
vernal surge
bruh isn't it just 0
is $\int_{-\infty}^{\infty} x dx = 0$?
grizzled pagodaBOT
rbit
pseudo crescent
why though?
In which order should I even be summing it?
wanton sentinel
I really just need to know how to write it without the dots but rather with the ...
You can't unless you have a specific order for every term, and even then it won't necessarily make any sense
pseudo crescent
I guess that since it's both directional, I can pick any order.
So 1/2 + 3/2 - 1/2 + 5/2 + 7/2 - 3/2 + 9/2 + 11/2 - 5/2....
whoops - that's not 0
vernal surge
the cauchy principal value of it is 0, but just applying the basic definitions it will diverge
wanton sentinel
Yeah, really this can evaluate to any rational number or -inf or +inf
pseudo crescent
Can't it evaluate to any real number actually
vernal surge
well to answer the question though
gusty stream
$\sum^\infty_{n=1} \frac{1}{(2n-1)^2}$ would be the series over the squared reciprocals of all positive odd numbers, right?
grizzled pagodaBOT
Akkaman
wanton sentinel
Can't it evaluate to any real number actually
All the terms are of the form n+1/2 (n integer), so I wouldn't say so, but maybe the fact it can evaluate to +inf and -inf means it can, idk
pseudo crescent
All the terms are of the form n+1/2 (n integer), so I wouldn't say so, but maybe...
There are series, all of whose terms are rational, that converge to pi
wanton sentinel
There are series, all of whose terms are rational, that converge to pi
Yes but they all have different denominators
pseudo crescent
**Akkaman**
And you are trying to compute this?
vernal surge
$\sum_{k=-\infty}^{\infty} \frac{2k+1}{2} = \sum_{k \in \mathbb{Z}} \frac{2k+1}{2}$ something like this, but it will really just diverge
grizzled pagodaBOT
rbit
pseudo crescent
Yes but they all have different denominators
Oh, you're right. This series is actually completely divergent, no matter how you rearange it
its partial sums will oscillate
vernal surge
$\sum^\infty_{n=1} \frac{1}{(2n-1)^2}$ would be the series over the squared rec...
yes
pseudo crescent
**Akkaman**
this surely converges, although it doesnt seem to be elementary
gusty stream
yes
If I multiply that by $\frac{1}{2}$, would I not just get the series over the squared reciprocals of $\frac{1}{2} + \frac{3}{2} + \frac{5}{2} + \dots$?
grizzled pagodaBOT
Akkaman
wanton sentinel
its partial sums will oscillate
that's another interesting point, does it necessarily oscillate or can you find an order such that it doesn't? I guess since the terms are growing absolutely on either side, you actually can't find such an order, so yeah it can't even evaluate to a specific number
gusty stream
this surely converges, although it doesnt seem to be elementary
Yeah it converges to $\frac{\pi^2}{8}$.
grizzled pagodaBOT
Akkaman
pseudo crescent
<:pandahmm:858834883760750602> that's another interesting point, does it necessa...
(It always oscillates or diverges completely, because all terms have magnitudes >= 1/2. So the partial sums must change by at least 1/2 at every "iteration")
gusty stream
Yeah sorry. 😄
pseudo crescent
and the series would be multiplied by 2 if im not mistaken
$2\sum_{n=1}^{\infty}\frac{1}{\left(2n-1\right)^{2}}=\sum_{n=1}^{\infty}\frac{2}{\left(2n-1\right)^{2}}$
grizzled pagodaBOT
MæthIsAlwaysRight
wanton sentinel
Anyway, like @pseudo crescent already said, you should just state the original problem instead
pseudo crescent
Anyway, like <@951190447185874994> already said, you should just state the origi...
he did 💀
what's the goal of multiplying it by 2 btw?
wanton sentinel
I must be blind
gusty stream
There should be a mathematical operation to go from $\frac{1}{2}, \frac{3}{2}, \frac{5}{2}, \dots$ to $1, 2, 3, \dots$, right?
grizzled pagodaBOT
Akkaman
wanton sentinel
Yes, +1/2
pseudo crescent
I think you are doing quite weird things here though
wanton sentinel
No
pseudo crescent
no
gusty stream
I think you are doing quite weird things here though
Yeah the topic is weird. 😂
pseudo crescent
Yeah the topic is weird. 😂
do you know value of zeta(2)?
there is a simple way to get value of this from that
gusty stream
do you know value of zeta(2)?
That's the topic. ^^
pseudo crescent
**Akkaman**
anyway, what would you do now?
are you trying to transform this to zeta function or sth?
gusty stream
do you know value of zeta(2)?
But my proof is not a typical algebraic proof but rather geometrical / physical.
wanton sentinel
**Akkaman**
All pairs of consecutive terms in both sequences differ by 1. If you multiply one sequence by some number (apart from 1), that will change and it cannot give you the other sequence
pseudo crescent
But my proof is not a typical algebraic proof but rather geometrical / physical.
well.. expect weird result then
vernal surge
I'm still confused, so you do not have proven zeta(2) yet, or do you? And now you want to prove the value for the odd squares?
gusty stream
I'm still confused, so you do not have proven zeta(2) yet, or do you? And now yo...
Explaining the entire proof here would be too time consuming, that's why I'm trying to break it down to the most important things. 🥲
I wanted to know how to get from $\frac{1}{2}, \frac{3}{2}, \frac{5}{2}, \frac{7}{2}, \dots$ to $1, 2, 3, 4, \dots$ by some mathemical operation.
grizzled pagodaBOT
Akkaman
pseudo crescent
add + 1/2 to each term
isnt the real goal here getting from sum of 1/(2n-1)^2 to the sum of 1/n^2?
gusty stream
No no.
vernal surge
you can also multiply by 2, index shift and divide by 2
pseudo crescent
multiply by 2, add 1, divide by 2
just a warning: I don't think you can prove this thing "geometrically" by just playing around with numbers
gusty stream
I think I made a mistake at some point.
wanton sentinel
This feels so directionless
vernal surge
also proving the value for zeta(2) is really not easy at all
I know an elementary proof but it's a long journey
gusty stream
I have already done it algrebraicly and geometrically.
But I wanted to modify the geometrical proof and now I am stuck. 😂
!close
.close
amber waspBOT
amber waspBOT
Available help channel!
sharp crater
how can this be proven in some other way
amber waspBOT
how can this be proven in some other way
sharp crater
its unclear how one would reach this choice of q
indigo cloud
one would reach this choice of q after hours of trying stuff
its not that crazy. you want that p^2-2 in there quite naturally
sharp crater
yes but that doesnt narrow down the choices for you so that you can reach this choice of q by trying some choices
because there are still too many choices that involve p^2-2
so there isnt a way to find these unless you gain more experience and gain this intuition naturally ?
indigo cloud
I mean thats how proofs generally go
sharp crater
thats right i understand your point
sharp crater
how can this be proven in some other way
is there another way to prove this so that i can gain more insight
indigo cloud
its also not like this is the only choice of q that will work
you would maybe start with q=p-(p^2-2), then square it and check what q^2-2 is. it doesnt work (presumably, otherwise they would have chosen that), so you maybe decide to use p-(p^2-2)/something. for that something you might decide it could be some multiple of p, so maybe kp. you try it out, maybe it works, maybe not. if it doesnt you might change it to kp+n
and then you are there
amber waspBOT
@sharp crater Has your question been resolved?
austere jungle
Hi, I've got a question I'm confused by... it's a really simple one but I have two different answers for it
A container will hold 106 ounces of grape juice. How many 6(5/8) ounce glasses of grape juice can be served from this container?
austere jungle
the picture shown is my working
the answer in the textbook says it is 16 (glasses)
but mathway says it is 11 (1/24)
a 106-ounce container being served into glasses that are 6(5/8) ounce
tropic wadi
Hi, I've got a question I'm confused by... it's a really simple one but I have t...
you did a mistake in second step
tropic wadi
lol
austere jungle
53/5
limpid sun
you did a mistake in second step
it is a kind of magic tric k
tropic wadi
:magician:
austere jungle
i couldn't work it out but as soon as i asked it...
some kind of quantum magic 🧙
thanks guys
loud maple
what u guys doing?
tropic wadi
what does that supposed to mean/
loud maple
i came to this help-41/ap button saw u guys here what's up
tropic wadi
i came to this help-41/ap button saw u guys here what's up
alright
tropic wadi
hey 77^2 i have a qn what's 1 and 2/5 power 3
what?
loud maple
i'm just curios of what way you will use
tropic wadi
i'm just curios of what way you will use
I didn't understand what your question even is?
tropic wadi
(1 and 2/5) ^3
1+2/5?
loud maple
yess
tropic wadi
{7/5}^3
loud maple
like the mixed fraction
austere jungle
i came to this help-41/ap button saw u guys here what's up
A container will hold 106 ounces of grape juice. How many 6(5/8) ounce glasses of grape juice can be served from this container?
hi btw sorry lol
loud maple
god that's 10
hoary musk
hi guys
night minnow
wassup
woven sparrow
How is this 11 ;-;
hoary musk
im facing a problem when i try to solve through my calculator it keeps saying syntax error
tropic wadi
im facing a problem when i try to solve through my calculator it keeps saying sy...
!occupied
amber waspBOT
im facing a problem when i try to solve through my calculator it keeps saying sy...
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).
austere jungle
im facing a problem when i try to solve through my calculator it keeps saying sy...
try typing it out on a keyboard, use a calculator online as well. it might be easier on a keyboard
austere jungle
yes, 11^2 = 121
night minnow
now what happened here
loud maple
yeah for 13 it'd be 143
stoic locust
!status quo
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
- i guess
loud maple
i'm trying to say 530 / 53 = 10 ap
austere jungle
i'm trying to say 530 / 53 = 10 ap
i'm sorry, i'm not thinking clearly at the minute lol -_-
woven sparrow
53*10/10 = 53
Yea
austere jungle
i will check with mathway again as well
loud maple
i'm sorry, i'm not thinking clearly at the minute lol -_-
it happens to the best of us no worries
austere jungle
16 is the answer that was given in the textbook, but i had the wrong answer (and working as well)
night minnow
16 is the answer that was given in the textbook, but i had the wrong answer (and...
Well in ur working out u got 11 and here im showing u why its 16
austere jungle
that's good, at least the tetbook is right lol 
stoic locust
are you a spammer jassbery?
night minnow
are you a spammer jassbery?
Sadly
tropic wadi
you did 53/5
it was supposed to be 53/8
night minnow
that's good, at least the tetbook is right lol <:sully:651816820122189834>
So are you all good now or still stuck ?
stoic locust
so the answer should be 2
night minnow
you did 53/5
it was supposed to be 53/8
Yeah i noticed that baha
stoic locust
i hate when people don't care to calculate things
tropic wadi
so the answer should be 2
what are you talking about btw?
loud maple
what how did i not see that good call 77
stoic locust
i mean 10
night minnow
@austere jungle so all good now :))?
night minnow
Yay!!
austere jungle
horay : )
austere jungle
yes, thank you all
austere jungle
yeah idk, i'm glad i clicked to show messages because i thought it might be a message from one of the bots at first
hope you guys all have a great day btw, thanks again
stoic locust
bro thinks life is all sunshine and rainbows
maiden kernel
Close
amber waspBOT
amber waspBOT
Available help channel!
cursive wasp
Could I get help with this question please
I am not sure where to start
split sail
Could I get help with this question please
I am not sure where to start
Do you know what a basis is?
cursive wasp
Do you know what a basis is?
Linearly Independent Set that Spans the space
split sail
Linearly Independent Set that Spans the space
And do you know what the notation [(2,5)]_B means?
cursive wasp
If I remember correctly it means that it is 2u + 5v where u = (1, 2) and v = (2, 3)
cursive wasp
Is [(2,5)]_B different from (2,5)_B?
split sail
I don't know what (2,5)_B means
cursive wasp
I don't know what (2,5)_B means
This is what is in my textbook
split sail
It's almost the same except [(2,5)]_B is vertical, I guess
cursive wasp
Is [(2,5)]_B different from (2,5)_B?
Ignore this. I get it
cursive wasp
[(2,5)]_B = [4 -1]^t means that 4u-1v = (2,5)
I don't get this though
split sail
This is what is in my textbook
(2,5) = au+bv, like here
amber waspBOT
amber waspBOT
Available help channel!
royal seal
Hello
royal seal
i’m a little confused on what i’m supposed to do for this problem
can anyone help me with it
and what does it mean by use any method
blazing cloak
g(x) is also a line
blazing cloak
do you know how to find the equation of a line given two points?
I assume there's also a tool in the e-tool thing that allows you to form a line with two points
royal seal
do you know how to find the equation of a line given two points?
no not really
we learned abt it in class today but i didn’t understand it
don’t you like set them equal?
royal seal
I assume there's also a tool in the e-tool thing that allows you to form a line ...
oh wrd pmo
blazing cloak
???
royal seal
do you know how to find the equation of a line given two points?
but how do you find the two points
that’s what i’m really worried abt
blazing cloak
any two points define the line
it doesn't matter which points you choose on g(x)
you can also notice that there's a constant difference in the g(x) values and a constant difference in the x values. this also indicates its a line
royal seal
it doesn't matter which points you choose on g(x)
so like -3, 21 and -1 13
blazing cloak
yes
you can use point-slope form
y-(y1)=m(x-x1)
where (x1,y1) is a point on the line
and m is the slope
you know how to find slope/gradient right
amber waspBOT
@royal seal Has your question been resolved?
mystic hull
I don't get what it means by "increasing" and "decreasing"
amber waspBOT
I don't get what it means by "increasing" and "decreasing"
pallid canopy
I don't get what it means by "increasing" and "decreasing"
increasing means slope/derivative is positive
mystic hull
Could that be related to the first derivative test maybe
pallid canopy
Could that be related to the first derivative test maybe
related, sure. but you're already given dP/dt so just solve for when the right side is positive/negative/zero
equilibrium means dP/dt equals what value?
mystic hull
zero
If you do that you just get P=0 or P=230
But if I remember those are called critical points of the function
pallid canopy
If you do that you just get P=0 or P=230
correct
if dp/dt is zero at only those two points, then you can determine the sign around those points
pallid canopy
,w plot x(1-x/230)
grizzled pagodaBOT
pallid canopy
your sign looks wrong for p < 0
mystic hull
I made a typo so it should be p less than 0 means it's decreasing
pallid canopy
see https://tutorial.math.lamar.edu/classes/calci/ShapeofGraphPtI.aspx
so do you know how to do your problem then after reading the link i sent here?
mystic hull
I don't know how I would phrase it, could I say for any p<0 the population is decreasing
pallid canopy
does p < 0 have physical meaning?
mystic hull
Most likely not
pallid canopy
do you understand why?
mystic hull
You can't have negative population
pallid canopy
right
pallid canopy
I don't get what it means by "increasing" and "decreasing"
do you understand how to answer your questions now?
amber waspBOT
amber waspBOT
Available help channel!
marble shoal
amber waspBOT
marble shoal
guys trying to solve this with L'H
i did someting wrong
but idk how
(e^1/x -1) derived
is chain rule right
.close
amber waspBOT
drowsy sedge
Hello! I understand you need to find the limit, right?
kindred trellis
Hello! I understand you need to find the limit, right?
try pinging them, they've closed the help channel so they might not see your message
amber waspBOT
Available help channel!
compact wagon
amber waspBOT
compact wagon
How to find left and right side limit
amber waspBOT
@compact wagon Has your question been resolved?
weak zinc
"Follow your finger from the left/right, what does it look like you're getting closer and closer to?"
compact wagon
i know thr right hand limit at x=0 but why does the left hand limit equal x=2 when there is ajump discontinuity
amber waspBOT
@compact wagon Has your question been resolved?
amber waspBOT
@compact wagon Has your question been resolved?
amber waspBOT
@compact wagon Has your question been resolved?
random epoch
How to find left and right side limit
at x = what?
amber waspBOT
amber waspBOT
Available help channel!
split sail
Is this correct?
amber waspBOT
Is this correct?
tender knoll
,w sqrt(3x+12)=sqrt(x+8)
grizzled pagodaBOT
amber waspBOT
amber waspBOT
Available help channel!
slate gale
amber waspBOT
slate gale
Guys, what should it be like? Is it number one or two?
I’m confused on how we’re supposed to connect the chords
Bcs i’m getting a gradient of 0 for the chord CB in the 2nd drawing
mint nacelle
number 2
mint nacelle
Bcs i’m getting a gradient of 0 for the chord CB in the 2nd drawing
that's correct
so that means the perpendicular bisector will be a vertical line
since its slope is undefined
actually notice that you have a right angle at B, due to the coordinates
so the centre is just the midpoint of CA
remember your circle theorems from IG
slate gale
so the centre is just the midpoint of CA
Ohhhh yeahhh
slate gale
number 2
How do i know if no 2 is the correct one in case CB and BA are not perpendicular to each other?
mint nacelle
How do i know if no 2 is the correct one in case CB and BA are not perpendicular...
well actually, for three points on a circle
you just need 2 out of the 3 perpendicular bisectors, so drawing 1 isn't wrong
it's just messier to work out
slate gale
you just need 2 out of the 3 perpendicular bisectors, so drawing 1 isn't wrong
Ohhh
Okk i’ll try to do it first
woeful temple
Just finished my As level on this yr may June got 73 on my p1 I'm pretty sure this has a formula
slate gale
it's just messier to work out
Thank you so much for your help
woeful temple
slate gale
Ohhh yess
woeful temple
Just replace x and y and u will get 3 unknowns and 3 equations
mint nacelle
yes so radius is|| sqrt((7 - 4)^2 + (9 - 5)^2)||
mint nacelle
Just replace x and y and u will get 3 unknowns and 3 equations
no need lol
mint nacelle
actually notice that you have a right angle at B, due to the coordinates
@woeful temple
split sail
sorry for interrupting but i think x and y are supposed to stay as x and y and others to be substituted by number values so as to be an equation?
slate gale
Thank youu for this!
mint nacelle
sorry for interrupting but i think x and y are supposed to stay as x and y and o...
that is correct, x and y are variables
h, k, r are constants which depend on the circle
If we know h, k, r we can sub those in and get the equation of the circle
split sail
ah k
split sail
that is correct, x and y are variables
i was thinking of the word that should be used to describe "x and y are supposed to stay as x and y"
woeful temple
h, k, r are constants which depend on the circle
If we know h, k, r we can sub ...
But we don't know h, k, r so don't we have to substitute x and y so that we can get h, k, r?
slate gale
so the centre is just the midpoint of CA
Btw we can also find the centre from the midpoint of BC right?
mint nacelle
Btw we can also find the centre from the midpoint of BC right?
woooops I meant CA
CA is the diameter
errant vortex
can someone explain venn diagram union and intersection im really confused
zenith summit
can someone explain venn diagram union and intersection im really confused
Union means or
Intersection means and
so for example, if we take a union b
we're saying a or b
in a venn diagram, it would be both the circles including the middle/overlapping section
however, if we say a intersection b
we're saying a and b
so you would only take the middle/overlapping section of the venn diagram
errant vortex
so does a or b mean both
and a and b means like
whatever is the same
because i get confused
errant vortex
okay thank you i get so confused
zenith summit
ight allgs
errant vortex
.close
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Available help channel!
soft comet
amber waspBOT
soft comet
what can i even do here
split sail
do you have the original version
soft comet
this is the original
soft comet
i feel like it is translated cause the english isnt really that well
yea ik
thing is aabb is a 4 digit perfect square where a and b are its digits
so we need to find the number
split sail
hm
soft comet
calculators arent allowed btw
soft comet
yea ik 😭
rancid raven
soft comet
ignore the GIF part , its the greatest integer function
soft comet
thing is aabb is a 4 digit perfect square where a and b are its digits
the question is basically asking this
tropic wadi
the question is basically asking this
I kinda got some method but it still involves some calculations
some significant calculation*
soft comet
whats the method?
tropic wadi
whats the method?
if you write the number in the form of 1000a+100a+10b+b
you can pair the a and b things together
soft comet
oh i see
tropic wadi
so it must be a multiple of 11^2?
erm
soft comet
like the whole number
tropic wadi
a multiple of 11 and also a square number
soft comet
yea
tropic wadi
so like 100a+b=11k^2
like this
so that both 11 makes 11^2
but there could be a more efficient method
soft comet
maybe
most of the questions on this test had a lot of trial and error involved tho so this may be correct
tropic wadi
most of the questions on this test had a lot of trial and error involved tho so ...
erm probably,
at least with this method you don't have to check all the numbers
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Available help channel!
sharp depot
In how many ways can 4 boys including John and Matthew, and 4 girls, including Sally, be arranges in a line if:
sharp depot
(ii) Girls and bous alternate and John and Sally stay together
amber waspBOT
@sharp depot Has your question been resolved?
sharp depot
<@&286206848099549185>
abstract seal
is 252 the answer?
amber waspBOT
@sharp depot Has your question been resolved?
sharp depot
<@&286206848099549185>
violet raven
for this
first we will make 8 spaces
and then we will make a block of john and sally
This is the first hint
@sharp depot
sharp depot
sure
then iget confused on how to rearrange the other around the block
while ensuring girl abnd boys alternate
amber waspBOT
@sharp depot Has your question been resolved?
midnight harbor
amber waspBOT
midnight harbor
HOw is 81% not right? I'm sick of this problem, please help
pallid canopy
HOw is 81% not right? I'm sick of this problem, please help
show how you got 81%
,calc (2 * 81 ^ 2 + 50) / (81 * (100 - 81))
grizzled pagodaBOT
Result:
8.5588044184535
yea that's not 30
midnight harbor
i did 2x^2 + 50/x(100-x) = 30
pallid canopy
,calc (2 * 81 ^ 2 + 50) / (81 * (100 - 81))
like here
grizzled pagodaBOT
Result:
31.421985815603
,calc (2 * 93 ^ 2 + 50) / (93 * (100 - 93))
grizzled pagodaBOT
Result:
26.648233486943
,calc (2 * 93.9 ^ 2 + 50) / (93.9 * (100 - 93.9))
grizzled pagodaBOT
Result:
30.874177272648
,calc (2 * 93.8 ^ 2 + 50) / (93.8 * (100 - 93.8))
grizzled pagodaBOT
Result:
30.344040167824
,calc (2 * 93.79 ^ 2 + 50) / (93.79 * (100 - 93.79))
grizzled pagodaBOT
Result:
30.291965519296
,calc (2 * 93.78 ^ 2 + 50) / (93.78 * (100 - 93.78))
grizzled pagodaBOT
Result:
30.240058315316
,calc (2 * 93.779 ^ 2 + 50) / (93.779 * (100 - 93.779))
grizzled pagodaBOT
Result:
30.23487677328
,calc (2 * 93.65 ^ 2 + 50) / (93.65 * (100 - 93.65))
grizzled pagodaBOT
Result:
29.580142177903
,calc (2 * 93.68 ^ 2 + 50) / (93.68 * (100 - 93.68))
grizzled pagodaBOT
Result:
29.730020862835
,calc (2 * 93.69 ^ 2 + 50) / (93.69 * (100 - 93.69))
grizzled pagodaBOT
Result:
29.780297129201
,calc (2 * 93.71 ^ 2 + 50) / (93.71 * (100 - 93.71))
grizzled pagodaBOT
Result:
29.88132925056
,calc (2 * 93.73 ^ 2 + 50) / (93.73 * (100 - 93.73))
grizzled pagodaBOT
Result:
29.98300592271
,calc (2 * 93.74 ^ 2 + 50) / (93.74 * (100 - 93.74))
grizzled pagodaBOT
Result:
30.034087895893
,calc (2 * 94 ^ 2 + 50) / (94 * (100 - 94))
grizzled pagodaBOT
Result:
31.421985815603
@pallid canopy so if im rounding its 94%\
,calc (2 * 93 ^ 2 + 50) / (93 * (100 - 93))
grizzled pagodaBOT
Result:
26.648233486943
,calc (2 * 93.5 ^ 2 + 50) / (93.5 * (100 - 93.5))
grizzled pagodaBOT
Result:
28.851501439737
left spire
not sure how to approach both questions
amber waspBOT
not sure how to approach both questions
mortal dust
According to google itself you should use:
Cauchy-Schwarz Inequality
AM-GM Inequality
lusty pine
for 7 am-gm should work i think
left spire
hmm i think im missing something
i got (a+1/a)^2 + (b+1/b)^2 >= 8
did i apply AM-GM incorrectly?
shell osprey
how did you get >= 8
shell osprey
oh nvm i misunderstood
lusty pine
did something similar for b and added the 2
that lets a,b=1, which isnt possible with a+b=1 (i also did the same thing lmfao)
left spire
hmm
lusty pine
am i stupid or does the inequality not hold
restive harness
am i stupid or does the inequality not hold
can both be true
lusty pine
amber waspBOT
@left spire Has your question been resolved?
amber waspBOT
@left spire Has your question been resolved?
lilac sky
hi
lilac sky
so in my class we are getting groups of 4 that we will be using for some time and i want to calculate the probability of getting paired with a certain person
A for ease of use
The groups will have 4 people and there's 26 people in total
That's 6 groups with a remainder of 2
So 7 groups where 2 of them will have 3 rather than 4
Now I could just go 1/7=14.29%
but
now that the groups arent equally sized, that introduces a whole other can of worms that i dont know how to deal with
that's what i need help with
lusty pine
so in my class we are getting groups of 4 that we will be using for some time an...
do you want to know how to do it?
lilac sky
do you want to know how to do it?
Yes
mortal dust
itll just be around 16% im like 90% sure
mortal dust
oh wait 2 groups of 3
in that case itll be more like 10-11%
i assuming there would be 1 group of 2 but that sounds kinda dumb now that i think about it
lusty pine
say you are A and the certain person is B
label the groups to be groups are
a,b,c,d,e,f,g where f and g are the 3 groups
try finding the P(A in a)×P(B in a)×ammount of groups of 4+P(A in f)×P(B in f)×ammount of groups of 3
im pretty sure
wait nk
there
we multiply by ammount of 4 so we take into consideration goinf into a,b,c,d,e
so here, P(A in a) is 4/26, ill let you do the rest
lilac sky
Hm
P(A in a) = 4/26
P(B in a) = 4/26
So 5(4/26)(4/26)
=80/676
=20/169
P(A in f)=3/26
P(B in f)=3/26
So 2(3/26)(3/26)
=18/676
=9/338
So 20/169+9/338
180/57122
=0.03%
Oh wait
I multiplied
=14.5%
Is that right?
.close
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Available help channel!
errant vortex
can someone explain the difference between or, and because i'm confused in probability when it says or n and what does it want me to do
errant vortex
hm so i'm confused
so idk how to tell the difference and how to always get the right answer
graceful coral
or = either or both sides are true
and = both sides are true
false or false = false
false or true = true
true or true = true
false and false = false
false and true = false
true and true = true
errant vortex
ohhh okay
little dagger
or just understand it with simple english
you have to eat fries or burger
you have to eat fries and bruger
errant vortex
ohhh so or limits you to one category
graceful coral
or just understand it with simple english
you have to eat fries or burger
you...
The first can easily be confused with xor here
graceful coral
ohhh so or limits you to one category
No, that's xor
errant vortex
The first can easily be confused with xor here
what's xor
graceful coral
false xor false = false
false xor true = true
true xor true = false
stoic locust
[;
graceful coral
or means that either side is true (including both being true), xor means that exactly one side is true
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Available help channel!
woven sundial
did 1, need help with 2
amber waspBOT
did 1, need help with 2
bleak shoal
did 1, need help with 2
they probably meant express with a rather than A.
Here is a hint: what is PQ:AD? can you, through parallel properties, get some equalities?
woven sundial
they probably meant express with a rather than A.
Here is a hint: what is PQ:AD...
No they meant exactly to express with A
The answer says 2/3a
I just have no idea how to get to it
PQ is a straight line
So it should be PQ= a+2a/2
that would be 3a/2
bleak shoal
No they meant exactly to express with A
yeah i mean they probably meant "a" instead of the capitalized one
bleak shoal
The answer says 2/3a
try to follow my hint
woven sundial
yeah i mean they probably meant "a" instead of the capitalized one
Oh yeah
woven sundial
they probably meant express with a rather than A.
Here is a hint: what is PQ:AD...
Hm
I mean
you can prove that some triangles are similar? maybe
bleak shoal
you can prove that some triangles are similar? maybe
oh yeah ofc!
bleak shoal
but do you know some parallel lines ->equal ratio properties?
woven sundial
but do you know some parallel lines ->equal ratio properties?
Wait no i dont
bleak shoal
Wait no i dont
welp lets prove it then
woven sundial
but do you know some parallel lines ->equal ratio properties?
Wait hold on what do you mean by this, can you give an examle
bleak shoal
Wait hold on what do you mean by this, can you give an examle
if DE is parallel to BC
woven sundial
Yes
bleak shoal
then AD:AB=DE:BC=AE:AC
bleak shoal
wait thats what you meant?
yeah lol
bleak shoal
they probably meant express with a rather than A.
Here is a hint: what is PQ:AD...
since PQ is parallel to AD, can you transform the ratio PQ:AD to something else?
bleak shoal
👍
bleak shoal
if DE is parallel to BC
similarly if the triangles are like this we have some ratio properties
woven sundial
similarly if the triangles are like this we have some ratio properties
Yeah thats another variation
bleak shoal
MP/PA= MQ/QD= AN/ND
ok, MP/PA seems hard to compute, can you translate it to something easier?
notice BM is parallel to AN
woven sundial
Right
Lets see
AN/BM=AP/PM=NP/BP
Its the same
Exept AN is a
and BM is 0.5a
Lets see
If it helps
bleak shoal
should be MP/AM
it should be MP/AM and MQ/MD
woven sundial
Ok hold on ill write it down rq
bleak shoal
I forgot this variation
welp, since the proof is easy, you can just try to derive it on the spot if you forget
woven sundial
welp, since the proof is easy, you can just try to derive it on the spot if you ...
Ok so i still have no idea
i wrote it down but theres only ad that we know
bleak shoal
Ok so i still have no idea
yeah thats why we wanna transform PQ/AD to some ratio we might know
we see that PQ/AD=MP/AM
bleak shoal
AN/BM=AP/PM=NP/BP
also you see that AP/PM is in very similar form here
woven sundial
Oh shit
bleak shoal
and AN/BM have a known value: 0.5a/0.25a=2
woven sundial
and AN/BM have a known value: 0.5a/0.25a=2
Wait wait what
AN is a
BM is 0.5a
isnt it
woven sundial
Oh right
bleak shoal
AN/BM=2
woven sundial
Yeah
bleak shoal
we see that PQ/AD=MP/AM
so AP/PM=2.... note the similarity between AP/PM and MP/AM here...
maybe you can try to transform one to the other?
hint: write everything as multiples of PM
woven sundial
Ok ok
bleak shoal
I got no clue
what is AP in terms of PM?
bleak shoal
I got no clue
you will need to use AP/PM=2
woven sundial
you will need to use AP/PM=2
Yeah i get it
bleak shoal
No idea
the length of AP in terms of the length of PM
since AP/PM=2 we have AP is 2PM
woven sundial
Arent AP=PM
woven sundial
🤔 why is that so?
I had an explanation to 1at was that DM and AM meet at the midpoint M and CN and BN meet as midpoint N and because they intersect, I think it would form a straight line that’s parallels to the base AD
woven sundial
if AP=PM then AP/PM=1
Exactly thats why i got confused
bleak shoal
I had an explanation to 1at was that DM and AM meet at the midpoint M and CN and...
what straight line is formed? PQ you mean?
woven sundial
what straight line is formed? PQ you mean?
yes
woven sundial
well how does that give you AP=PM?
shouldnt have P turned into a midpoint
And Q too
because does it just turn into a straight line without them being midpoints
bleak shoal
shouldnt have P turned into a midpoint
as long as P and Q have the same height above AD, then they are parallel?
PQ being paralle to AD doesn't tell us a lot
bleak shoal
its just that P and Q arent midpoints
i think a lil bit more rigor needs to be added
you want to put PQ parallel to AD into ratio equalities
what would imply PQ being parallel to AD?
woven sundial
what would imply PQ being parallel to AD?
MP/AP=MQ/QD
Oh wait
that gives us that
MQ/QD is 2
bleak shoal
MP/AP=MQ/QD
correct
bleak shoal
Yes
i think your argument for why AP=PM is maybe just getting a lil bit carried away by some wrong intuition
woven sundial
i think your argument for why AP=PM is maybe just getting a lil bit carried away...
I understand that it makes no sense but i had no other explanation
bleak shoal
I understand that it makes no sense but i had no other explanation
things regarding intuition is hard to help with, for now my suggestion is to not trust anything unless you know the full rigorous proof.
you build intuition through those proofs and example
woven sundial
you build intuition through those proofs and example
yes that AP=PM
while thats not the case
But is PQ really a straight line
bleak shoal
But is PQ really a straight line
wdym by that? PQ is defined to be a line that is straight
woven sundial
<:blobwg:1130147597428998184> wdym by that? PQ is defined to be a line that is s...
My explanation to 1 didnt really state that P and Q are midpoints
I just stated how it could be a staright line
bleak shoal
i don't understand what you mean by straight line here
u can't have a wiggly line connecting PQ by definition
woven sundial
i don't understand what you mean by straight line here
Ah ill try to explain it to you
I dont really know the meaning in english
but ill find it rq
Google translate says it means "Means section"
do you know what that is?
bleak shoal
Google translate says it means "Means section"
not rlly
woven sundial
not rlly
ok then ill try to find an accurate one
midsegment
Right
I remembered
bleak shoal
midsegment is the name
midsegment of?
woven sundial
midsegment of?
my explanation in 1 was to prove that PQ is a midsegment
bleak shoal
PQ is a midsegment of AMD iff P and Q are midpoints
woven sundial
Exactly
Thats why i was confused when AP/PM was 2
that means i also proved 1 incorrectly
💀
bleak shoal
Exactly
the midsegment is defined for a triangle
but you are "extending" this to the intersection of two triangles
which doesn't quite work
woven sundial
but you are "extending" this to the intersection of two triangles
Yeah
I dont know how to prove that PQ is parallel to AD
bleak shoal
this is sort of a scenario where you really have to ask yourself whether the "intuition" you have is correct
woven sundial
this is sort of a scenario where you really have to ask yourself whether the "in...
i thought it made sense
that why you gotta put it formally
woven sundial
<:KEK:586240877358350341> that why you gotta put it formally
Can you help me prove 1 then continue to 2
bleak shoal
Wait what how
parrallel <-> same ratio
if you want to prove it, try to use similar triangle
ok lemme state it formally
woven sundial
parrallel <-> same ratio
if you want to prove it, try to use similar triangle
How did we get MP/AP=MQ/QD before proving its parallel
bleak shoal
How did we get MP/AP=MQ/QD before proving its parallel
oh im just saying we want to show that
bleak shoal
Shouldnt it be 2
you might've gotten the variable mixed up look at the graph again
MQ/QD is MC/ND
woven sundial
Yes
bleak shoal
0.5a/a
bleak shoal
MP/AP isnt 1/2 tho or am i mistaken
it is 1/2
woven sundial
it is 1/2
bleak shoal
so they are equal!
bleak shoal
just to make sure, you know why the equal ratio implies parallel right?
woven sundial
1/2 is much easier to work with
woven sundial
just to make sure, you know why the equal ratio implies parallel right?
Yes
bleak shoal
ok good!
woven sundial
ill use the 1/2
bleak shoal
so you see the ratio isn't really 1, but 1/2
woven sundial
so you see the ratio isn't really 1, but 1/2
We said it was 2 then 1 and now 1/2
bleak shoal
which sort of proves that your intuition originally was wrong
woven sundial
which sort of proves that your intuition originally was wrong
True
bleak shoal
We said it was 2 then 1 and now 1/2
for the 2 we had the fraction flipped
its correct
woven sundial
Ok ill try to put it in other ratios
bleak shoal
we said AP/PM=2
woven sundial
see if i can get somethin
bleak shoal
but PM/AP=1/2 is still correct
woven sundial
yes
bleak shoal
Ok ill try to put it in other ratios
👍 PM/AP=1/2 is a known ratio now, and you can try to make it in some way equal to PQ/AD
(they are not equal but you can do something to the fractions)
woven sundial
👍 PM/AP=1/2 is a known ratio now, and you can try to make it in some way equal ...
if we use thales on triangle AMD and use a varation we get MP/MA=MQ/MD=PQ/AD
AM=2PM
Or am i dumb
MD=2MQ
bleak shoal
Or am i dumb
AP=2PM not AM
woven sundial
Right
bleak shoal
👍 PM/AP=1/2 is a known ratio now, and you can try to make it in some way equal ...
from this ratio
woven sundial
MQ=2QD
bleak shoal
how many PM is AM?
woven sundial
MP is x AP is 2x
bleak shoal
hint: AM=AP+PM
bleak shoal
YES!
woven sundial
PQ=3AD?????
bleak shoal
if we use thales on triangle AMD and use a varation we get MP/MA=MQ/MD=PQ/AD
so what is this?
woven sundial
No wait
woven sundial
so what is this?
1/3
bleak shoal
and you are done!
bleak shoal
AD is 2a isnt it?
woven sundial
It is
woven sundial
what is PQ?
Wait uhhh
woven sundial
Thats crazy
thank you so much
I have more problems that idk how to do but woudve helped me for a hour so i wont bother you
bleak shoal
no worries you got that PQ is 2a/3 right?
bleak shoal
no worries
woven sundial
no worries
ill prob open a new help channel in a couple of hours since the deadline is tomorrow....
I got 5 more problems
Thank you again ill close this channel now
.close
high berry
amber waspBOT
high berry
idk how to being
summation of F_x and summation of F_y = 0?
can someone solve it and send me the answer, i know its not allowed, but i just need to see the working of one question, so i can attempt the rest on my own
amber waspBOT
Available help channel!
sonic gazelle
hi
sonic gazelle
can someonehelp me
hard monolith
Ok.