,w second derivative ln(2t) - sqrt(6t) with respect to t
#help-33
cunning fiber
elfin berryBOT
cunning fiber
@drifting goblet this is just straight up wrong
drifting goblet
<@509014527736676393> this is just straight up wrong
Is my answer correct?
cunning fiber
algebra lol
haughty zinc
Never seen a problem like this sos 
( can anyone please help?
marsh citrusBOT
Never seen a problem like this sos <:CastoSob:1353846244648292372> ( can anyone...
haughty zinc
void elm
do you remember how numbers are written in other bases? 
void elm
so you know how the 1s digit in base 10 corresponds to, well, ones?
and the tens digit corresponds to tens, the hundreds corresponds to hundreds, etc?
haughty zinc
Kinda
void elm
it turns out that you can write this as a sum
for example, the number 123 in base 10 is really $1 \times 100 + 2 \times 10 + 3 \times 1$
elfin berryBOT
higher!
void elm
you can also write that as $123 = 1 \times 10^2 + 2 \times 10^1 + 3 \times 10^0$
elfin berryBOT
higher!
void elm
does this make sense so far? 
all we're doing is writing 123 as a sum of powers of 10 instead of in its usual way
haughty zinc
uhh
void elm
**higher!**
you can read this as "one hundred + two tens + 3 ones"
stoic saddle
the plan btw is to simply convert these numbers from quaternary and quinary into decimal and then add "as normal"
void elm
mhm
haughty zinc
lem see rw
void elm
you can read this as "one hundred + two tens + 3 ones"
the point here is that we can do the same thing for numbers in other bases
but instead of using powers of 10, we're gonna use powers of the base instead
for example, the number $101_{\text{two}}$ is the sum [101_{\text{two}} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5]
elfin berryBOT
higher!
void elm
as Ann said, we can just turn all our numbers into decimal form via this process and add normally 
haughty zinc
so like if its 5 like 4,3,2,1,0 as ^4,3,2,1,0
I think Im kinda stupid at this point
haughty zinc
yea
stoic saddle
right
so you know that when writing a number in the ordinary way, going right to left you have a ones place, a tens place, a hundreds place and so on, yeah?
stoic saddle
the value of each place is ten times the one before it. that is what makes our number system "base ten".
haughty zinc
oh yea
stoic saddle
but the fun thing is that you could conceive of numeration systems with another number as the base.
haughty zinc
but then if i do that the answer will be over 1000 right?
stoic saddle
for example, in base six, you would have a ones place followed by a sixes place, then a thirty-sixes place, and then a two-hundred-sixteens place, and so on. (i am stating these in familiar/decimal terms so it is a bit clunky)
stoic saddle
but then if i do that the answer will be over 1000 right?
we'll get back to your problem in a bit
haughty zinc
Alright
stoic saddle
for now i want to go over in a bit more detail about how alternative bases work
so just to show you how the same number looks in two different bases
the number 176 (decimal)
its decimal representation can be read as:
- 1 hundred
- 7 tens
- 6 ones
(and in fact this structure is reflected in English number words. "seventy" instead of "seven tens", but still)
haughty zinc
stoic saddle
the same number written in base six, however, would look like 452, to be read as:
- 4 "thirty-sixes"
- 5 sixes
- 2 ones
haughty zinc
how would it be six?
stoic saddle
wdym
haughty zinc
like why 4" thirty-sixes"
stoic saddle
are you asking why we're counting thirtysixes, or are you asking why we got 4 of them
haughty zinc
why counting thirtysixes
stoic saddle
it's six times six
haughty zinc
oh
stoic saddle
a thirty-six is six sixes in the same way as a hundred is ten tens
stoic saddle
omg why are you multiplying these
no
(decimal) 4Γ36 = 144, but 5Γ36 = 180, which is too much.
stoic saddle
stoic saddle
i thought you meant 6^4
if i wanted to talk about powers of six then i would
stoic saddle
for example, in base six, you would have a ones place followed by a *sixes* plac...
read this again. in base six, each place has value equal to six times the previous.
stoic saddle
6**^2** = 36
haughty zinc
oop
stoic saddle
the "4" in "452_six" means 4Γ6^2
stoic saddle
yes
stoic saddle
that's 1234(quinary) spelled out, yeah
stoic saddle
yeah that's 123(quaternary)
stoic saddle
yeah it works out to 221
haughty zinc
Thank youu
I think i js didn't know that kinda problem <3
thank you for helping <3
humble lichen
Can someone help me to understand the conclusion of this proof? I understand the intention is to show that we have a homeomorphism from the restriction of p to U, but I don't undestand how Munkres actually... gets to the conclusion
marsh citrusBOT
Can someone help me to understand the conclusion of this proof? I understand the...
humble lichen
I see that he proved surjectivity and I understand that, but he only proved injectivity for the closure so saying the closure is a homeomorphism makes sense to me, but then he just says that the open sets are also fine but how?
indigo nest
Restriction of a homeomorphism is a homeomorphism still
So since he's proven it for the closure, he can restrict to the interior
humble lichen
Okay, that makes sense... I guess I wasn't really thinking about the fact that the closure is bigger
indigo nest
Understandable
marsh citrusBOT
marsh citrusBOT
Available help channel!
rugged falcon
Can u solve number 35 I got 25 as answer
marsh citrusBOT
Can u solve number 35 I got 25 as answer
wary lichen
,rccw
elfin berryBOT
wary lichen
show your work prob
rugged falcon
I did my work In exam this morning
wary lichen
Have you at least noted something or somewhat remember your procedure?
rugged falcon
Ye
Lemme type it
Nvm I will write and send 1 min
Oh gosh I screwed up so bad
I did it wrong
wary lichen
In fact, well, ill suppose ill guide you back through it
Ill take it as you know your trig basics
rugged falcon
K
wary lichen
First of all, you know that PQO is an isosceles with two sides = 5, other = 8
wary lichen
For ease of use, we will discard half the diagram and end up with something like this
rugged falcon
Kk
wary lichen
height is known but not base
okay we looking at it from a different perspective, but yeah
tiny burrow
base is 3
wary lichen
Given the nature of the problem, where we asked by the tangent of the circle, we dont really care for the other "side" anyways
Do you know how to find that angle?
rugged falcon
How base is 3 guys? My friends told the same
tiny burrow
How base is 3 guys? My friends told the same
it's just pythagorean theorem man
wary lichen
How base is 3 guys? My friends told the same
Is one of the most known right triangles, but you could also find it using pythagoras, any clue how?
rugged falcon
Wait how u find 5?!
tiny burrow
Wait how u find 5?!
dude....radius
wary lichen
is the radius of the circle, its just info they gave you
tiny burrow
i think knowing TR is more important
rugged falcon
OHHH
tiny burrow
since law of cosines could really help here
wary lichen
since law of cosines could really help here
not needed really
rugged falcon
So what is TO?
wary lichen
#help-33 message
coming back, do you know how to find this angle?
rugged falcon
Given the nature of the problem, where we asked by the tangent of the circle, we...
I understood from here
tiny burrow
not needed really
i abuse cosine law so dont blame me lol
wary lichen
I understood from here
not precisely sure what this means π₯
silk sable
Might be easier to just show they are similar triangles.
rugged falcon
DUDE THEY DIDNT TEACH THAT LAW IN SCHOOL
Proportionality and similarity that's all lol
wary lichen
Might be easier to just show they are similar triangles.
oh, then they do expect similarity
well, time to show they are similar then
tiny burrow
I'm 10th grade bro
cosine law is in 10th grade
rugged falcon
It's not in my syllabus...
tiny burrow
Might be easier to just show they are similar triangles.
yeah i think its possible to do congruency
rugged falcon
calm harbor
DUDE THEY DIDNT TEACH THAT LAW IN SCHOOL
Sadge
rugged falcon
Given the nature of the problem, where we asked by the tangent of the circle, we...
U meant this?
wary lichen
rugged falcon
Oh yeah
wary lichen
Yeah, i was thinking you knew a few more laws about trig, np anyways, it can be solved like this too
rugged falcon
Oh okey
wary lichen
If you look at it carefully, you can see that you have two right triangles sharing a side, and they have a right angle in common.
You could take the smaller (the one in the right), rotate it, and find they are similar.
Still, you will have to find a factor of proportion. Can you see what you need to match?
silk sable
AAA proves similarity.
wary lichen
You know the bottom side from the small one is 3.
You know the right side of the bigger one is 4, and since those are the sides that are similar, you need to find a number that makes it so:
3 * a = 4
Once you find it, you can multiply 5 by it, and youll get the answer
silk sable
Similar triangles have corresponding sides. Determine which sides correspond to each other.
wary lichen
Yeah, thats correct.
rugged falcon
O
Hey can u gimme a piece of advice to get better on math
I'm only getting 57/80 in this test
silk sable
Hey can u gimme a piece of advice to get better on math
What kind of advice are you looking for?
rugged falcon
To get better marks
silk sable
Let me ask you this question. What do you think is the purpose of school?
rugged falcon
To study
silk sable
That's it?
rugged falcon
Uh yeah 
silk sable
Public school serves several purposes. One of those purposes is to introduce you to areas of study that you not otherwise have had access to. It's not uncommon for children to go into the same field of work as their parents. This is because parents pass on the knowledge of what they know to their children. Children grow up and go into the same field of work because it is what they are mostly knowledgable about.
rugged falcon
Well yeah
silk sable
Another purpose is to teach you the skills that you will need to learn on your own. This is an aspect which causes rural students to fail in college. High schools which do not challenge a student enough to force them to develop good studying habits hinder students in college.
rugged falcon
O
indigo nest
Another purpose is to teach you the skills that you will need to learn on *your ...
Can confirm, rural student who struggled through college here
silk sable
You should be learning how to study. Taking notes is a skill that needs to be developed.
rugged falcon
So uh what's ur conclusion?
silk sable
That's it. Develop your studying skills.
rugged falcon
Oh okey
silk sable
Everybody has different studying techniques that work for them. I have my own.
rugged falcon
Btw can I ask smth?
silk sable
Yes.
silk sable
I was a web developer. In college, I had my own difficultiies related to my previous comment about rural schools. It took quite some time for me to understand why I was failing. At some point, I took a philosophy class that taught me how to ask questions. A well-thought out question gives you well-thought out answers.
rugged falcon
Oh that's rlly cool
I wanna study law in canada in fact my dad knows a person who can arrange me for it and my seat git confirmed
My dad studied law too so I'm doing it too
rugged falcon
Public school serves several purposes. One of those purposes is to introduce yo...
Same thing u said
silk sable
My one tip for learning math well. As you are solving a math problem, write out your thought process as you are solving the problem. Those notes to yourself are useful when it comes to studying. If the notes don't make sense when you re-read them, redo the notes so they do make sense.
If you need to use a formula, write out the formula. Repetition makes things easier to remember.
rugged falcon
Oh okey but I need to tell u some harsh truths abt me
silk sable
Ok.
tropic minnow
I'm so lethargic and I don't write and study
suck it up and deal with it
silk sable
That's something you will have to correct. If concentrating is problematic for you, eliminate distractions. If you have a study area, get a big cardboard box and make a wall in front of you.
tropic minnow
no one really cares unless it makes them feel good
rugged falcon
suck it up and deal with it
Sheesh it's easy for u to say lol
tropic minnow
Sheesh it's easy for u to say lol
do you think I don't struggle with it?
rugged falcon
That's something you will have to correct. If concentrating is problematic for ...
Dude it almost seem impossible
rugged falcon
do you think I don't struggle with it?
Idk
U sound u unalive every distractions in ur life jeez lol
But I will try
tiny burrow
You *should* be learning how to study. Taking notes *is* a skill that needs to ...
notes isnt exactly the biggest thing but self study other than tuitions and school by your own completely is important
tropic minnow
Idk
suffer because you tried
or suffer because you didn't try
the second option mostly leads to a net positive happiness
tiny burrow
anyways i think this is drifting off topic
rugged falcon
notes isnt exactly the biggest thing but self study other than tuitions and scho...
Yeahh
I don't get the mood to study in my home lol but in tution I have big fire in me lol
tiny burrow
it doesn't matter if you like it or not you absolutely have to
delete every single game that you might be using too much
or app
rugged falcon
Ye your right
tiny burrow
i did that
rugged falcon
Oh
tiny burrow
use .close
ornate leaf
hello there a reason general form isnt used ?
marsh citrusBOT
hello there a reason general form isnt used ?
ornate leaf
is it not true for y' = f(at,by)
stoic saddle
i think you misunderstand
ornate leaf
on the previous page it covered this form
stoic saddle
adding those extra a and b simply introduces more moving parts that are completely unnecessary
ornate leaf
so couldnt be f(at,y)
fervent rampart
y ' = G(ax + by) is a very specific form of ode which is not "the most general form an ode can take"
ornate leaf
t isnt a function is it ?
ornate leaf
y ' = G(ax + by) is a very specific form of ode which is not "the most general f...
i didnt say the most
fervent rampart
y ' = G(ax + by) is a very specific form of ode which is not "the most general f...
in fact it's the most general form an ode that can be solved with a very specific substitution can take
y' = f(t,y) is just the most generic form you can write a first order ode in, where t is understood to be the independent variable and y is the dependent variable
ornate leaf
y' = f(t,y) is just the most generic form you can write a first order ode in, wh...
oh so this consists of all the types of first order odes
fervent rampart
yes, because the theorem is intended to apply to all first order odes
ornate leaf
yes, because the theorem is intended to apply to all first order odes
is the theorem true both ways
in other words is there a unique solution to a first order ode if and only if those conditions are met
fervent rampart
no
the partial derivative being continuous is actually a stronger condition than strictly necessary
fervent rampart
the less strong condition than f_y being continuous is lipschitz continuity in y. but you aren't expected to know what that means yet so they chose a condition which implies that instead
ornate leaf
ok so if df/dy isnt continious
there can still be a unique solution
nvm read that wrong
ornate leaf
the less strong condition than f_y being continuous is lipschitz continuity in y...
ok so if the conditions arent met i cant make any conclusion
fervent rampart
yes. it's likely that it will fail to exist or be unique but not necessarily guaranteed
ornate leaf
yes. it's likely that it will fail to exist or be unique but not necessarily gua...
ok
ty for your time
.close
midnight flower
hhi
past thicket
Hi!
midnight flower
i need help
past thicket
you can post your question
midnight flower
ill send
hard lantern
Post question first so bot can pin it.
calm harbor
,rccw
hard lantern
,rccw
elfin berryBOT
calm harbor
calm harbor
elfin stone
anyone here
Are you just having problem with y?
or both
lemme rephrase my problem: What's your current progress?
Please ping me when you're back.
midnight flower
lemme rephrase my problem: What's your current progress?
wdym
midnight flower
q19
elfin stone
i tried all prperties i know
okay, have you found either x or y?
elfin stone
midnight flower
only 110 is there
elfin stone
Your x is correct
midnight flower
and bcd is 80 in question
elfin stone
ill get half marks then
lemme verify y real quick
midnight flower
hmm
elfin stone
yeah, your y is incorrect
midnight flower
whats the ans
elfin stone
y is apparently half of ADC
elfin stone
You can figure it out, right??
You already got DCB = 80
midnight flower
topper of class said x is 30
midnight flower
You can figure it out, right??
You already got DCB = 80
sure thanks
elfin stone
topper of class said x is 30
Sure, totally legit answer
midnight flower
and i thought "wtf?"
elfin stone
π₯²
midnight flower
π
elfin stone
and i thought "wtf?"
They're probably gaslighting you lmao
elfin stone
nah, you'll get half of the marks for this question
hard lantern
,rccw
elfin berryBOT
hard lantern
What did you even try
elfin stone
y is simply 50, because DCB is 80 so the other angle must be 100, divde by 2 = 50
midnight flower
What did you even try
i added extension
elfin stone
If you're curious
calm harbor
elfin stone
No, you're supposed to share your work in the first place
That's not how things work in this server
midnight flower
can i whiteboard
elfin stone
you mean activity? No, it's been disabled
midnight flower
hmm
i added triangle pmx such that sp=px and pm bisects angle m
then sas
thats all
marsh citrusBOT
@midnight flower Has your question been resolved?
fathom cypress
have you solved this? (you can ping me if you still need help. if you have done, pls close ts channel)
fathom cypress
what is the question again
midnight flower
wdym
fathom cypress
so we have sr parallel to pq right?
what do we know abt the angles if sr is parallel to pq?
midnight flower
that makes no sense
midnight flower
so we have sr parallel to pq right?
yes
midnight flower
what do we know abt the angles if sr is parallel to pq?
its a ||gm?
fathom cypress
no:β)
midnight flower
π
fathom cypress
since i cant actually get a question for u right, ima say it
we have srm congruent to rmq by alternate interior angles
and bc MR bisects QRS, we have SRM congruent to MRQ
since SRM= RMQ, and QR= SRM,
we have RMQ =QRM
midnight flower
we have to prove pm = sp
fathom cypress
i understand that
midnight flower
and?
fathom cypress
then we have isoceles triangle qrm
midnight flower
ok?
fathom cypress
then we have isoceles triangle qrm
do you understand ts
fathom cypress
where?
midnight flower
how is it isoceles
fathom cypress
since SRM= RMQ, and QR= SRM,
we have RMQ =QRM
does ts make sense to u?
fathom cypress
then qrm isoceles by property
midnight flower
continue
fathom cypress
ok
we have mq=mp bc m is midpoint of pq and ps=qr right
and qrm isoceles, so mq=qr
then we have mp=mq=qr=ps
does ts make sense to u, if not, why?
marsh citrusBOT
@midnight flower Has your question been resolved?
ocean helm
marsh citrusBOT
ocean helm
what concept am I learning here
the prof has a thick accent, his slides are incoherent and he doesnt post book chapters
I just need to know what am I learning to know what im supposed to look up in the book and youtube
I wish there were other sections with different prof;-;
ocean helm
Ur learning integral calculus I think
yeah calc 2
but this specific thing that im just trying to find out
and the c seems to just be a label
im not sure
hm, seems that average value is the thing
thanks
.close
marsh citrusBOT
paper raptor
im not sure
Mean Value Theorem for Integration
(\exists c\in[a,b]:f(c)(a-b)=\int_a^bf(x)dx)
elfin berryBOT
PajamaMamaLlama
marsh citrusBOT
Available help channel!
finite forum
marsh citrusBOT
wet holly
Use cos(2theta) = 1 -2sin^2(theta) to rewrite sin^2(2theta) in terms of cos(4theta)
zinc heart
First you can move the constant out
zinc heart
Use cos(2theta) = 1 -2sin^2(theta) to rewrite sin^2(2theta) in terms of cos(4the...
cant he just make sin^2theta cos^2theta into sin^2theta(1-sin^2theta)?
and then distribute
lavish pelican
no
zinc heart
yeah he cano
wet holly
cant he just make sin^2theta cos^2theta into sin^2theta(1-sin^2theta)?
what you do with the sin^4theta term then
zinc heart
reduction identity
wet holly
what's the reduction identity? Google just says it's the same one I said and then you'd just end up with a cos^2 term after expanding the sin^4 term
ebon geyser
x = sint
lavish pelican
what's the reduction identity? Google just says it's the same one I said and the...
zinc heart
I'm not gonna do it
cause im lazy
but its possible
you'll get the same answer if you use my way
wet holly
oic
lavish pelican
obviously
its just that its the worst way possible
best if u like wasting ur time
marsh citrusBOT
@finite forum Has your question been resolved?
finite forum
Use cos(2theta) = 1 -2sin^2(theta) to rewrite sin^2(2theta) in terms of cos(4the...
idk how i didnt see that
.close
native minnow
Hello great math fellows, I need some help regarding understand the following proposition from a paper I'm reading.
marsh citrusBOT
Hello great math fellows, I need some help regarding understand the following pr...
native minnow
If we take a non-continuous bijective additive mapping f : R β R, the natural extension g: C β C, g(Ξ± + iΞ²) = f(Ξ±) + if(Ξ²) is an additive bijection preserving orthogonality in both directions. We shall see next that this counterexample can only occur when the inner product space in the domain is oneβdimensional.
first, why the map f must be non-continuous?
Also the "natural extension" of f which is g. is it something dedicated to complex spaces?
marsh citrusBOT
@native minnow Has your question been resolved?
main idol
probably need the actual context of the paper to answer your question
a couple sentences usually isn't enough
marsh citrusBOT
@native minnow Has your question been resolved?
violet jasper
This the question
marsh citrusBOT
This the question
elfin stone
This the question
Do you know the definition of displacement?
violet jasper
Ya
elfin stone
So what seems to be the problem?
violet jasper
Now done, it's clear
violet jasper
Ty
violet jasper
Kk
calm harbor
.solved
timber imp
marsh citrusBOT
timber imp
,rccw
elfin berryBOT
cunning fiber
Intuition tells me to ||rotate triangle ADE about A onto AB so D' = B||
timber imp
idk everything with x just cancels out and doesnt make sense
timber imp
so 115-x?
lavish pelican
yeah but ur right it is cancelling
silk sable
There are quadrilaterls ABFE and AFCE. That may help.
timber imp
oh yeah
timber imp
There are quadrilaterls ABFE and AFCE. That may help.
how would we use them
cunning fiber
Intuition tells me to ||rotate triangle ADE about A onto AB so D' = B||
yeah this kills it (actually it kills both parts)
silk sable
There are four inner quadrilaterals. You could make a system of equations, me thinks. π€
Or maybe not. I haven't done the mental gymnastics yet.
silk sable
Give me a moment.
cunning fiber
yeah this kills it (actually it kills both parts)
^
timber imp
yeah this kills it (actually it kills both parts)
wdym by kills?
cunning fiber
everything else is trivial from then on out
aka you basically solved the question by doing 1 thing
timber imp
so like make an isosceles triangle
cunning fiber
where is isosceles coming from
cunning fiber
timber imp
where is isosceles coming from
what would weo do after then?
timber imp
i meant after the rotation
cunning fiber
I'm aware of that
timber imp
I'm aware of that
isnt rotation just moving it around and we already did that
cunning fiber
lemme rephrase
what do rotations preserve
you can use your intuition based on moving things around to answer this if you want to
timber imp
the lengths and angles of the shape?
cunning fiber
correct
so you can actually fill in some more information now
fill in what you can and send a picture of what you have after that
timber imp
fill in what you can and send a picture of what you have after that
This is what I got but idrk what to do
cunning fiber
angles are fine
what happened to labeling the lengths
also maybe draw a nicer diagram without the scribbles because that will be helpful in not getting confused
timber imp
its a rough sketch i can fix next time
cunning fiber
ok
timber imp
timber imp
o wait oops
cunning fiber
also you can use variables or tickmarks to label equalities that you don't have concrete numerical values for
so that you can actually label everything
timber imp
@cunning fiber
cunning fiber
also you can use variables or tickmarks to label equalities that you don't have ...
also you can use variables or tickmarks to label equalities that you don't have concrete numerical values for
timber imp
do u mean like extra variables
timber imp
ex. you can label both of these a
what would weo d after?
cunning fiber
you tell me
timber imp
idk what to do
cunning fiber
you can take some time to make observations
I don't expect you to get it instantly
cunning fiber
Intuition tells me to ||rotate triangle ADE about A onto AB so D' = B||
I mean, neither did I ^ (part 1)
cunning fiber
yeah this kills it (actually it kills both parts)
^ (part 2)
(observe the time gap)
cunning fiber
you can take some time to make observations
oh yeah feel free to list what you see in chat
and don't worry if your observations feel "too obvious"
that's how you gain intuition/acclimate yourself (source: personal experience)
timber imp
that's how you gain intuition/acclimate yourself (source: personal experience)
theres like a right angle
with the new angles formed
cunning fiber
you're talking about this one right
timber imp
the 25 20 and 45
timber imp
thats all i hav found rn
cunning fiber
that's fine
I have like 13 minutes before I need to leave anyway
and I'm just killing time lol
timber imp
and I'm just killing time lol
could i have a few hints
cunning fiber
idt you need them
your first observation is already pretty good if you state it from a different perspective
cunning fiber
90 = 45 + 45
timber imp
90 = 45 + 45
how would we use that? to help find x
timber imp
Donβt try to find x
isnt that what the question is asking tho
cunning fiber
Yeah but donβt try to get to x immediately
timber imp
Yeah but donβt try to get to x immediately
could we do something isosceles with the 2 a's
or the 2 1s
@cunning fiber
silk sable
Don't feel bad. It took me a while to figure out what Pigeon was doing.
timber imp
Don't feel bad. It took me a while to figure out what Pigeon was doing.
do u know how to do it now?
silk sable
Here's a better drawing.
Think about which segments have the same length.
The caveat here is that one segment will be looked at twice.
timber imp
The caveat here is that one segment will be looked at twice.
is it AB=AD?
timber imp
Pigeon had you move the triangle up to the top and it formed another triangle.
so its one of the lines in AFE' ?
silk sable
Yes.
timber imp
is it AF?
silk sable
What about AF?
timber imp
the segment thats looked at twice
timber imp
And there is a reason why the top-right point is called E'.
its part of the point e in the original right
timber imp
they are equal
silk sable
Do you see the two triangles that extend from point A?
timber imp
AFE and AFE'?
timber imp
Note that the angles from A are both 45 degrees.
what do we do with this info?
timber imp
Or are you currently taking geometry?
currently taking
silk sable
What do you know about triangles that have equal SAS?
timber imp
oh they are congruent right
timber imp
so x should be 65 degrees
silk sable
Yes. I've taken geometry many moons ago and I would not have figured this out on my own either. π
It's an interesting trick to see. I'm not sure I'd recognize to do it again if I came across a similar problem.
timber imp
It's an interesting trick to see. I'm not sure I'd recognize to do it again if ...
wait do u know how we would approach part b of the question?
silk sable
Without using trigonometry, I don't know.
marsh citrusBOT
@timber imp Has your question been resolved?
timber imp
Without using trigonometry, I don't know.
wait whats ur method with trig cause id rather just solve it than not put anything
o wait nvm with trig its easy
silk sable
o wait nvm with trig its easy
Right. π
timber imp
<@&286206848099549185> any ideas for part b :)
silk sable
AI is so wild for this explanation. It took some finessing and several corrections but it came up with a solution.
You have already seen that triangle AEF and triangle AFD' are congruent triangles.
From triangle AFE', you can show that EF is equal to FE' which is just DE + BF. This is a long-winded way of saying that EF is equal to DE + BF.
silk sable
<@&286206848099549185> any ideas for part b :)
.
timber imp
From triangle AFE', you can show that EF is equal to FE' which is just DE + BF. ...
isnt that already given tho
kinda
oh wait ef not e'f
silk sable
The point here is that you can reframe the length of EF in terms of DE and BF.
EF = DE + BF.
silk sable
Yes.
timber imp
i did x+y+1-x+1-y
silk sable
Yes.
timber imp
ohhh i get it now
silk sable
Or more formally.
EF = DE + BF
EC = 1 - DE
CF = 1 - BF
P(ECF) = EF+EC+CF
I wonder what type of psycho originally figured this one out. π
timber imp
I wonder what type of psycho originally figured this one out. π
my teacher always find weird questions every now and then and I never know where its from
silk sable
That whole shifting triangle ADE, I would have never thought of it.
timber imp
im surprised pigeon found that out
silk sable
Pigeon has probably seen this type of problem before.
timber imp
ill try keep like a mental note of those types but i highy doubt ill find answers for them
silk sable
Well ... we both learned something today. π
timber imp
tysm for helping to explain to me it was kinda hard to understand
silk sable
yw
timber imp
.close
young mantle
can i have help being walked through how to answer these questions? i think the answer is unsure without proof but im not sure and im not exactly sure how id explain it
marsh citrusBOT
can i have help being walked through how to answer these questions? i think the ...
main idol
just identify which of the sets contain [0, 4]
young mantle
so, none of them?
or wait
question 14 could contain it, right?
if y starts at 4 then moves up 1
main idol
draw [0, 4] and [1, 5] on a number line and see
A set S "contains [0, 4]" means every number in [0, 4] is also in set S
in other words, [0, 4] is a subset of S
young mantle
but the question says i shouldnβt use a number line, right?
i also dont remember how to write those on a number line
main idol
where does it say that
young mantle
well it says only use the knowledge provided so i thought i couldnβt do anything else but think
main idol
i mean it should be obvious without a number line that 0 is in [0, 4] but not in [1, 5]
i was just suggesting using a number for you to convince yourself
young mantle
well yeah i know that
queen sun
The problem is asking which of these intervals contains [0,4] basically
main idol
question 14 could contain it, right?
so why do you think B could contain [0, 4] ?
queen sun
So make sure every number from 0 to 4 is included
young mantle
let me draw something so you understand how im thinking of this hold on
i only learned functions a few hours ago so bare with me i appreciate your patience thank you
i apologize im not that bright when it comes to math
queen sun
Not really sure what the question is asking exactly
marsh citrusBOT
@young mantle Has your question been resolved?
young mantle
Not really sure what the question is asking exactly
me too
marsh citrusBOT
@young mantle Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
finite forum
yo
keen mist
just underlining it maybe?
wary lichen
Where have you gotten this from to start with
junior copper
what does the 2 lines after an answer mean
lmao it just means when you are done and want to underline the solution
its not anything deep or mathematical
finite forum
lmao it just means when you are done and want to underline the solution
fairs
.close
marsh citrusBOT
bleak ledge
Some use boxes
some just write Q.E.D.
Its doesn't mean much aside from end of your problem
vernal mantle
I do this but it looks more like a #
violet folio
Where do i ask for help
finite forum
some just write Q.E.D.
never seen that
glossy flint
Where do i ask for help
!occupied
marsh citrusBOT
Where do i ask for help
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #βhow-to-get-help for instructions).
Available help channel!
willow rampart
Pls help with 11
marsh citrusBOT
Pls help with 11
willow rampart
i divided whole equation by 2
past thicket
Iβm not seeing what that does here
willow rampart
u misunderstood i came for 11
willow rampart
no worries
elfin berryBOT
πΈπππππππΒ³
willow rampart
yes
willow rampart
**πΈπππππππΒ³**
do u mean that it looks like a root of smth
@past thicket ?
past thicket
No I just wrote it in latex so. I could see it without having to look at the paper
willow rampart
oh well now pls help me further
past thicket
Yep just lemme think about thisβ¦
use substituion
let π₯ = 2π΄ and π¦ = 2π΅
past thicket
so now we have $\sqrt{3}\sin(x)=\sin(y)$
elfin berryBOT
πΈπππππππΒ³
willow rampart
its still same but yea it still helped to reduce my effects in writing
past thicket
We can use the identity sinΒ²(π₯) = (1-cos 2π₯)/2 to transform
β3 β’ (1-cos π₯)/2 + (1-cos π¦)/2 = (-1+β3)/2
Multiply by 2 on both sides
β3 (1-cos π₯) + (1-cos π¦) = -1 + β3
marsh citrusBOT
willow rampart
thank you
marsh citrusBOT
Available help channel!
finite forum
hey
finite forum
can someone tell me where i went wrong
sending pics 1 sec
this is the answer
quick kindle
why is it 3(x-4) rather than just x - 4
stark sandal
this is a mess
finite forum
why is it 3(x-4) rather than just x - 4
yeah thats it
finite forum
like why r u doing a substitution
im doing a substitution worksheet
so i assumed i needed a sub
stark sandal
its not like the sub helped 
obtuse umbra
limpid pond
so i assumed i needed a sub
Like I could see your point but think about it even if you subbed there is nothing you could cancel/help simplify the integral
finite forum
Like I could see your point but think about it even if you subbed there is nothi...
yeah that makes sense
thanks
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
hard laurel
Can anyone tell me a short method without calculator?
marsh citrusBOT
Can anyone tell me a short method without calculator?
obtuse umbra
for question 13
a number is divisible by 6 when it's divisible by 3 and 2
if a number is divisible by 2
it's obvious to see
if a number is divisible by 3
then the sum of its digit is divisible by 3
(this can be proven btw)
trim owl
Can anyone tell me a short method without calculator?
V is proportional to t
obtuse umbra
and i don't see what i can do to 12
obtuse umbra
well i don't see how
hard laurel
π
obtuse umbra
i mean, that's literally why they asked you to round to 2 decimal places lol
sick walrus
those numbers don't look friendly enough for a short method without using a calculator.
chrome ether
We know that ||A+xb ||^2 = ||A ||^2 + x^2 ||B || ^2 +2x Aβ§B. So We know that ||A+xB||^2 - x^2||B||^2 = ||A||^2 2x Aβ§B. Then we can see that ||A+xB|| > ||A||.||A+xB || = ||A|| iff x = 0 and Aβ§B = 0. But you can't still write something that is > as >=. This leads to my issue since we know that it can only equal if the dot product is 0 but you can rewrite the inequality sign to have the equality
marsh citrusBOT
We know that \||A+xb \||^2 = \||A \||^2 + x^2 \||B \|| ^2 +2x Aβ§B. So We know t...
copper raven
We know that \||A+xb \||^2 = \||A \||^2 + x^2 \||B \|| ^2 +2x Aβ§B. So We know t...
write \|| if you want your norm bars to show up
copper raven
A+xB that's such a spoiler
chrome ether
do you guys have any suggestions on how to resolve this?
vagrant raft
I'd do b by showing the contrapositive I think
chrome ether
but don't you get the same issue with the inequalities sign if you try to show the contrapositive?
vagrant raft
wdym
chrome ether
by this I mean this statement only has equality if x = 0 and Aβ§B = 0.
vagrant raft
I didn't get this
||A+xB|| > ||A||.||A+xB || = ||A|| iff x = 0 and Aβ§B = 0
even if x = 0 and A.B = 0, |A|.|A+xB | = |A|^2 no?
chrome ether
ok so we can show that||A+xB||^2 - x^2||B||^2 = ||A||^2 2x Aβ§B. so if we take away the - x^2||B||^2 . we get ||A+xB||^2 > ||A||^2 2x Aβ§B
vagrant raft
also
|A+xB|^2 - x^2|B|^2 = |A|^2 2x Aβ§B.
did you mean
|A+xB|^2 - x^2|B|^2 = |A|^2 + 2x Aβ§B.
chrome ether
yes sorry
chrome ether
even if x = 0 and A.B = 0, |A|.|A+xB | = |A|^2 no?
thats the only time it is equal
chrome ether
don't we sqrt both sides?
vagrant raft
how do you get |A+xB| > |A|.|A+xB |
you didn't sqrt the left side
oh I get it
you didn't write the sqrt
chrome ether
from what I understand the equation simplifies to ||A+xB|| > ||A||. if the dot product is 0
wait do you think we can start from the top. because I think im confusing myself
vagrant raft
let me see if I understand:
you're saying that $|A+xB|^2 - x^2|B|^2 = |A|^2 + 2x Aβ§B$ thus $|A+xB|^2 \geq |A|^2 + 2x Aβ§B \geq |A|^2$ with equality iff x = 0 and A.B = 0 \
And at the same time, $|A+xB| \geq |A|$
I think that working with the contrapositive of statement b) is easier
elfin berryBOT
bloubbloub
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vagrant raft
i.e. assume A and B are not orthogonal and find x such that |A+xB| < |A|
chrome ether
**bloubbloub**
Compile Error! Click the <:errors:504266556054962196> reaction fo...
Well I was having trouble with was saying that I could get > with dot produc equal 0. But I think I'm going to drop that train if thought since I'm confusing myself
chrome ether
i.e. assume A and B are not orthogonal and find x such that |A+xB| < |A|
Isn't it all real x?
vagrant raft
for the contrapositive you only need to show that there exists one
negation of "for all" is "there exists"
chrome ether
Ok I see
marsh citrusBOT
@chrome ether Has your question been resolved?
molten quiver
i have to simplify and use conditions of existence but I'm not sure how to
molten quiver
(the red thing is the result im supposed to get btw)
elfin cairn
find a common denominator
molten quiver
find a common denominator
ok so 2 right then what?
elfin cairn
ok so 2 right then what?
I don't understand you
are you saying the common denominator is 2?
molten quiver
yeah
elfin cairn
a common denominator will be a multiple of both other denominators, 2 is not what you are looking for here
molten quiver
oh
elfin cairn
naturally a common denominator will be something like (x^2-2x)(x^2+2x) but there is a more reduced version. Can you see it?
molten quiver
a more reduced version in what sense? (sorry I'm bad at math)
so im not sure what your referring to
molten quiver
specifically of degree 3
ah sorry its not there
molten quiver
aight
elfin cairn
naturally a common denominator will be something like (x^2-2x)(x^2+2x) but there...
do you agree this is a common denominator?
molten quiver
do you agree this is a common denominator?
i think i must learn about common denominators first before we proceed with this exercise
plus im not sure what ^ is supposed to be in this case
elfin cairn
plus im not sure what ^ is supposed to be in this case
power
sick walrus
^ denotes an exponent.
elfin cairn
x^2 is x squared
molten quiver
ohh
oh wait nvm
i think i understand
so just write everything together?
but does that include the upper part or just the lower part?
elfin cairn
if you multiply the denominator by something you have to multiply the numerator by the same thing to preserve the value of the fraction
$\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad+cb}{bd}$
elfin berryBOT
ExpertEsquieESQUIE
molten quiver
so I have to multiply the first one with x^2+2x
and the second one with
x^2-2x
right?
(including the top part)
queen sun
It would be easier if you factorised these quadratics first
Then you can see what is needed to create a common denominator
As long as you multiply the numerator and denominator by the same thing even a polynomial like x+2/x+2 it will still be the same, so try to use that
molten quiver
It would be easier if you factorised these quadratics first
wait what
elfin cairn
what did you end up with
molten quiver
molten quiver
It would be easier if you factorised these quadratics first
(i have to use conditions of existence)
molten quiver
I ended up with this
queen sun
(i have to use conditions of existence)
I donβt understand what you mean
molten quiver
yk C.E
queen sun
I ended up with this
Now add the fractions together
elfin cairn
you combine the fractions now, and it should simplify nicely
queen sun
yk C.E
I think thatβs a thing your curriculum teaches idk what that means
Also I donβt see why you canβt factorise first
molten quiver
Also I donβt see why you canβt factorise first
whats that
queen sun
$x^{2}-2x=x*(x-2)$
elfin berryBOT
BBMaths
queen sun
Maybe factorize in us spelling
molten quiver
you combine the fractions now, and it should simplify nicely
how do i combine them?
elfin cairn
**ExpertEsquieESQUIE**
like this
molten quiver
ohhh
molten quiver
Maybe factorize in us spelling
i dont know either but since i already started in another way i think i might aswell finish it
elfin cairn
||it should be times 2||
molten quiver
one small mistake with your simplification of the numerator
oh so it's supposed to be x^2?
queen sun
So a fraction like 12/8 can be simplified to 3/2
The same applies to these polynomials
Polynomials is like x^2-2x
queen sun
**BBMaths**
Using this can you turn your denominator into 4 things multiplied together instead of 2
molten quiver
||it should be times 2||
as in x^2 or xβ’2
molten quiver
Using this can you turn your denominator into 4 things multiplied together inste...
oh
elfin cairn
as in x^2 or xβ’2
2x
elfin cairn
is this how its supposed to be?
so just multiply this by 2
queen sun
as in x^2 or xβ’2
2x^2
elfin cairn
you did (x^2 + 2x) + (x^2-2x)=x^2 but its actually 2x^2
queen sun
$\frac{2x^{2}}{(x^{2}-2x)(x^{2}+2x)}$
elfin berryBOT
BBMaths
molten quiver
like this guys?
queen sun
No
molten quiver
oh nvm the bottom dosent need the extra ^2 right
queen sun
The denominator was fine
molten quiver
ohh ok
queen sun
Do you know how to factorise x^2-2x?
molten quiver
nope
queen sun
Okay so do you know how to distribute like $(x+2)(x-1)=x^2+x-2$
elfin berryBOT
BBMaths
molten quiver
Okay so do you know how to distribute like $(x+2)(x-1)=x^2+x-2$
i guess but wait what happened to -1
queen sun
This is* just an example not related to the problem or do you mean in the example?
molten quiver
i guess but wait what happened to -1
actually nevermind i dont
molten quiver
This is* just an example not related to the problem or do you mean in the exampl...
nevermind sorry
(example)
queen sun
Wait Iβm confused now do you know distribution?
molten quiver
Wait Iβm confused now do you know distribution?
no i meant that i dont know distribution , sorry for confusing you
queen sun
This question seems hard to do without knowing distribution or factorisation
molten quiver
Ohh im just supposed to multiply
elfin cairn
yes
molten quiver
nevermind
sorry im not familiar with math lingo
so i get confused a lot
okay after i use distribution then what?
queen sun
We want to do the opposite of distribution here
Factorisation is doing this in reverse
$x^2+2x \rightarrow x(x+2)$
elfin berryBOT
BBMaths
queen sun
There we go
We need to do this to x^2+2x and x^2-2x
Then the denominator will be fully factorised (usually better that way)
molten quiver
Then the denominator will be fully factorised (usually better that way)
oh ok lemme try
molten quiver
We need to do this to x^2+2x and x^2-2x
like this?
elfin berryBOT
BBMaths
molten quiver
like this?
molten quiver
If they share a factor they can go
did i do it right?