@still temple Has your question been resolved?
#help-33
marsh citrusBOT
steep dawn
how do I begin these problems 😥 where do I start help
marsh citrusBOT
how do I begin these problems 😥 where do I start help
crude valve
both of these questions are unsolvable with the information given.
main idol
how do I begin these problems 😥 where do I start help
!original
marsh citrusBOT
how do I begin these problems 😥 where do I start help
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
steep dawn
both of these questions are unsolvable with the information given.
this is all she wrote uhmmm
main idol
Did your teacher verbally give any instructions
crude valve
this might be a stupid question but are the x's the same for all the equations
main idol
No
steep dawn
I don’t think she said anything else guys I’m sorry
dreamy pollen
Lots of questions
steep dawn
all I remember is her saying we had to have these solved by next class yada yada
dreamy pollen
First one you can not find solution unless = 0 was missed
Second one something more is needed like what kind of triangle is that, are any sides equal etc etc
Third no idea
4th can be solved
5th function is given, what needs to be found?
steep dawn
so am I just screwed orrrr
main idol
all I remember is her saying we had to have these solved by next class yada yada
Uhhh you probably missed her instructions then
crude valve
you might want to contact your teacher on questions 1, 2, 3 and 5.
dreamy pollen
I swear I’m smart!!
You are smart but questions are incomplete
Maybe your friend didn't hear properly
steep dawn
number 1 does = 0
okay so 2 of them are doable
then the others are… just
bruh
.close
marsh citrusBOT
flint jolt
To find orthogonal trajectory of any family of curve, why we need to write d.e. of the curve
marsh citrusBOT
To find orthogonal trajectory of any family of curve, why we need to write d.e. ...
flint jolt
For ex.
xy=c we can write y=c/x and then differentiate it y'= -c/x²
then we find orthogonal trajectory from here
static quarry
what do you to find the orthogonal trajectory from here?
flint jolt
replace dy/dx -> -dx/dy
static quarry
so clearly you need dy/dx in order to do this
so i guess i'm not sure what you're asking
static quarry
can you explain what you did here
flint jolt
I replaced
And then dx/dy=y/x => xdx=ydy
Then integrate both sides
This c is different from the c in the xy=c
static quarry
ok
you should probably write out more details
and use a different letter instead of c
what is your question though?
flint jolt
and use a different letter instead of c
Yeah my mistake
flint jolt
what is your question though?
Are they both(left and right) orthogonal trajectory of xy=c?
marsh citrusBOT
@flint jolt Has your question been resolved?
flint jolt
<@&286206848099549185>
still temple
Can you look up my doubt
Ok show
flint jolt
Read upper msg@still temple
flint jolt
@still temple in which grade are you studying?
marsh citrusBOT
@flint jolt Has your question been resolved?
flint jolt
<@&286206848099549185>
marsh citrusBOT
@flint jolt Has your question been resolved?
flint jolt
.close
sleek lake
@still temple it seems impossible in the first place
marsh citrusBOT
<@456226577798135808> it seems impossible in the first place
sleek lake
because they are all different, and there's not enough integers
they would grow further apart but then suddenly have to be close again
placid warren
marsh citrusBOT
placid warren
idk the idea to solve this
fallow fossil
is this tech active?
velvet cedar
Can you think of any ways to find ACD
placid warren
isnt acd just 90 degrees
placid warren
which grade is this?
8th grade olympiad
placid warren
and is this physics?
no
fallow fossil
oh then theres no tech
still temple
placid warren
there was a question that requires me to use tan x
placid warren
im in 9th grade bruh
fallow fossil
didnt u have to use tanx
placid warren
maybe teach me sin cos tan rules
placid warren
didnt u have to use tanx
i only know about tan x sin x and cos x
velvet cedar
isnt acd just 90 degrees
My bad CAD I mean
fallow fossil
wait 9th grade is where trig is taught
still temple
think of alternate interior angles and youll get the answer
tell me the given answer
fallow fossil
soh cah toa is a good acronym
placid warren
wym
placid warren
My bad CAD I mean
trigonometry?
In the figure, BCDE is a rectangle where 𝐵𝐶=24 𝑐𝑚, 𝐴𝐸=68 𝑐𝑚, and ∠𝐴𝐸𝐵=36°. ABC is a straight line. Calculate reflex ∠𝐸𝐴𝐷. Round off your answer to the nearest degree.
thats the informations
fallow fossil
what i got: ||49||
placid warren
soh cah toa is a good acronym
isnt that for right triangles
still temple
your attempt
fallow fossil
isnt that for right triangles
it's for all
still temple
im not going to just tell you the answer
still temple
????
placid warren
it's for all
how
still temple
how did u get a negative angle 😭
fallow fossil
cuz hypotenuse is longest side
placid warren
since idk how to round them up
placid warren
wym
still temple
they asked reflex
placid warren
yeah
still temple
tell me the given answer
fallow fossil
crazy
placid warren
so how do you like
fallow fossil
wait no
placid warren
i mean the steps
to get it
like the idea
how do you apply sin cos tan
to get the answer
fallow fossil
sin(theta) = opposite side/ hypotenuse side
still temple
you dont apply trignometry here 😭
at your stage these angles arent known
this is simple geometry
fallow fossil
but grade 9 is pretty far, and it's an olympiad
fallow fossil
yea it's 347
placid warren
sin(theta) = opposite side/ hypotenuse side
what
i thought it was only for like
right triangle
fallow fossil
placid warren
but EAD isnt a right triangle???
fallow fossil
but there are right angle triangles???
fallow fossil
u use the other information to help aid u to find the answer
like they are the tools to help u get to a goal
fallow fossil
yea i used those
fallow fossil
so with a calculator u can work out the lengths as sin(theta) = o side divided by h side[from my diagram]
still temple
because they are all different, and there's not enough integers
Yeah I just fricking read that
I was doing this in my car actually
So I didn’t pay attention
still temple
Sorry to intrude btw
placid warren
its ok
still temple
placid warren
so with a calculator u can work out the lengths as sin(theta) = o side divided b...
is this in cad
fallow fossil
did u get how to find the other side
placid warren
or other triangles
placid warren
did u get how to find the other side
not really
fallow fossil
is this in cad
u can do that in all right angled trigles
fallow fossil
so eg we look at ABE (only angle is inside that triangle)
we can work out BA and AE with sin and cos
since sin(36) = BA/68 (o/h)
we can times sin(36) by 68
*remember ur calc has to be in degrees
u get BA as somewhere around 39.969
now are u able to figure out BE? (BE/AE = cos(36))
still temple
do you know how to find the value of sin18 and sin36? u shouldnt as thats taught in like grade 11
still temple
Just find line AD using cosine rule and then use cosine rule again to find the angle EAD
That’s it
still temple
Just find line AD using cosine rule and then use cosine rule again to find the a...
bro he doesnt know that sintheta=o/h 😭
placid warren
olympiad tho, for that you should be knowing basics of trigo
i guess
placid warren
bro he doesnt know that sintheta=o/h 😭
i know that i just dont know the next idea
still temple
Then why is he even doing the question
still temple
i know that i just dont know the next idea
its okay, dw
still temple
im in indonesia so i use sidemi cosami and tadesa
Is there a law cosamis?
in like 2 more years youll find the exact value of sin36
placid warren
Is there a law cosamis?
wym
still temple
or cosine law (im not a big fan of this rule)
placid warren
theres like 5 to 3 questions that requires me trigonometry
placid warren
I mean I can teach you it here if you’d like
sure
placid warren
i need to learn trigonomtry
still temple
So you do you know how to label triangles already for basic trig?
placid warren
yea
placid warren
k
still temple
basically finding unknown angles/sides in a non right angle trianlge using trignometry
still temple
Here
Notice how the angles of the triangle are labelled with upper case
And the sides with lower case
still temple
Also the side and the angle opposite it will always be the same letter
still temple
i need to memorize this
Yes
placid warren
Also the side and the angle opposite it will always be the same letter
alr
still temple
So in this case for the question first we can use cosine rule to find the line AD
placid warren
lemme try
still temple
That line
im thinking , what about simple geometry
The diagram isn’t to scale so how can simple geo be applied tbf
eh
trigno
still temple
Let me check on my calc
You should get 7118.531063
And then obviously you square root
Giving 84.37
still temple
a^2 = 5200 - 2 x 24 x 68 x cos(126)
It might be that you didn’t use brackets in your calculator
So it did the order of operations wrong
still temple
Did you get 84.37 cm
placid warren
yea
still temple
nice
still temple
Okay so now we have the length of all three side sides to the triangle
placid warren
yea
still temple
sure
placid warren
cos (a) = 0,973?
fallow fossil
cos rule is 1 step but problem is if they even learned cos rule, ik yr 9 must have touched on trig but idk abt cos rule
still temple
cos rule is 1 step but problem is if they even learned cos rule, ik yr 9 must ha...
I did cosine rule in year 9
placid warren
cos rule is 1 step but problem is if they even learned cos rule, ik yr 9 must ha...
my school just learned about indices
still temple
Depends on the curriculum
still temple
cos (a) = 0,973?
yea
fallow fossil
trur
still temple
Now we need to get the angle by itself
still temple
So we multiply that by cos-1
There should be a small cos- button above the regular cos button on your calculator
placid warren
yea
fallow fossil
i think most places it's yr 10/11 or advanced yr 9 classes
placid warren
i think most places it's yr 10/11 or advanced yr 9 classes
im placed in gifted class for math and still havent learned about trigonometry is crazy
placid warren
ok hold on
still temple
Press that and put the answer we just got in the brackets
The 0.973 one
fallow fossil
bruh lol
still temple
im placed in gifted class for math and still havent learned about trigonometry i...
Maybe you’re learning other topics first. Have you done series?
placid warren
Maybe you’re learning other topics first. Have you done series?
what is series (because idk the translate in my country)
placid warren
The 0.973 one
it gives 13
still temple
what is series (because idk the translate in my country)
In my country it’s called iteration but in America I think it’s called sequences series one second I’ll find a picture
fallow fossil
like patterns kinda?
still temple
it gives 13
Yes 13.304
placid warren
cool
placid warren
like patterns kinda?
oh if its about that,
my school havent learned it but i already have
fallow fossil
hm
still temple
Like have you ever been taught problems that look like this?
Because it could be your school is teaching other topics before geometry
fallow fossil
ah arithmetic and geometric sequencing stuff
fallow fossil
ur school is crazy
placid warren
fr
still temple
i learned it somewhere else
Oh cool
fallow fossil
what r u even learning
placid warren
idk bro
fallow fossil
algebra?
still temple
Yeah just make sure you do loads of self study at home bro
still temple
we learned like about venn diagram
😭
fallow fossil
oooh probability?
placid warren
Yeah just make sure you do loads of self study at home bro
do you have any suggestion on what to learn
and where
placid warren
oooh probability?
yea
fallow fossil
prob is fun
placid warren
i hate prob
fallow fossil
:0
still temple
do you have any suggestion on what to learn
I’d suggest looking at your countries national curriculum
placid warren
i have to learn like star and bars theorem if im not wrong
still temple
And going through every topic
placid warren
for olympiad
still temple
for olympiad
Ah i see
placid warren
I’d suggest looking at your countries national curriculum
where should i learn
do i watch like youtube
or something
or buy a book
btw what do we do afterwe get 13.304
still temple
Watch loads of YouTube videos and go through books regularly. You can see #competition-math for more info and tips for olympiads
placid warren
alright
fallow fossil
360-13.304 cuz reflex
still temple
You can also ask on #book-recommendations for Olympiad books
placid warren
cool
still temple
and i also missed alot of school
Due to Covid?
placid warren
360-13.304 cuz reflex
ohhh yeah
still temple
Ah ok
placid warren
is there no rule for tan
or is it to advanced for me
and if i got like 73.5 do i round it up to 74
fallow fossil
there is none
fallow fossil
and if i got like 73.5 do i round it up to 74
yea
fallow fossil
cuz closest degree
placid warren
then i basically got one question wrong
still temple
is there no rule for tan
I think so but it’s very advanced
fallow fossil
i dont think they teach this
placid warren
damn
fallow fossil
ah thats why
still temple
btw can we get the angle using the sin rule
Depending on the values the question gives you, you will have to decide on which rule to use
fallow fossil
u need to use normal sin/cos/tan to get another angle
still temple
Like for sine rule you can only use it if you have a side AND the angle opposite THAT side and then another side which you will find the opposite angle of
I’d recommend doing plenty of questions
Khan academy has resources I believe
placid warren
ohhhh
i see
but in this case
i can use both right
i can use sin(c)/c = sin(a)/a
and also the cos(a)
still temple
Yes for the last step we could have done sin(36)/ 84.3 = x/24
still temple
Okay so basically
fallow fossil
1 on 1 tutoring 🤩
still temple
Normally we would divide 25 by 5 right?
placid warren
ye
still temple
But for sin cos and tan you can’t exactly divide by them
So instead you simply multiply the value by minus version i guess for sin cos tan
still temple
the inverse
Yess
placid warren
i see
still temple
nice
marsh citrusBOT
still temple
No problem
marsh citrusBOT
Available help channel!
silver mantle
found this relation in wikipedia, when i graph them they don't like up, is it because i need to have more terms?
marsh citrusBOT
found this relation in wikipedia, when i graph them they don't like up, is it be...
silver mantle
increased it to 300 nothing happened
especially sus how they are exactly 1 unit apart
red nimbus
increased it to 300 nothing happened
I think the equality holds if it goes to infinity
Try 201 and let the other be 200
silver mantle
oh so it doesn't work when s is about smaller than 0
red nimbus
No not that
silver mantle
2 i mean
red nimbus
The sum has to have infinite terms
red nimbus
I figured for example η(0) = 1 - 1 + 1 - 1 + ... etc
Make one odd and the other even
Make the blue 201
red nimbus
So with infinity I assume they converge to the same thing
marsh citrusBOT
marsh citrusBOT
Available help channel!
near elbow
marsh citrusBOT
near elbow
guys what formula is that in letter B?
vast forum
first find ab (pythag) then minus db,
if b is the centre of the circle then db has to be 8 :P
terse turtle
the only thing i could imagine is using trig on this
silver mantle
the only thing i could imagine is using trig on this
yeah this
vast forum
how would you find ab using pythagoras
oh my bad lmao, I didn't look properly
proud kiln
CB = DB is radius
so if you have AB you can find AD
i can't imagine 2 * 8cm * cos(0.9rad) being a nice expression
silver mantle
guys what formula is that in letter B?
to answer your question, the formula used is $\cos(\alpha)=\tfrac{\text{projection of C onto AB}}{BC}\Leftrightarrow \text{projection of C onto AB}=r\cos(\alpha))$
afterwards we multiply by 2 to obtain AB, because it's isosceles
elfin berryBOT
pixel
near elbow
first find ab (pythag) then minus db,
if b is the centre of the circle then db h...
ohhhh yeahhh
severe owl
Ahh my discord is broken
vast forum
ohhhh yeahhh
no ignore me I was being silly, late night exhaustion thingz
near elbow
no ignore me I was being silly, late night exhaustion thingz
but CB=DB is right
near elbow
so if you have AB you can find AD
ohh yess
near elbow
to answer your question, the formula used is $\cos(\alpha)=\tfrac{\text{projecti...
ok i’ll try to understand it
near elbow
to answer your question, the formula used is $\cos(\alpha)=\tfrac{\text{projecti...
ohhh so we find the length of the line from C to midpoint of AB?
silver mantle
yes
wait
not exactly
we find this length
where the red scribble is under
that's why we use cos
because it's adjacent
near elbow
oops wait, yes that one!
okkk thank you so much
i get it now
thank you everyone!!
severe owl
🥲
vast forum
@near elbow close the channel boo
spark otter
it's up to them to close the channel...
vast forum
it's up to them to close the channel...
well I assume theyre done lmao
marsh citrusBOT
@near elbow Has your question been resolved?
pine junco
i would really appreciate help, thanks
i can solve a limit, but an issue is that i dont know what an end result is
after solving it i get 5/0, is that ∞, is that what? how can i know, i really searched the internet but no help
marsh citrusBOT
i would really appreciate help, thanks
i can solve a limit, but an issue is tha...
pine junco
another example of me trying to understand the pattern
we often to functions with ln, so that means ln0 is -∞, so i understand that
figuring out the asymptotes on a function*
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
swift olive
marsh citrusBOT
swift olive
I know that sin^-1(2/3) = x
Is sec^-1 the same as cos^-1 with adj and hyp swapped?
So if I put cos^-1(4/5) is that alright? -- the hw didn't like my answer after I did that
I think I made progress, but it didn't like my new answer either :/
glass silo
Well, the idea is that you want to write out sin(x + y), and find the trig function values you may not directly know...
swift olive
Well, the idea is that you want to write out sin(x + y), and find the trig funct...
so like
sin(sin^-1(2/3) + cos^-1(4/5))?
glass silo
Not exactly like that, you don't want to do it like that
You know how to expand out sin(x + y) in general right?
(don't worry about what x and y are, for now)
swift olive
It's not the same as sin(x) + sin(y) right?
glass silo
No 
swift olive
bingo
I got the same number after plugging in X and Y
X = 0.7297276562
Y = 0.6435011088
sin(x+y) =about 0.980547
It didn't like my answer though 🤔
vast forum
It didn't like my answer though 🤔
Tell the website to fuck itself
They always do stuff like that 😭
“The answer was a = x NOT x = a”
😐
marsh citrusBOT
marsh citrusBOT
Available help channel!
stark glacier
Hello! Question regarding "partial fraction decomposition"... Does this still work if you have a constant "b" multiplied by the "s" in the denominator? I.e. when you have 1/(bs^2 + s) and you factor out the s so that you get "1/((s)(bs + 1))". Can you still equate this to =(A/s) + (B/(bs+1))?
marsh citrusBOT
Hello! Question regarding "partial fraction decomposition"... Does this still wo...
stark glacier
I assume it's a "yes", but if there is a "no" as an answer, I would like to understand why 
final skiff
Hello! Question regarding "partial fraction decomposition"... Does this still wo...
Yes. Factor the b out of (bs+1)
marsh citrusBOT
@stark glacier Has your question been resolved?
void elm
main idol
marsh citrusBOT
Available help channel!
digital hatch
You have 21 cells that can contain a random value of 52 elements. each row contains 7 cells, each column contains 3 cells. what is the probability to have exactly no duplicates in a row. what is the probability of 2 duplicates, 3, 4, 5, 6?
marsh citrusBOT
You have 21 cells that can contain a random value of 52 elements. each row conta...
faint creek
!status
marsh citrusBOT
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 believe i have the probability of no duplicates: P(52, 7) / 52^7), but the rest i cant quite figure out
faint creek
P(52,7) being the number of ways of taking 7 items out of 52?
If so that seems correct to me
faint creek
Cool, now lets look at 2 duplicates
So... how many different ways do you think they can be placed?
Like, if I have 4 slots and 2 of them are the same, my options are
[S S _ _]
[S _ S _]
[S _ _ S]
[_ S S _]
[_ S _ S]
[_ _ S S]
Where S is used to label which of the two slots have the same value
digital hatch
P(52,5) ?
faint creek
You have 21 cells that can contain a random value of 52 elements. each row conta...
Actually, when you say "the probability of 2 duplicates" do you mean "the probability that a row has 2 of the same value"
digital hatch
yes sorry, and then 3 of same value, ... 7 of same value
faint creek
Great, just wanted to be sure I wasn't trying to solve the wrong problem 🙂
faint creek
P(52,5) ?
So I think you're on the right track here, but you're maybe a bit off
Well, if you have 2 duplicates that means that there will be 6 unique values right?
So in that case P(52,6) would seem a likely answer
faint creek
Yeah, there's 5 unique values and 1 duplicated value, so 6 values total
digital hatch
yea
faint creek
However, if you only care about that then you might fail to account for both of these cases
[1 1 2 3 4 5 6]
[1 2 2 3 4 5 6]
Both of these have a duplicated value, and all the values are in order, but the way they're duplicated isn't
Does that sort of make sense?
digital hatch
right, the order of which they are the same value doesnt matter
faint creek
I'm not quite sure what you mean
What I'm trying to say is that where the duplicated values are in the list matters
faint creek
Yup!
digital hatch
there are 2 4's and they arent adjacent
faint creek
Yeah, in my example above I put them adjacent for ease of viewing rather than anything else
faint creek
Yeah not quite, it needs to be modified slightly
So do you think you can come up with a formula for the number of ways the duplicate pair could be placed in the list?
faint creek
Like, if I have 4 slots and 2 of them are the same, my options are
```
[S S _ _]...
Like I have in this example
btw, I'm assuming you're in a probability or combinatorics class
If that correct?
digital hatch
yes but this is for a side project which is so confusing to me
faint creek
Well alright in that case I'll be a bit less vague
digital hatch
i got something like **(C(7, 2) * C(52, 1) * (52 - 1)^(7 - 2)) / 52^7 ** for having 2 duplicates(3 of same value)
faint creek
oh
Now I get it lmao
Okay so there's 4 unique values and 1 value that shows up 3 times
faint creek
Right right
Okay then, well you'll have 5 different values so P(52,5) is right for funding those values
But for each pick of 5 values, there is a number of ways the duplicates can be placed in the row
So there will be 3 positions out of 7 that will have the same value, do you know a formula that can give you all different combinations of positions?
i.e, you have the values a,b,c,d,e and know that a will be present 3 times, how many different ways can the a values be put in the row
digital hatch
C(7,3)?
faint creek
Okay
faint creek
I believe i have the probability of no duplicates: P(52, 7) / 52^7), but the res...
Well working from this equation, P(52,7) is the number of ways you can pick 7 unique elements from 52 in order, and 52^7 is the number of ways you can have 7 elements out of 52 in order
So P(52,7)/52^7 gives the probability of the 7 being unique, because it's the # of options that meet our criteria divided by the total number of options
If you understand how that all works, do you think you can use what we've discussed in order to find the # of ways that there are 2 duplicates in the row?
Feel free to tell me if you need me to clarify
faint creek
All good!
Well, in the example of a,b,c,d,e where a is duplicated 3 times, there were C(7,3) ways those duplicates could be distributed right?
So for any pick of 5 values there should be C(7,3) different ways for the duplicate values to be distributed
digital hatch
right
faint creek
And there are P(52,5) ways to pick 5 unique values with order
So there are P(52,5) ways to pick the values, and for each pick of values there is C(7,3) different ways they could be distributed
Does that make sense? I am still skipping a couple details in my thinking so I could get into them
digital hatch
think so
faint creek
Cool cool, so then do you think you can come up with a formula for the number of ways the row could have 2 duplicates?
Like how P(52,7) is a formula for the number of ways a row could have no duplicates
digital hatch
P(52,5) = 5 unique elements out of the 52
C(7,2) = 2 different ways to choose
P(52,5) * C(7,2) / 52^7
not too sure tho
faint creek
That's correct!
digital hatch
wat
faint creek
Or, close to correct actually
You would actually want C(7,3), since having 2 duplicate values means there are 3 positions with the same value
P(52,5) * C(7,3) is the number of ways to order 7 elements where 3 are the same
faint creek
lmao no prob
digital hatch
sorry 1 more thing, shouldnt this equal out to 1
faint creek
sorry 1 more thing, shouldnt this equal out to 1
Well sum of the probabilities of:
- no duplicates
- 1 duplicate
- 2 duplicates
- 3 duplicates
and so on up to 6 duplicates should be 1, is that what you mean?
digital hatch
Right
faint creek
Is that not what you got?
digital hatch
I got .97
faint creek
I got something similar, I'm looking to see if I screwed up somewhere...
OH!!
I see the problem now, this won't add up to 1 because it doesn't account for multiple duplicates
Like, duplicates of different values within the same row
@digital hatch does that make sense?
faint creek
Yeah, glad I could help 🙂
faint creek
Alright that is all then , really appreciate it
If you think you're done with this channel, you should use .close to free it up for someone else
digital hatch
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
young bobcat
is it nessecary to denote positive or negative infinity in a union set?
marsh citrusBOT
is it nessecary to denote positive or negative infinity in a union set?
@young bobcat Has your question been resolved?
quiet anvil
16 + 4 * 8
I don't understand how you got 16 + 3 * 4
And 2^3 = 8
Yeah
Nw
@fresh fiber because there's only one way to have a first instance of something
It would have gotten slightly more complicated if there were more than 8 bits though
You're very welcome
marsh citrusBOT
marsh citrusBOT
Available help channel!
crude reef
I need help with a Linear Algebra quesition: Show that the span of any non-empty subset is a vector subspace. My answer so far is that the span of a vector space was a subset of the vector space. What I have for an answer is: let V be a vector space in R^2. Suppose x = [a b] and y = [c d]. Then the span of V = A_1 x + A_2 y = e_1 and e_2 depending on the values of A_1 and A_2 and both of these basis vectors are subspaces of the vector space V
marsh citrusBOT
I need help with a Linear Algebra quesition: Show that the span of any non-empty...
brave marsh
I don't think you should go into bases here.
I'm also not sure what you mean by "V = A_1 x + A_2 y = e_1 and e_2".
The span of some collection of vectors from a space V is the set of all possible linear combinations of the vectors in that collection.
If you take some nonempty subset W of a vector space V, then W is a vector subspace if :
- W is closed under vector addition (from vectors in W)
- W is closed under scalar multiplication.
So in particular, take two arbitrary vectors in the span, W, make sure their sum is in W.
Then take a vector and scale it, make sure it's still in W.
crude reef
So, what I am getting from your explanation is that we will set V to be a vector space and W to be V's span. We will then assign two arbitrary vectors x and y. Understadning what a span is, the linear combination of x + y = W. We then scale the vectors to make sure that it reamins within W?
brave marsh
No. We set V to be a vector space, and W to be the span of some collection of vectors in V.
crude reef
Alright so we have the Vector Space V and the span of W which is some collection of vectors in V?
brave marsh
Since W is a span of some collection of vectors ${v_1, v_2, \ldots, v_n}}$, any vector in W is a linear combination of those, that is they all have the form
$$b_1 v_1 + b_2 v_2 + \ldots + b_n v_n$$ where $b_i$'s are scalars.
elfin berryBOT
Azyrashacorki
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crude reef
Okay yes, I understand up to here
How do I then take what we have here, to prove that the span is a subspace of the vector space V?
brave marsh
If you take two vectors of that form with arbitrary scalars, can you show that their sum is also some linear combination of vectors in the collection?
crude reef
Well I know you could, but I cant think about how you would in a general sense?
Like I can think of examples, however I cannot think of a generalized solution
brave marsh
Let's say we just have 3 vectors for the sake of my hands.
Then one vector in $W$ could be $$u = a_1 v_1 + a_2 v_2 + a_3 v_3$$ and another could be $$w = b_1 v_1 + b_2 v_2 + b_3 v_3.$$
elfin berryBOT
Azyrashacorki
brave marsh
What does u+w give you?
crude reef
Would $$ u + w = v_1 (a_1 + b_1) + v_2 (a_2 + b_2) ... ?$$
elfin berryBOT
Zerofall
brave marsh
Yes, and so is it still a linear combination of the starting vectors ?
crude reef
Yes?
crude reef
Yeah its just a different scalar
brave marsh
Say c_i = a_i + b_i
So that means it's closed under vector addition.
You need to show it's also closed under scalar multiplication. Do you think you can tackle this one?
crude reef
Yes I can!
marsh citrusBOT
@crude reef Has your question been resolved?
small stream
Let ( f(x) ) be a differentiable function. The curve ( y = f(x) ) and the curve ( y = \arctan(x) ) have a common tangent line at the point ( \left(1, \frac{\pi}{4}\right) ). Then find the limit:
[ \lim_{n \to \infty} n \left[ f\left(\frac{n}{n+1}\right) - \arctan\left(\frac{n}{n-1}\right) \right] ]
marsh citrusBOT
Let \( f(x) \) be a differentiable function. The curve \( y = f(x) \) and the cu...
elfin berryBOT
miyo
small stream
My idea is using the definition of derivative maybe, but idk how to use it
marsh citrusBOT
@small stream Has your question been resolved?
sharp vessel
I would first get rid of the arctan(n/(n-1)) by splitting up the limit
You can add and subtract arctan(n/(n+1)) which doesn't change the expression
So you'll have one +arctan(n/(n+1)) and one -arctan(n/(n+1))
Take the negative one, pair it up with the f term
Take the positive one, pair it up with the arctan(n/(n-1)) term
Then split up the limit
[\lim_{n \to \infty} n\left[\pmap{f}{\frac{n}{n+1}} - \pmap{\arctan}{\frac{n}{n+1}}\right]]
damn my latex
small stream
Why do we do this
sharp vessel
Because now we have n/(n+1) in both the f and the arctan
The second limit should be doable, haven't tried it but I'll leave it to you
For the first limit, it might be easier to see what's going on if you define g(x) = f(x) - arctan(x)
If f and arctan are tangent at x = 1, what does that imply about g?
@small stream ?
small stream
I was thinking how to use the definition to compute the second limit😭
sharp vessel
It should be related to the derivative of arctan(x) at x = 1
small stream
If f and arctan are tangent at x = 1, what does that imply about g?
[ ( f(1) = \arctan(1) ), so: g(1) = f(1) - \arctan(1) = 0 ]
small stream
[ g'(1) = f'(1) - \frac{d}{dx}\left[\arctan(x)\right]{x=1} = 0 ]
elfin berryBOT
miyo
small stream
It should be related to the derivative of arctan(x) at x = 1
[ \arctan\left(\frac{n}{n+1}\right) \approx \arctan\left(1 - \frac{1}{n}\right) \quad \text{and} \quad \arctan\left(\frac{n}{n-1}\right) \approx \arctan\left(1 + \frac{1}{n}\right) ]
elfin berryBOT
miyo
small stream
Hmmm but how to continue
sharp vessel
Hint: ||compute n/(n+1) - n/(n-1)||
That's a hint for the arctan difference limit
small stream
The difference is 1/2n
elfin berryBOT
RedstonePlayz09
sharp vessel
This is also true in general
You can prove it by adding and subtracting f(x) in the numerator I'm pretty sure
small stream
Wow!!
[ \lim_{n \to \infty} n \left(\arctan\left(1 - \frac{1}{n}\right) - \arctan\left(1 + \frac{1}{n}\right)\right) = \lim_{n \to \infty} -\frac{1}{2} \cdot \frac{\arctan\left(1 + \frac{1}{n}\right) - \arctan\left(1 - \frac{1}{n}\right)}{\frac{2}{n}} ]
elfin berryBOT
miyo
sharp vessel
Yup
Well done
Now it's just a matter of converting limits in x to a limits of a sequence
But that should be obvious, taking the sequence x_n = 1/n
small stream
[ -2 \cdot \lim_{h \to 0} \frac{\arctan(1+h) - \arctan(1-h)}{2h} ]
elfin berryBOT
miyo
sharp vessel
Alright so what do you get?
small stream
Wait why -2😭
sharp vessel
To cancel out the 2
sharp vessel
**miyo**
In the original limit here, we have the arctan(1 - 1/n) being the positive term
We switch the order of the atctans, and get a minus in front
The n becomes 1/n in the denominator, and we add a 2 in the denominator and in the front (to not change the value)
You got it?
small stream
Yes
small stream
Alright so what do you get?
-1
sharp vessel
Now write g'(1) using limit definition
.
small stream
Now write g'(1) using limit definition
[g'(1) = \lim_{h \to 0} \frac{g(1 + h) - g(1)}{h}]
elfin berryBOT
miyo
sharp vessel
I recommend writing it using the other definition
with x and x_0
$f'(x_0) = \lim_{x \to x_0} \frac{f(x) - f(x_0)}{x - x_0}$
elfin berryBOT
RedstonePlayz09
sharp vessel
Wait
Actually it doesn't matter
Ehh
I just want my variable to go to 1
instead of 0
So either use h, and the substitute
sharp vessel
**RedstonePlayz09**
Or use this for x_0 = 1
elfin berryBOT
miyo
sharp vessel
Yeah
Ok that's fine I guess
Ok actually it's a bit annoying
Would be better if we had + there
Wait
sharp vessel
**RedstonePlayz09**
We could've just used this immediately without splitting up the limit
Goddamit
😂
My bad
small stream
Wwwdym
sharp vessel
**miyo**
Well out limit is that, with h = 1/n and with - inside the arctan in front of the h
f(1 + h) - arctan(1 - h)
sharp vessel
With 2h
elfin berryBOT
miyo
small stream
So it's just 0?
sharp vessel
No
Wait
Uh
Ok subbing h = 1/n gives us
well actually
h = -1/(n+1)
Or not
Does it not work?
How do we get the n-1
small stream
h= n/(n+1) - n/(n-1)?
sharp vessel
That's 2/n
Ok wait
let me just write it down
It's actually not really working idk
Just because of the n+1 and n-1
Well I guess splitting up the limit is fine
sharp vessel
**miyo**
We can't just sub in some h = x_n to this
It wont give us what we need immediately
small stream
Sub in h = -1/(n+1) here
Where does -1/(n+1) come from
sharp vessel
I just chose it so that 1 + h will be the n/(n+1) we need
And it's fine since as n goes to infinity, -1/(n+1) = h goes to 0
Technically we're only using the 0- side of the limit I think
small stream
$g'\left(1\right) = \lim_{n \to \infty} \frac{f\left(1 - \frac{1}{n+1}\right) - \arctan\left(1 - \frac{1}{n+1}\right)}{-\frac{1}{n+1}}$
elfin berryBOT
miyo
small stream
This leads us nowhere
sharp vessel
Why not
1 - 1/(n+1) is??
Oh bruh its n+1
Man I messed up somewhere I swear it works
One sec
Ok
$\lim_{x \to 1} \frac{g(x)}{x - 1} = 0$
elfin berryBOT
RedstonePlayz09
sharp vessel
That's from g'(1)
Now, sub in x = 1 - 1/n
$\lim_{n \to \infty} \frac{\pmap{f}{1 - \frac1n} - \pmap{\arctan}{1 - \frac1n}}{-\frac{1}{n}} = 0$
elfin berryBOT
RedstonePlayz09
sharp vessel
**miyo**
Yeah just plug in h = -1/n I'm dumb
FUCK
kill me
What is going on I'm confusing the n and n+1
Forgive me
Ok you know what
It's fine with n+1
You just need an extra factor
Which you can get
It's fine
h = -1/(n+1)
Sorry :Xd:
$\lim_{n \to \infty} n\left[ \pmap{f}{\frac{n}{n+1}} - \pmap{\arctan}{\frac{n}{n+1}} \right]$
elfin berryBOT
RedstonePlayz09
sharp vessel
$=\lim_{n \to \infty} (n+1)\left[ \pmap{f}{\frac{n}{n+1}} - \pmap{\arctan}{\frac{n}{n+1}} \right]$
elfin berryBOT
RedstonePlayz09
sharp vessel
It's the same
Just add a copy of f(n/(n+1)) - arctan(n/(n+1))
The limit of that is 0
sharp vessel
**RedstonePlayz09**
And you can get this from here
sharp vessel
**miyo**
.
That should be it
Anyways maybe someone that isn't a monkey can find a cleaner way to do this
All of these n's, (n+1)'s and (n-1)'s are really making me go insane
On another note: I remember I tried answering your question with f''(e) = 2f'(e)/(1 - e) and the channel timed out.
My hint for you on that one is define g(x) = (1 - x)^2 * f'(x)
small stream
Lmao but this really give me headaches, i need to reorganize a bit
sharp vessel
And use rolle's theorem on g (the interval is not necessary (0, 1))
sharp vessel
Lmao but this really give me headaches, i need to reorganize a bit
Yeah I understand
Alright I have to go, good luck
small stream
Thank you!
sharp vessel
Np!
small stream
All of these n's, (n+1)'s and (n-1)'s are really making me go insane
These also make me feel confused btw
ember saffron
I need help with this physics problem. I'm lost at what equation to use. The equations I'm given in my physics sheet don't fit.
marsh citrusBOT
I need help with this physics problem. I'm lost at what equation to use. The equ...
ember saffron
What I got so far is Velocity Initial at 0m/s, Velocity final at 32m/s, Position final at 0m and Position final as ?
worthy obsidian
do you know the equations of motion?
fervent rampart
do you have the "timeless" kinematic equation?
royal flicker
What I got so far is Velocity Initial at 0m/s, Velocity final at 32m/s, Position...
u could assume acceleration?
ember saffron
u could assume acceleration?
At 0m/s?
ember saffron
Oh right
sour plover
WTF UR HERE
ember saffron
But is it going to be acceleration due to gravity or just g
sour plover
I watch ur vids everyday 😭❤️@ember saffron
sour plover
Nicee
ember saffron
I'm lowkey kinda a dumbass rn because I just started class
sour plover
Gl on school :)
ember saffron
Thx g
sour plover
I'm lowkey kinda a dumbass rn because I just started class
Nah is ok, we all learn by time
royal flicker
I watch ur vids everyday 😭❤️<@484527828914929685>
wtf the geo dash yt 😭
sour plover
I suck at maths to xd
royal flicker
I never noticed lmfao
sour plover
Oh , I suck at that too lmao
ember saffron
Anyway lets continue the problem
sour plover
I only good at chemistry
sour plover
Anyway lets continue the problem
Yea sorry for interfering
worthy obsidian
tell me the 3 equations of motion
ember saffron
Velocity final = Velocity Initial + Acceleration x time
royal flicker
tell me the 3 equations of motion
he has the equations they give for ap I think
sour plover
tell me the 3 equations of motion
Summation of Fx = 0
worthy obsidian
Velocity final = Velocity Initial + Acceleration x time
ok
but this wont help for this problem
there are 2 more equations which have been given
ember saffron
Position final = Position initial + velocity initial x time + 1/2 times acceration x time squared
worthy obsidian
look at the first 3 equations of this page
worthy obsidian
Position final = Position initial + velocity initial x time + 1/2 times accerati...
this also wont help us i will explain later why
ember saffron
look at the first 3 equations of this page
ik those are the ones I'm referring too
worthy obsidian
what is the last equation?
ember saffron
Velocity final squared = Velocity initial squared + 2 x acceleration (position final - position intial)
ember saffron
What I got so far is Velocity Initial at 0m/s, Velocity final at 32m/s, Position...
This is what I got so far
and ig we can assume acceleration is -9.8 m/s
worthy obsidian
yes
worthy obsidian
Velocity final squared = Velocity initial squared + 2 x acceleration (position f...
then you use this equation
ember saffron
Velocity final squared = Velocity initial squared + 2 x acceleration (position f...
Ok let me try it
I'll let you know when I finish it and we can go over it.
worthy obsidian
ok
ember saffron
This is where I am at
I think I did something wrong
Because my answer would be -0.019 m
worthy obsidian
yes you made a mistake in solving the equation formula is correct
ember saffron
What did I do wrong?
worthy obsidian
its a mathematical error you should try to find the error yourself
if you are unable to i will help
ember saffron
oh is X initial suppoted to be negative?
ember saffron
Wait hold on
just for clarity
Is this equation
(32) squared = 2x -4 times 8x - velocity initial?
worthy obsidian
no
ember saffron
OHHH WAIT
worthy obsidian
This is where I am at
this eqution simplified witll look like this
ember saffron
Do you guys help with Chemistry
wrong channel
Go to #help-21｜아리스킨충1
and then you would be dragged into a private session
ember saffron
multiply 2x times -9.8x
worthy obsidian
worthy obsidian
multiply 2x times -9.8x
divide 9.8x2 both sides to find x
ember saffron
Could u just mutliply them first then divide?
Thats the step I would have taken
but it doesn't make since in the equation I have
worthy obsidian
yeah
worthy obsidian
yes
worthy obsidian
yes
ember saffron
(32m/s)^2 = 1024 m^2/s^2
worthy obsidian
yes
ember saffron
then it would equal
1024m^2/s^2 / 2(-9.8m/s) = x
So 1024 m^2/s^2 / -19.6 m/s = x
Will give me -52.244 m
But that still doesn't make logical sense
worthy obsidian
why