do that
#help-39
junior loom
short path
when you find the first and second derivative of Acos(t) + Bsin(t) you plug them into the original snd set it equal to cos(t)
i'm saying what if the terms with B cancel out and you just have A
junior loom
using the y''+y=cos t exanple you mean
short path
yes
junior loom
i'm saying what if the terms with B cancel out and you just have A
then B is just "some constant" and you dont know enough to say more, thats what im trying to say
short path
i don't see how having 2 initial conditions matters though
junior loom
i don't see how having 2 initial conditions matters though
so what do you get for y''+y=cos t
short path
Here's a problem i did earlier, when i found Yp i got the values of A1 and A0 without using the initial conditions, i only used the initial conditions to find C1 and C2
junior loom
,rotate ccw
jolly parrotBOT
junior loom
you dont have initial conditions at all?
short path
i do i didn't write them, it's y(0) = 4 and y'(0) = -8
but to get the values of A1 and A0 for Yp i didn't use them
junior loom
okay, so, yoy asked me for what happens when ....
and i answered and gave you a concrete example
what more can i do
short path
ok what if when trying to solve for Yp, the A1 terms cancelled out and i just had the A0 terms = 16te^-t
junior loom
then you cant solve for A1 uniquely
short path
so does that mean you can't find the solution or do you have to do something else
junior loom
it means you have an infinite family of solutionsb
look,
,w solve y''+y=cos t, y(pi)=1
jolly parrotBOT
junior loom
for this case
any function of the form y(t)=1/4 c1 sin t
is a solution
what's c1? some constant
any constant
junior loom
maybe in certain scenarios you can narrow it down, like, 1 < c1 < infty
junior loom
sorry i took so long explaining
np
junior loom
maybe in certain scenarios you can narrow it down, like, 1 < c1 < infty
but maybe you know nothing at all about c1
that's what happens in the situation youre asking about
junior loom
š
short path
.close
pearl pondBOT
pearl pondBOT
Available help channel!
graceful spire
One end of a light inextensible string is attached to a particle A of mass 3 kg. The other end of the string is attached to a particle B of mass 4 kg. Particle A is in contact with a rough plane inclined at 30Ā° to the horizontal, and particle B is in contact with a smooth horizontal plane. A second light inextensible string is attached to B. The other end of this second string is attached to a particle C of mass 5 kg which hangs vertically.
Both strings are taut and pass over small smooth pulleys that are fixed at the ends of the horizontal plane. The part of the string from A to the pulley is parallel to a line of greatest slope of the inclined plane, and A, B and C are in the same vertical plane (see diagram).
The system is released from rest. In the subsequent motion, C moves vertically downwards with acceleration 2 m sā»Ā², and neither A nor B reach a pulley.
(a) Find the tensions in eachĀ ofĀ theĀ strings.
graceful spire
and an unrelated note is finding coefficient of friction possible?
pearl pondBOT
@graceful spire Has your question been resolved?
main marsh
and an unrelated note is finding coefficient of friction possible?
this is physics and yes, you just have to figure out whether its dynamic or static
graceful spire
this is physics and yes, you just have to figure out whether its dynamic or stat...
im doing a math paper š mechanics
graceful spire
cant u explain wym by dynamic n static
graceful spire
but yea u can find the coefficient of friction
yeah i tried it out
T2-(mgsina+mewmgcosa)=ma
main marsh
Ī¼ = Ff/n
main marsh
so u got it?
graceful spire
yesyes
pearl pondBOT
buoyant tide
ah wait
suppose $\exist \Omega : x\in\Omega\iff x $ is an obj.
can't I use teh axiom of specification: A a set $\implies\lbrace x:x\in A \wedge P(x)$ is true$\rbrace$
to get the axiom of unrestricted comprehension?
jolly parrotBOT
Yeatte
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
pearl pondBOT
spiral pivot
This is a little cheeky.
If p is prime then it is either 1 mod 3 or 2 mod 3, unless it is 3 itself. So p^2 is 1 mod 3 regardless, and so p^2 + 2 is 0 mod 3.
Thus the only number where p is prime and p^2 + 2 is prime is exactly the number 3. And it happens that p^3 + 2 is also prime
Oh, you deleted it
buoyant tide
I posted the wrong question, I posted someone elses oops
I meant the thing about the sets
spiral pivot
Well, you'll need to open a new channel
pearl pondBOT
Available help channel!
valid drum
if there are 6 colours of labubu's with equal chances and a special edition labubu that has a probability of 1/72
and you pull 5 of the normal colours + the special edition in 6 tries
whats the probability that you pull the last normal colour on the 7th try
- There are 6 regular Labubu colors, each with an equal probability.
- There's a special edition Labubu with a probability of 1/72.
- You pulled 5 of the regular colors + the special edition in 6 tries.
- We want to find the probability of pulling the last regular color on these
- Probability of each regular color:
Since there are 6 regular colors with equal chances, the probability of pulling any specific regular color is 1/6.
- Probability of NOT pulling a specific regular color:
This would be 1 - (1/6) = 5/6
- Probability of pulling the last regular color on the 7th try:
To pull the last regular color on the 7th try, it means you haven't pulled it in the first 6 tries. So, the probability is 5/6.
Therefore, the probability that you pull the last normal colour on the 7th try is 5/6.
valid drum
<@&286206848099549185>
past perch
!15m
pearl pondBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
past perch
out of spite i refuse to even read your question, you've pinged 3 times in the span of 10 minutes
jovial kiln
if there are 6 colours of labubu's with equal chances and a special edition labu...
lets work here
close your other channel
do you think opening each box is independent
valid drum
How do I close it Iām sorry
jovial kiln
use .close
valid drum
Thank you
jovial kiln
do you think opening each box is independent
so opening one box's probability doesnt effect the others
jovial kiln
okay then u cannot use the reasoning
"To pull the last regular color on the 7th try, it means you haven't pulled it in the first 6 tries. So, the probability is 5/6.
Therefore, the probability that you pull the last normal colour on the 7th try is 5/6."
valid drum
Wouldnāt it be independent since itās talking about the last color
jovial kiln
this is for dependent events
jovial kiln
well the question would need to be more specific
let us look at the context
could u tell me whata a labubu is
oh its those cute dolls
valid drum
Ye I think itās a doll thing
jovial kiln
yes, the events should be independent because the stock is so massive
it is essentially opening boxes with replacement
valid drum
Yes so should the colours be independent too?
jovial kiln
$\text{Probability(any regular)} = 1-\frac{1}{72}= \frac{72}{72}-\frac{1}{72}= \frac{71}{72}$
jolly parrotBOT
mia
jovial kiln
so choosing any regular is equal to:
1 - choosing any special
this is for all 6 regulars
so we get
$P(\text{one specific regular colour})
=\frac{71/72}{6}
=\frac{71}{72}\times\frac{1}{6}
=\frac{71}{432}$
jolly parrotBOT
mia
jovial kiln
1/72 is the odds of choosing a special labubu in the entire event of opening boxes
so if we do 1-special labubu odds
we get the odds of all the regular lububu's
jovial kiln
yes
just to be clear, if the events were dependent, your calculations would be correct
valid drum
Ohhh
Okkk
So the actual answer since itās independent should be 71/472
But dependent would be 5-6
jovial kiln
yes
pearl pondBOT
pearl pondBOT
Available help channel!
magic olive
pearl pondBOT
magic olive
Guys I donāt understand which area they want
Hereās the diagram
I donāt think itās what I colored in red
toxic lichen
can you show the entire q from the paper
magic olive
Ok š
I can also send the mark scheme if u want
Ight
I just donāt know what they mean šŖ
@toxic lichen š
toxic lichen
hmm
ok im gonna give this a closer look once i finish lunch
i think it's this lune shape
magic olive
Ohhh
So the arc is not the straight lineš
Itās the curve
Ight thank youš
.close
pearl pondBOT
pearl pondBOT
Available help channel!
prime bane
guys i dont understand the last sub qn can someone explain
pearl pondBOT
guys i dont understand the last sub qn can someone explain
weak fulcrum
e?
weak fulcrum
i mean the last part is kinda weirdly framed
what dows the āother value of xā mean?
prime bane
uh it basically means the other value of x found in c
in d they asked to use a suitable value and use the other value in e
<@&286206848099549185>
weak fulcrum
lol i forgot i was here
I mean ig with other value they mean the other root
it is not lile you can not use it
it is just that youāll need more terms for a better approximation cz the number is that way
pearl pondBOT
@prime bane Has your question been resolved?
eager jewel
pearl pondBOT
toxic lichen
frac(1/x) = frac(x^2)
what interval does 1/x lie in? and what about x^2? what are the floors of each?
tropic saddle
between what integers is 1/x?
eager jewel
0 and 1?
tropic saddle
so whats the fractional part of 1/x?
tropic saddle
whats the fractional part of x^2?
eager jewel
not sure..
eager jewel
2
tropic saddle
so whats the fractional part?
eager jewel
x^2-2?
tropic saddle
yw
eager jewel
.close
pearl pondBOT
pearl pondBOT
Available help channel!
cerulean smelt
isnt this BN, not the limne parallel to OB
pearl pondBOT
isnt this BN, not the limne parallel to OB
cerulean smelt
pearl pondBOT
@cerulean smelt Has your question been resolved?
pearl pondBOT
@cerulean smelt Has your question been resolved?
junior loom
isnt this BN, not the limne parallel to OB
the question came with the blue line drawn that way?
cerulean smelt
the question came with the blue line drawn that way?
no
junior loom
show the original problem please
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
pearl pondBOT
midnight haven
where do i go from here
spare lark
you compute each 6th root of unity and calculate each
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
you compute each 6th root of unity and calculate each
how tho
spare lark
using the formula of unit root
spare lark
e^(2*pi*k)/n where n = 6 and you make k go from 0 to 5 as an integer
spare lark
well you have to write it in rectangular after
where 5omega isn't really rectangular form i think
spare lark
and u just multiply it to 5
no to 2 so
midnight haven
spare lark
e^(2\*pi\*k)/n where n = 6 and you make k go from 0 to 5 as an integer
this but n = 3 and so k go from 0 to 2
the pi/2 comes from the fact they used the e^i3pi/2 and apply cube root and so it becomes pi/2
and they multiply by the three third-root of unity
midnight haven
sorry i donāt understand
spare lark
ok ima break it for you then
the nth root of unity are the root such that e^{i*2kpi/n} where k will walk through the integers from 0 to n-1;
how we use them :
you have your expression z^3 = -125i
but -i = e^{i*3pi/2} as exponential form
so you will write -125i as 125* e^{i *3pi/2}
and so you have
jolly parrotBOT
spare lark
you take the cube root both sides BUT for this you will need the unit root
where
you will have three solutions
spare lark
and you do each value of k
and simplify
using exponents proprety
and finally you go to rectangular form by using the definition of the complex exponent form which is e^ix = cos(x) + i*sin(x)
pearl pondBOT
@midnight haven Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
pearl pondBOT
sinful nebula
worldly epoch
Bro
cobalt hinge
<@&268886789983436800>
pearl pondBOT
cobalt hinge
Fre money ahh scam
worldly epoch
Can someone please explain the answer to me? I donāt understand how/why the x^2 was taken out of the square root
cobalt hinge
FInally i can get a bingo
cobalt hinge
Can someone please explain the answer to me? I donāt understand how/why the x^2 ...
New post pls!
spiral pivot
!help @worldly epoch
pearl pondBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #āhow-to-get-help for instructions.
cobalt hinge
This might close
worldly epoch
Alright! Sorry,
pearl pondBOT
Available help channel!
celest saddle
pearl pondBOT
earnest finch
Can you try rationalizing the denominator
Before you do that, let me try to solve it myself.
earnest finch
my teacher wants us to use change of variables
You mean u-substitution?
celest saddle
You mean `u`-substitution?
yea
earnest finch
How did you get du = x^2 x?
pearl pondBOT
pearl pondBOT
Available help channel!
hybrid trail
pearl pondBOT
hybrid trail
,rotate
jolly parrotBOT
jolly parrotBOT
hybrid trail
bruh what
hybrid trail
,w solve for y', y= e^y / (1+sinx)
earnest finch
,w solve for y', y= e^y / (1+sinx)
Add a comma after y'
Also remove the implicit differentiation
jolly parrotBOT
earnest finch
,w solve for dy/dx, y = e^y / (1 + sin(x))
jolly parrotBOT
pearl pondBOT
earnest finch
.reopen
@hybrid trail then can't you keep this channel open until someone answers?
hybrid trail
<@798353184338739221> then can't you keep this channel open until someone answer...
I give up I think my work is right
thanks tho
pearl pondBOT
Available help channel!
midnight haven
pearl pondBOT
midnight haven
how to evaluate this
midnight haven
as x goes to positive infinity
it goes to infinity
if the base is not fractional
otherwise zero
wait is this going to be
-1/infinity = 0
(2/3)^x would be 0
right
so i thik whole thing should be 0
toxic lichen
if the base is not fractional
ehhhhhhhhhhh you're not looking for "fractional" you're looking for "is it above or below 1"
toxic lichen
-1/infinity = 0
indeed.
toxic lichen
yup
pearl pondBOT
pearl pondBOT
Available help channel!
steady wolf
how do i do this
pearl pondBOT
how do i do this
steady wolf
how do i do vector proofs basically
snow sail
you must try to parameterize the line, no?
so be able to write any of oa, ob, oc ito some shared parameter
whatd you try?
this is just my thought, geometry is probably easier here
but you said using vectors
mental vine
I can help if you want to solve with geometry
snow sail
Cant we say like OA + OB = AB
no
broken fossil
can we not divide through by 2OB
snow sail
we can do a lot of things
mental vine
^ that is true
pearl pondBOT
@steady wolf Has your question been resolved?
steady wolf
why is there 3 crying emojis
snow sail
4
snow sail
why is there 3 crying emojis
i have a thougtt
maybe you can use oa + ab + bo = oc + cb + bo = 0
can you think of some things to try here?
steady wolf
maybe you can use oa + ab + bo = oc + cb + bo = 0
oh I had to prove a similar question like that before but I donāt get why itās equal to 0..
snow sail
because its a closed path
if you describe all the sides of a closed shape in sequence, you are back where you started
steady wolf
ohhhhhhh
snow sail
and you already proved it?
so use it freely 
so what can you think to try
say we start with oa + ab + bo = oc + cb + bo
how far are we from what we want to show
how can we get closer
steady wolf
say we start with oa + ab + bo = oc + cb + bo
okay
i redid the question and related OA and OC TO OB
instead of BO
snow sail
as long as you pay attn to orientation
snow sail
i redid the question and related OA and OC TO OB
idk wym but okay
snow sail
can we start where i suggested
steady wolf
sorry
snow sail
if youre open to it
snow sail
how far are we from what we want to show
.
steady wolf
nice
snow sail
if we can show a couple things were done
we need that:
-( ab + cb) = 0
and -2bo = 2ob
how do you feel about those?
if these are true, the equation you have is the end of the proof
steady wolf
-( ab + cb) = 0
i dont rlly get this one
snow sail
i dont rlly get this one
you see why we need it right?
just in the context of what you wrote
steady wolf
ab +bc = ac, how does -ac = 0
snow sail
we need those terms to disappear
steady wolf
you see why we need it right?
uhhhh
snow sail
so that we have something like oa + oc = 2ob
snow sail
theyre chilling as two extra terms wed like to vanish here
steady wolf
so that we have something like oa + oc = 2ob
oh
snow sail
if theyre just zero, itd really make our job easy
do you have that in general -ab = ba?
to use
steady wolf
do you have that in general -ab = ba?
yes
snow sail
okay
snow sail
and -2bo = 2ob
so this one is done
steady wolf
so this one is done
yeah
snow sail
we just need to show ab + cb = 0
steady wolf
š
snow sail
how do i do this
what do we know about these two lengths?
from way back when
we got a, and c, and b right between them
so from a to b must be the same as from c to b
steady wolf
Yes
steady wolf
opposite signs
steady wolf
yeah
snow sail
are ab and bc the same length and orientation
snow sail
yeah
then we are done
you just need to finish the tying together
thats all the pieces
steady wolf
okayy
hm
i get your way but
i was thinking what if we just isolated for. 2ob
as such
will this get us anywhere
steady wolf
im not sure i get what you mean
basically we get this expression, and i was trying to prove somehow that oa + oc can be simplified to LHS
is it erong š
steady wolf
haha
all g
btw do you know if im even allowed to ask these questions here
since itās vectors
steady wolf
okay thankss
snow sail
steady wolf
ty for helping me too, i appreciate it
pearl pondBOT
@steady wolf Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
loud urchin
How does this work I have no idea how ABC = 1/2 * 16x
pearl pondBOT
How does this work I have no idea how ABC = 1/2 * 16x
toxic lichen
How does this work I have no idea how ABC = 1/2 * 16x
do you know the "half base times height" formula
for the area of a triangle
dapper kraken
How does this work I have no idea how ABC = 1/2 * 16x
notice how if you take the base as AB and the height as that perpendicular from AB to C, you get a diffrent way of finding ABC, compare the areas
loud urchin
oh im dumb
So you do not use the 8 at all
Its just normal Area of a triangle is 1/2 b*h
toxic lichen
So you do not use the 8 at all
you do but not in that place
toxic lichen
Its just normal Area of a triangle is 1/2 b*h
yes exactly. the trick though is that you express the area of the same triangle in two different ways
loud urchin
.close
sharp smelt
Just trying to figure out what's wrong with my argument here : Consider 2 sets $A, \bigcap_{\lambda \in I} C_{\lambda}$
\
I know $A \subseteq \bigcap_{\lambda \in I} C_{\lambda}$
\
Now I want to show $\bigcap_{\lambda \in I} C_{\lambda} \subseteq A$
\
So $x \in \bigcap_{\lambda \in I} C_{\lambda} \implies x \in A$
\
We consider the contrapositive:
$x \notin A \implies x \notin \bigcap_{\lambda \in I} C_{\lambda}$ Which is true.
\
So if $A \subseteq \bigcap_{\lambda \in I} C_{\lambda} \implies \bigcap_{\lambda \in I} C_{\lambda} \subseteq A$
sharp vigil
but that last part is not true purely based on A being a subset of that union
jolly parrotBOT
What a wonderful world !
sharp smelt
but that last part is not true purely based on A being a subset of that union
Which part
toxic lichen
what is any of that
sharp vigil
A = {1,2}
C = {1,2,3}
A is a subset of C
claim: x not in A implies x not in C
false; counterexample: 3
toxic lichen
where are you getting it from that the contrapositive is true
what is A, what are the C_lambda
sharp smelt
what is A, what are the C_lambda
Just arbitrary sets
toxic lichen
ok then refer to what cloud says
sharp smelt
A = {1,2}
C = {1,2,3}
A is a subset of C
claim: x not in A implies x not in C
fa...
Yea, thought of something like this
pearl pondBOT
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.
sharp smelt
im gonna call XY on this
two muinutes
Define $Z_F$ to be $\bigcap_{B_{\lambda} \in A} B_{\lambda}$ where the set $A$ is the set of all additive subgroups of $F$ containing $1_F$ . Then show $Z_F = N_F \cup {0} \cup -N_F$
sharp smelt
im gonna call XY on this
here
sharp smelt
$N_F ={k \cdot 1_F \mid k \in \N}$
jolly parrotBOT
What a wonderful world !
sharp smelt
F is a field
toxic lichen
is the B_Ī» notation taken directly from your book
cause it's ugly as hell
also i think as written this is false
sharp smelt
is the B_Ī» notation taken directly from your book
My notes uses some other letter, but yea, essentially the same
toxic lichen
{0} is an additive subgroup of F, so there's no way the intersection of all additive subgroups of F is any larger than that
toxic lichen
make sure and then when you've made sure make sure a SECOND time
toxic lichen
I can't share ss as it's a profs notes
prof explicitly forbade screenshotting?
sharp smelt
prof explicitly forbade screenshotting?
I don't know, I don't want to risk it
He'll only be my prof next year
toxic lichen
does he have a track record of hunting down people who disseminate his notes
sharp smelt
does he have a track record of hunting down people who disseminate his notes
not reallt
jolly parrotBOT
What a wonderful world !
toxic lichen
one thing that weirds me out is why do you call the arbitrary additive subgroup B_Ī» instead of like
a single letter like G or whatever
sharp smelt
toxic lichen
anyway
following your notation, i claim $N_F \cup {0} \cup -N_F$ is in fact itself an additive subgroup of $F$ that contains $1_F$.
jolly parrotBOT
Ann
sharp smelt
I've proven that
toxic lichen
ok right
sharp smelt
Which is what I used to prove it's a subset of the intersection
toxic lichen
so you know that it is one of the sets being intersected
maybe it would be good to give it a name
let's call it G
sharp smelt
sure
sharp smelt
Wait, doesn't this prove the other way
toxic lichen
i don't know what you did, so i cannot possibly tell you what you did and didn't prove...
sharp smelt
i don't know what you did, so i cannot possibly tell you what you did and didn't...
I mean the fact that it's an additive subgroup proves that it's a subset of the intersection
sharp smelt
so you have proven that G ā (intersection)
ok, so this
I need to show the intersection is a subset of G
toxic lichen
I mean the fact that it's an additive subgroup proves that it's a subset of the ...
no actually
that G is one of the sets being intersected proves (intersection) ā G
bc yknow $A \cap B \subseteq A$ and all...
sharp smelt
oops
jolly parrotBOT
Ann
sharp smelt
yea my bad
toxic lichen
now you need to show every member of G belongs to the intersection
i.e. let x ā G and let B be an additive subgroup of F containing 1_F. you need to show x ā B.
go.
sharp smelt
every element of $G$ is of the from ${k \cdot 1_F \mid k \in N_F \cup -N_F \cup {0} }$
jolly parrotBOT
What a wonderful world !
toxic lichen
every element of $G$ is of the from $\{k \cdot 1_F \mid k \in N_F \cup -N_F \c...
nope
this is bad notation and misspoken in like 2 different ways
and formally nonsensical
every element of G is one of three things:
- k * 1_F for a natural k (said notation being shorthand for the sum of k copies of 1_F)
- -k * 1_F for a natural k (said notation being shorthand for the sum of k copies of -1_F)
- 0
do you allow yourself closure under finite sums for subgroups or is that something that you are obligated to treat as needing proof?
sharp smelt
do you allow yourself closure under _finite_ sums for subgroups or is that somet...
I allow that
toxic lichen
ok
then use the fact that 1_F ā B to your advantage
i think the proper formulation will be harder than the logic here
sharp smelt
I think to start I can prove B is an inductive set
then show that PMI works for it
That is the property of mathematica induction
sharp smelt
every element of G is one of three things:
- k * 1_F for a _natural_ k (said not...
and then finally use that to show that every element of these form are in it
toxic lichen
I think to start I can prove B is an inductive set
no
unnecessary!
you don't need induction if you already say closure under finite (but length >2) sums is OK in your book.
sharp smelt
hmm, okay
sharp smelt
i think the proper formulation will be harder than the logic here
So how does this sound :
\
As the group is closed under finite sums, adding 1_F an arbitrary number of times gets us $k \cdot 1_F$ , adding it;s inverse k times gets us $k \cdot -1_F$ and adding $1_f and its inverse gets us 0$
jolly parrotBOT
What a wonderful world !
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
toxic lichen
don't like the "arbitrary number of times"
adding \underline{$k$ copies of} $\pm1_F$ gets us $k \cdot 1_F$ and $-k \cdot 1_F$ respectively.
jolly parrotBOT
Ann
polar rivet
4plus5
ruby cargo
4plus5
If, 4 = S(S(S(S(0)))), 5 = S(4), then, result is S(4) + 4 = S(4 + 4) = S(5 + S(S(S(0))) = S(S(5 + S(S(0)))) = _____= S(S(S(S(5)))
This is using the Peano definitions
on natural numbers but for other fields as mentioned by @steady crescent it maybe different
steady crescent
on natural numbers but for other fields as mentioned by <@648060265459482624> it...
Are you implying the natural numbers are a field š¤
pearl pondBOT
@polar rivet Has your question been resolved?
ruby cargo
Are you implying the natural numbers are a field š¤
No, because they don't have additive or multiplicative inverses
They're just a commutative, ordered, semi-ring
sweet cedar
need help w this question
pearl pondBOT
need help w this question
sweet cedar
not really sure where to start
plush moss
Convert to Cartesian vectors, add the two vectors then convert back to the magnitude and bearing form
sweet cedar
Convert to Cartesian vectors, add the two vectors then convert back to the magni...
what is cartesian vectors
plush moss
what is cartesian vectors
Vectors with a X and Y component
toxic fractal
start by drawing it
toxic fractal
now, for each vector, decompose it into a vector parallel to X axis, and a vector parallel to Y axis
sweet cedar
i dont get what that means š like i think ur telling me to like turn it into component form but
i dont know how to with the information i have
plush moss
i dont know how to with the information i have
Me when trig function
sweet cedar
š
toxic fractal
i dont know how to with the information i have
does this help?
sweet cedar
its kinda like my drawing
toxic fractal
so see that you can form a right triangle with the red, the black, and the endpoints and red and black vectors
same with green, black, and the endpoints of green and black
sweet cedar
hmm okay wait i think i got it now but
how do i apply what i learned now in different contexts like
š nevermind
sweet cedar
need help w this question
is resultant the sum
toxic fractal
yes
hollow perch
hey guys, anyone that has done the Math standard IB paper yet
toxic fractal
!occupied
pearl pondBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
sweet cedar
does this work look right
toxic fractal
,rotate
jolly parrotBOT
toxic fractal
assuming you did the actual computations right, it does look right.
i'd include the units in the sqrt as well
as in (321.56mph)^2...
sweet cedar
my teacher doesnt really mind if we dont do that
plush moss
Id put the direction as a bearing though
Since the question gave the angles in the bearing form
sweet cedar
how do i give it as a bearing
toxic fractal
you start counting from Y axis, clockwise, instead of from X axis counterclockwise
see how you put 135Āŗ bearing as -45Āŗ angle?
pearl pondBOT
@sweet cedar Has your question been resolved?
pearl pondBOT
@sweet cedar Has your question been resolved?
wise hedge
Help on 3?
pearl pondBOT
Help on 3?
verbal whale
A 4th degree polynomial maybe
Which satisfies P(0) = 25, has a single root at x=1 and a triple root at x=5
wise hedge
Thank u
wet osprey
Something about the sign of the first coefficient as well
pearl pondBOT
@wise hedge Has your question been resolved?
torpid saffron
how to figure out these types of questions?
pearl pondBOT
how to figure out these types of questions?
cursive wraith
Here's a trick
you know a parabola is symmetric along the vertical line that goes through the vertex
so if you have two points on your parabola that have same y-coordinate
then the vertex x coordinate is straight in the middle
you have in the second example
sonic hound
Well the vertex is (-b/2a) = (-b/a)(1/2) = sum of roots * 1/2
cursive wraith
(11,0) and (5,0) points of the parabola
they do have the same y coordinate
it's a particular case where it's even the roots that are given
all we care about is that they have same y coordinate
so the x-coordinate of the vertex
is just the mean of the x-coordinates given
junior loom
so add the x's then divide by 2 if the y coord. is the same?
try to draw any parabola going through those 2 points given
it might bevome more obvious what the answer is
cursive wraith
so add the x's then divide by 2 if the y coord. is the same?
yeah
https://www.desmos.com/calculator/1iqxlqorg7 Here's something to visually tinker with if you want
no matter the point you choose on your parabola
the other point on the parabola that will have the same y-coordinate
is in complete "mirror"
if you consider the mirror being the vertical line at the vertex
So vice versa
having two points of same y coordinate on the parabola
reveals that the vertex is straight in the "middle" (for the x coordinate)
torpid saffron
okay I see
pearl pondBOT
Available help channel!
pearl pondBOT
Available help channel!
pearl pondBOT
dusty flame
,rotate
jolly parrotBOT
balmy obsidian
pearl pondBOT
atomic oracle
!status
pearl pondBOT
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
@balmy obsidian Has your question been resolved?
torpid saffron
pearl pondBOT
brave hawk
so you messed up the sign
so you should get y = (x+4)(x-3)
so the values of x that make it 0 would be -4 and -(-3) = 3 (plug it in and see why)
pearl pondBOT
pearl pondBOT
Available help channel!
torpid schooner
Can someone explain to me how II is a
pearl pondBOT
Can someone explain to me how II is a
torpid schooner
Unit sphere
autumn fossil
Unit sphere
unit vectors are all vectors with length 1
torpid schooner
unit vectors are all vectors with length 1
Oh I see
autumn fossil
so it's the set of all points with distance 1 from the origin
pearl pondBOT
pearl pondBOT
Available help channel!
proven dew
why are these not the same?
pearl pondBOT
why are these not the same?
proven dew
oh rightt
west sapphire
in fact, you could just pull the 2-x out of the inner integral, then you are left with $\int_0^2 (2-x)(4 - x^2),dx$
jolly parrotBOT
Bungo
lucid ibex
Hey, im trying to prove the term you can see on top here using induction, but this doesnt seem right to me. What i did here was check if the term is fulfilled for n = 1 and then, when checking with n+1 substituting n for a^n, (the part with the braces that says I.V), since i have already shown the term is correct for n. Can i do it like this? and if yes is this enough or do i need more steps for the induction to be correct?
autumn fossil
even assuming c ist allways 1?
mhm
n <= 1.01^n isnt true for low n
once n gets high enough, it is true
but for the low n it isnt
youll have to choose higher c for low n
lucid ibex
ye but thats no problem, ican do that
but the general structure of the induction is correct?
because thats my biggest problem atm š
autumn fossil
it is correct, up to here
this isnt always true
if it was true, the induction would be right
pearl pondBOT
autumn fossil
okay ill try with another c, tyvm :)
no constant c will work
you'll have to choose c dependent on a
I'd try doing the induction with general c first, and then deciding what kind of requirements to put on c
pearl pondBOT
Available help channel!
viscid pivot
how did this happen?
pearl pondBOT
how did this happen?
warm patio
how did this happen?
we know tan(pi/6)
so probably due to tan(2x) formula
$\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}$
jolly parrotBOT
zzzz
viscid pivot
so probably due to tan(2x) formula
wouldn't that make tan into (pi/24)?
midnight haven
oh
warm patio
wouldn't that make tan into (pi/24)?
set x = pi/12
warm patio
we can rewrite and we get a quadratic
viscid pivot
we can rewrite and we get a quadratic
how?
warm patio
let x = tan(pi/12)
sonic hound
,w solve 1/root(3) = 2x/(1-x^2)
jolly parrotBOT
warm patio
$\frac{2x}{1-x^2}= \frac{\sqrt{3}}{3}$
jolly parrotBOT
zzzz
warm patio
we can multiply by $1-x^2$, since we know $-1 <\tan(\frac{\pi}{12}) < \tan(\pi/4) = 1$
so we get a quadratic which we can solve using the quadratic formula
viscid pivot
hm
jolly parrotBOT
zzzz
viscid pivot
so we get a quadratic which we can solve using the quadratic formula
you mean 2x=sqrt(3)/3 * (1-x^2)?
warm patio
you mean 2x=sqrt(3)/3 * (1-x^2)?
yes
warm patio
and
`x=sqrt(3)/3*(1-x^2)*2`
we want to multiply everything out so that we can apply the quadratic formula so get to ax^2+bx+c=0
viscid pivot
right
warm patio
tan(pi/6)=tan(2(pi)/12)
its true but what does this do
viscid pivot
ohhh yeah I see it
viscid pivot
its true but what does this do
I just started writing it and you're right I got it
I got what you meant
warm patio
okay nice good job
viscid pivot
okay nice good job
right, so I got to the sqrt(3)/6 tg^2(pi/12) -tg(pi/12) + sqrt(3)/6=0
so I can substitute tg(pi/12)=x
to solve it such so
sqrt(3)x^2-6x^2+sqrt(3)=0
right?
warm patio
sqrt(3)x^2-6x^2+sqrt(3)=0
uh -6x not x^2
warm patio
sqrt(3)x^2-6x+sqrt(3)=0
hm actually I think you messed up the sign somewhere it should be sqrt(3)x^2+6x-sqrt(3)
viscid pivot
right
pearl pondBOT
@viscid pivot Has your question been resolved?
manic harbor
im thinking it's either this or 2.35
pearl pondBOT
im thinking it's either this or 2.35
snow sail
earnest finch
earnest finch
im thinking it's either this or 2.35
Can you explain your reasoning behind both your values x = 1.59 and x = 2.35
earnest finch
so i was right it was b
Still, I highly recommend figuring out where you went wrong in finding x = 1.59 to avoid this mistake in the future.
manic harbor
i thought it was d because
i wasn't plotting it right
i don't think i was
thank you bro
.close
round mountain
hi could someone explain why the gradient is normal to the plane?
flint basalt
if you are looking for the fastest increase, the dot product of the gradient and some vector u is 0
and as you know, if the dot product is 0 then it is perpendicular (or normal) to the plane
pearl pondBOT
@round mountain Has your question been resolved?
silver oracle
how does this skipto 1 + tan^2
pearl pondBOT
how does this skipto 1 + tan^2
silver oracle
pythag trig identity
So which one was used exactly?
light helm
first col, third one down
pearl pondBOT
pearl pondBOT
Available help channel!
silver oracle
how does this step happen?
pearl pondBOT
how does this step happen?
grim fractal
using sin/cos = tan
leaden egret
Lol
silver oracle
i hate this stuff
spent 5 hours on the first unit and i have 3 more to go
lovely
leaden egret
u got this bro
junior loom
how do you factor this kind of stuff? never done it before
how would you factor an expession with two variables, call them s and t, that looked like sĀ²tĀ²-tĀ²?
silver oracle
how would you factor an expession with two variables, call them s and t, that l...
take tan squared out
junior loom
what would that look like
wheat finch
Prove:
((secx+1)/(secx-1)) + ((cosx+1)/(cosx-1)) = 0
pearl pondBOT
Prove:
((secx+1)/(secx-1)) + ((cosx+1)/(cosx-1)) = 0
wheat finch
do NOT ask me to use syntax
idk how to do that
also dont ask me for my working out its 8 pages long
i am not taking a photo of those
compact ridge
what happens if you multiply (sec x + 1) by -cos x, and also multiply (sec x - 1) by -cos x
wheat finch
ok look
i have no idea but
what i was doing was
turning the sec into cosines
but
idk how to really do that
since it turns into
(1/cos)+1/(1/cos)-1
which is very messy and idk how to divide that
oh also
only basic identities can be used
toxic lichen
also dont ask me for my working out its 8 pages long
eight fucking pages?????
compact ridge
turning the sec into cosines
yeah that's my idea too
wheat finch
***eight fucking pages?????***
i got stuck so i just kept spamming solutions
i somehow got cos+1/0
which is like
technecally right ig
toxic lichen
i got stuck so i just kept spamming solutions
please do not call me "bro"!
wheat finch
https://en.wikibooks.org/wiki/LaTeX/Mathematics
whats the command here
toxic lichen
could you edit that word out
wheat finch
could you edit that word out
uhh...
its
one word..
like i get that
but
bro is a gender neutrual term
toxic lichen
it is one word which i do not want to be called.
wheat finch
most of the time
toxic lichen
and also, gender neutrality be damned,
if someone tells you not to call them by a word, you don't call them by that word
wheat finch
š
toxic lichen
cause i asked you to
wheat finch
ok
toxic lichen
you literally spent 10 times more time arguing about this than it would be to just do it
wheat finch
yeah but i need to know the reasoning
its like
if i said go jump of a cliff
you wouldn't do that
you would ask why first
compact ridge
turning the sec into cosines
this idea is correct
toxic lichen
the reasoning is:
if someone tells you not to call them by a word, you don't call them by that word
toxic lichen
if i said go jump of a cliff
ok but i didn't ask you for anything nearly as destructive
compact ridge
then sec x * cos x = 1
1 * cos x = cos x
toxic lichen
what does editing the sentence do
it erases the misgendering
wheat finch
okayz
wheat finch
how do i
divide that
i dont know how im decent at math
when i cant divide four numbers
toxic lichen
maybe it would be good to rewrite the problem in my shorthand
and instead of cos(x) just write c
toxic lichen
and accordingly sec(x) is 1/c
toxic lichen
$\frac{\frac{1}{c}+1}{\frac{1}{c}-1} + \frac{c+1}{c-1}$
jolly parrotBOT
Ann
wheat finch
$\frac{1}{cosx} + (cosx-1)$
jolly parrotBOT
haku
wheat finch
like i swear this is how it works
is it not
wait no
theres a missing number
$(\frac{1}{cosx} + 1) + (cosx-1)$
jolly parrotBOT
haku
wheat finch
wait
toxic lichen
$\frac{1}{cosx} + (cosx-1)$
i think you already messed something up
wheat finch
$(\frac{1}{cosx} + 1) (cosx-1)$
jolly parrotBOT
haku
toxic lichen
$(\frac{1}{cosx} + 1) (cosx-1)$
i think this is also wrong
wheat finch
yep im turning insane
toxic lichen
"how is this wrong" or "how do i do it right"?
wheat finch
$(\frac{1}{cosx} + 1) / (\frac{1}{cosx} + 1)$
jolly parrotBOT
haku
wheat finch
"how is this wrong" or "how do i do it right"?
if i figure out why its wrong ill get it in like