Biscuity
#help-10
warm shaleBOT
glossy basalt
$\log_c c =1$
warm shaleBOT
Biscuity
glossy basalt
yea
brave halo
So C
glossy basalt
very good
brave halo
TYYYY VERY MUCHH
glossy basalt
Cheers!
brave halo
Cheers!
CHEERS!
My mind is warm istg
Like its burning
I have a test tmrw i still have 4 section left
glossy basalt
I have a test tmrw i still have 4 section left
good luck!!! šÆ
brave halo
Tyy
glossy basalt
yes?
brave halo
Thats where i get stuck
glossy basalt
4Ā²=16
brave halo
ITS LIKE ITS MY FIRST TIME LEARNING POWER
brave halo
Ty again
glossy basalt
Cheers!
obtuse pebbleBOT
@brave halo Has your question been resolved?
obtuse pebbleBOT
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opaque crater
I do not understand kirchoff laws
obtuse pebbleBOT
I do not understand kirchoff laws
opaque crater
So I understood the theory but i don't know how to set the equations
obtuse pebbleBOT
@opaque crater Has your question been resolved?
chilly kernel
So I understood the theory but i don't know how to set the equations
Have you tried any solved examples?
chilly kernel
So I understood the theory but i don't know how to set the equations
Do you still need help?
obtuse pebbleBOT
@opaque crater Has your question been resolved?
azure eagle
Does anyone know what I did wrong here? I got the wrong answer and I canāt figure out what Iām doing wrong
obtuse pebbleBOT
Does anyone know what I did wrong here? I got the wrong answer and I canāt figur...
shut lagoon
,rccw
warm shaleBOT
chilly kernel
this is wrong
shut lagoon
this is wrong
They're just separating it's ok
zenith raft
not bad handwriting
azure eagle
omg bro
thank you
i didnt have a calculator so i was using google and it thought that i meant (sqrt1)/8
shut lagoon
obtuse pebbleBOT
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oak oyster
obtuse pebbleBOT
oak oyster
"In the circle with center in O and radius of 10cm, AC is a diameter, OB is perpedicular to AC, and the angle AOD is 2/3 pi radians, whats the area of the shaded region?
Is the area around 327cmĀ²? Could anyone give it a try and tell me what their results are?
ornate sable
Is the area around 327cmĀ²? Could anyone give it a try and tell me what their res...
Why are the areas of the bottom triangle 50?
oak oyster
Because they add up to 100
rose scroll
area of the circle is pi*r^2 which would be 100pi so 314cm^2
shaded region cant be more than that right?
oak oyster
Yes area of shaded region is area of circle minus area of cyclic polygon
ornate sable
Mb I was tripping
rose scroll
Yes area of shaded region is area of circle minus area of cyclic polygon
your 327 > 314 tho
oak oyster
Oh wait
I got that the area of the 2 triangles on top is 50 root 3
And the area of the ones below is 100
So the area of the cyclic polygon is 50 root 3 + 100
ornate sable
I got that the area of the 2 triangles on top is 50 root 3
Thereās your error
You forgot the 1/2
Or maybe you meant the total area of both upper triangles
oak oyster
Or maybe you meant the total area of both upper triangles
Yes thats what I meant
They both have area 25 root 3
ornate sable
Yes thats what I meant
Alr then itās correct
rose scroll
So the area of the cyclic polygon is 50 root 3 + 100
just subtract it from the area of circle
oak oyster
Thats what I diddd
ornate sable
You canāt get 327
rose scroll
then howd you get a number larger than 314?
ornate sable
Plug it again and check
oak oyster
Remember the + 100
rose scroll
Remember the + 100
yes, hence the 186
rose scroll
you probably went wrong on sqrt3
oak oyster
I forgot to change signs
Since the area as a whole is 2 separate terms (root 3 and normal number) I shouldve changed sign
I think thats what I got wrong
Yeah
It gives 127 now
I was doing 100pi - 50 root 3 + 100
Wait
oak oyster
I was doing 100pi - 50 root 3 + 100
Why when I put this does it give me 327
And when I put 100pi - 50root3 - 100 it gives me 127?
Where does the 100 go
Oh its cause 100 pi-50root3 is 227
Approx
obtuse pebbleBOT
@oak oyster Has your question been resolved?
obtuse pebbleBOT
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empty pewter
can someone explain why the last number is 10 instead of 8 bcs I thought the last number in the sequence was the period?
obtuse pebbleBOT
can someone explain why the last number is 10 instead of 8 bcs I thought the las...
empty pewter
oh wait is it only the last number in the sequence if the sequence starts at 0?
brazen viper
@empty pewter exactly.
Because you start with 2 you end with 2+8 = 10
(note, this is true for any value A and any period T, in this case A = 2 and T = 8, so one period spans from 2 to 10, but it could also span from 0 to 8 or -4 to 4.)
I suppose in this case, because of the phase shift it is expecting you to specifically start with 2. (But you could start at -6 and go to 2 or start with 10 and go to 18)
empty pewter
I suppose in this case, because of the phase shift it is expecting you to specif...
yeah I get it now tysm for the explanation
u just keep multiplying by the phase shift right and thats how you get the subsequent x values?
obtuse pebbleBOT
@empty pewter Has your question been resolved?
obtuse pebbleBOT
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forest coyote
How to solve " find x problems"
obtuse pebbleBOT
How to solve " find x problems"
shut lagoon
That is very very vague
shut lagoon
You need to be more precise or give specific examples of problems youāre struggling with
shut lagoon
Itās not harsh or anything I just mean that āfind xā comes in VERY diverse forms that have different ways of dealing with them.
So to help you efficiently itās good to know what youāre dealing with 
distant laurel
How to solve " find x problems"
I can give a general idea
For equations, you want to isolate x
Very simple
For advanced topics, you need to know that specific topic
And treat x as a constant
And same as before, isolate x
I hope this helps even a bit
inner sierra
How to solve " find x problems"
have you learned quadratic equations yet?
if not we can probably focus on $ax + b = cx + d$ or maybe some finding $x$ problems on fractions
warm shaleBOT
1 divided by 0 equals Infinity
obtuse pebbleBOT
@forest coyote Has your question been resolved?
obtuse pebbleBOT
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prisma kraken
How is ${78, -402, 45, {\emptyset}} \supseteq {-402, 45,\emptyset}$ not true?
obtuse pebbleBOT
How is $\{78, -402, 45, \{\emptyset\}\} \supseteq \{-402, 45,\emptyset\}$ not tr...
warm shaleBOT
PainAndLight
tardy epoch
{emptyset} is not equal to emptyset
pallid willow
also, 78
mild sandal
wow thats some fast help
tardy epoch
oh nevermind the containment is reversed
pallid willow
oh supseteq
cosmic cove
The set containing nothing vs the set containing the set containing nothing
cosmic cove
oh nevermind the containment is reversed
The supposed superset still doesn't contain the empty set
tardy epoch
all sets contain the empty set
prisma kraken
but -402 and 45 are part of the ${78, -402, 45, {\emptyset}}$ and \subseteq is just reversed \supseteq, or?
warm shaleBOT
PainAndLight
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
past sand
but -402 and 45 are part of the $\{78, -402, 45, \{\emptyset\}\}$ and \subseteq ...
Yes but \emptyset is an element of the RHS but not of the LHS
prisma kraken
i thought it just matters if atleast one element is of the other
past sand
... no
prisma kraken
also, whats rhs and lhs
past sand
Right-hand side, left-hand side
past sand
The definition of $A \subseteq B$ is $\forall x \in A, x \in B$
warm shaleBOT
Nel
past sand
That's a for all, meaning all elements of A must be in B
obtuse pebbleBOT
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shrewd plover
Help me understand the diff bw solving limits which approach negative infinity and others which approach infinity cuz I am confused with signs
obtuse pebbleBOT
Help me understand the diff bw solving limits which approach negative infinity a...
shrewd plover
As an example the limits below
shrewd plover
But do remember that it is infinity
Can u show me by solving the first limit below?
opal fractal
Can u show me by solving the first limit below?
Just take xĀ² common in denominator
shrewd plover
Ye x comes out
Divided by x on numerator and denom
Resulted in my answer being - 3/2
Book says 3/2
opal fractal
Root will cancel x
It will be mod x
Instead of x
Now x is tending to be a negative number
Mod will open with negative sign
You will get 3/2
shrewd plover
Now x is tending to be a negative number
We get this hint from x approaching negative infinity?
opal fractal
Yess
shrewd plover
Thanks alot
opal fractal
No problem buddy
stark jolt
If I have 3 chocolates and at present I am having 1/4 . How many chocolates did I eat?
last pilot
If I have 3 chocolates and at present I am having 1/4 . How many chocolates did ...
!help
obtuse pebbleBOT
If I have 3 chocolates and at present I am having 1/4 . How many chocolates did ...
To ask for mathematics help on this server, please open your own help channel or help thread. See #āhow-to-get-help for instructions.
@shrewd plover Has your question been resolved?
obtuse pebbleBOT
ivory kraken
<@&268886789983436800>
obtuse pebbleBOT
neon vector
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iron gyro
If two field extensions of $F$ are isomorphic, say, $F(a) \cong F(b)$, does this mean that the isomorphism must map $F$ onto $F$? That is, for every $x \in F$, do we have $f(x) = x$?
Or is this an independent property that needs to be required additionally?
obtuse pebbleBOT
If two field extensions of $F$ are isomorphic, say, $F(a) \cong F(b)$, does this...
warm shaleBOT
Dedekind
olive yew
If two field extensions of $F$ are isomorphic, say, $F(a) \cong F(b)$, does this...
https://math.stackexchange.com/a/4067351/259363
Take the example (b) from this answer: you may also consider complex conjugation from two null extensions of the same field F=C (aka a=b=1)
This is an additional assumption you need to add, that you're also a linear map over the two F-vector spaces. For some fields F, this is automatic (e.g. F=Q), but it needs not hold in general!
Now the question might have been: If F(a) and F(b) are isomorphic as fields, then does there exist some isomorphism that is F-linear? The answer might then be yes in this case
iron gyro
Now the question *might* have been: *If* F(a) and F(b) are isomorphic as fields,...
Yes, probably, this question would better serve my purpose. Could you please direct me to how to build one?
If it make things easier, let's restrict to finite fields
olive yew
,,,\application{f}{\kk(a)}{\kk(b)}{\sum_{i=0}^n\lambda_ia^i}{\sum_{i=0}^n\lambda_ib^i}
That should do the trick, no?
Or rather, sorry, I'm thinking algebraic extensions only
warm shaleBOT
\TeXplotlib
olive yew
That's only for algebraic extensions, but since you restricted to finite fields it works, as all extensions of finite fields which are also finite fields are trivially algebraic
obtuse pebbleBOT
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trim island
Need help with this question
obtuse pebbleBOT
Need help with this question
trim island
Now i know i need to do march income + (april x 1.05)+ (may x 1.05^2)+.........
But is there any faster way to do it? Had about 45seconds for the question š
obtuse pebbleBOT
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obtuse pebbleBOT
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spark patrol
Can someone help with these please? I'm stuck on where to begin for the first one as Idk how to write the contradiction and the last one doing the basic first steps of induction.
obtuse pebbleBOT
Can someone help with these please? I'm stuck on where to begin for the first on...
zenith raft
for 7 you could just look at how 4^n and 5^n cycle mod 9
for 6 i would start with putting a - c = (d-b)sqrt(2)
then ask yourself if a nonzero multiple of sqrt(2) can be an integer
why am i being 
'd
spark patrol
for 7 you could just look at how 4^n and 5^n cycle mod 9
idk what modulo is
we havent learnt it
zenith raft
ok for that one you can probably use induction then
spark patrol
after i have 4^(k+1) + 5^(k+1) what do I do
dark stirrup
why am i being <:thinkies:827642567775748163>'d
I do that for ideas i find creative
zenith raft
means n can be expressed as 2x+1 for any integer x?
you don't need to worry about that i think. if you assume it is true for k, you should show 4^(k+2) + 5^(k+2) is divisible by 9
spark patrol
you don't need to worry about that i think. if you assume it is true for k, you ...
why +2 i thought induction we use +1
zenith raft
we want to show it is true for n = 1, 3, 5, 7, etc
spark patrol
ohh
zenith raft
means n can be expressed as 2x+1 for any integer x?
you can also do this if you are more comfy with it
but i think my way will be cleaner
spark patrol
then it'd be 4^(k+2)+5^(k+2) = 9m for some integer m?
zenith raft
yes that is what you would want to show
assuming that 4^k +5^k = 9a for some integer a
spark patrol
16(4^k) + 25(5^k) = 9a?
is this true
then i think split the 25 into 16 + 9
so that 16(4^k) +(16+9)(5^k) = 9a
then 16(4^k+5^k)+9(5^k)=9a
wait i dont keep writing =9a right
i can divisibility after?
zenith raft
16(4^k) + 25(5^k) = 9a?
well maybe you should write 16(4^k) + 25(5^k) = 9m here to be consistent with the symbols we already introduced
spark patrol
ok
spark patrol
then 16(4^k+5^k)+9(5^k)=9a
then after from here according to the inductive hypothesis, 4^k+5^k = 9m for some integer m
so 16(9m) +9(5^k)
wait oops
ok there we go
now factor out 9
?
9(16m+5^k)
since m is an integer and k is an integer then the thing in brackets will be
integer
and it is clearly divisible by 9
@zenith raft is this it?
sorry fro ping
zenith raft
i do not mind pings
ok let me go through your argument. we assume 4^k +5^k is divisible by 9 and want to show 4^(k+2)+5^(k+2) is divisible by 9. and 4^(k+2)+5^(k+2) = 9m is equivalent to 16(4^k+5^k) + 9(5^k) = 9m. then since 4^k +5^k is divisible by 9, yes i agree there is such an m
just be careful about writing the proof correctly
spark patrol
oh but the lesson wants us to use contradiction
spark patrol
wouldm you still want to help?
zenith raft
@wild swallow check this out
zenith raft
wouldm you still want to help?
sure
spark patrol
thank you
zenith raft
ok so we will still put a - c = (d-b)sqrt(2) but then we will assume for no reason that a \neq c or b \neq d
spark patrol
ok lol
zenith raft
if b \neq d, do you have any thoughts?
spark patrol
Uh Im not sure
zenith raft
ok let me say it in plain english. a nonzero integer multiple of sqrt(2) is equal to an integer (the integer a-c)
that should raise some red flags
spark patrol
oh yse
zenith raft
since d-b is not 0, we can put sqrt(2) = (a-c)/(d-b)
zenith raft
all good for that case then? contradiction achieved?
spark patrol
wait sorry where is the contradiction?
zenith raft
we just wrote sqrt(2) as a fraction of integers
zenith raft
yes
spark patrol
can you show me your method with direct proofs
spark patrol
yes
oh yeah and then you continue because you need either a-c or d-b to be 0
ok i got that now thanks a lot
zenith raft
can you show me your method with direct proofs
let a,b,c,d be in Z with a + b\sqrt(2) = c + d\sqrt(2). then we have b = d (because otherwise sqrt(2) = (a-c)/(b-d)). and a + b\sqrt(2) = c + b\sqrt(2) implies a = c.
spark patrol
ohh
ok i actually understand that better its just the contradiction one but more easy to understand for me
thank you
zenith raft
also i'm not really hiding a contradiction in the (because otherwise sqrt(2) = (a-c)/(b-d)) part. it's more like contrapositive reasoning, from that fact that if a,b,c,d are integers, then sqrt(2) \neq (a-c)/(b-d)
night thorn
can anyone help w 3
obtuse pebbleBOT
can anyone help w 3
fossil pendant
can anyone help w 3
the median point of a triangle is exactly its "middle" so if you know how to find the "middle" of 3 points then you can find the median. and that will allow you to a lot of approaches.
Unless I'm overcomplicating stuff
fossil pendant
the median point of a triangle is exactly its "middle" so if you know how to fin...
midpoint of 3 points is a formula by the way
night thorn
the median point of a triangle is exactly its "middle" so if you know how to fin...
i donāt know how thatās supposed to help me find the perpendicular bisector though
past sand
Unless I'm overcomplicating stuff
You really are
night thorn
this is so complicated
fossil pendant
apologies then.
past sand
can anyone help w 3
Prove PQR is isosceles
night thorn
canāt i do that by finding the distances between all 3 points
night thorn
wait why not 3
past sand
What is an isosceles triangle?
night thorn
it has 2 same sides then one diff
past sand
Right, so do you care about the different one?
past sand
canāt i do that by finding the distances between all 3 points
Just do that
past sand
I mean sure, that part, but you already said that
night thorn
oh okay
itās fine ill just skip that question
do u happen to know how to do this
past sand
... why?
night thorn
3
past sand
canāt i do that by finding the distances between all 3 points
Why are you skipping the question instead of doing this
night thorn
Why are you skipping the question instead of doing this
so it makes sense itās an isosceles
but how does this connect to showing the median
sorry if thatās a completely stupid question
i suck at math with pictures
past sand
Let M be the midpoint of PR
QM is the median, by definition
The perpendicular bisector of PR also goes through M, so all you need to do is show that QM and PR are perpendicular
night thorn
The perpendicular bisector of PR also goes through M, so all you need to do is s...
by finding their slope?
past sand
You can do that, but it's even easier to consider the triangles QPM and QRM
night thorn
this is just really confusing for some reason š
i will figure it out though thank u anyways
past sand
this is just really confusing for some reason š
Have you drawn a picture?
night thorn
Have you drawn a picture?
no but I donāt even understand it for it to help itās just frustrating me
and my test is tomorrow this is the only lesson idk how to do
silk snow
i have a quick question
obtuse pebbleBOT
Available help channel!
silk snow
can someone do 63 real quick
obtuse pebbleBOT
can someone do 63 real quick
silk snow
i got (x-1)^2 +(y+7)^2 = 16
shut lagoon
That's good.
silk snow
oh ok but i have a follow up to that, how can I assume that the points 3,-7 and 5,-7 are diameter endpoints which i can use to get the center of the circle?
past sand
You can calculate the distances
silk snow
what do you mean?
past sand
Well if you think the center O is the midpoint between (-3,-7) and (5,-7) then once you have O, you can check whether its distance to (1,-11) is also the same
past sand
You can also check whether the points form a right triangle
But I don't think that's easier than just figuring out the equation in the first place
silk snow
true but my teacher will give us a lot fo questions and not much time on our quiz so i need the fastest method
silk snow
But I don't think that's easier than just figuring out the equation in the first...
yeah
silk snow
wait is that the proper way to do these types of questions?
i just got the midpoint of the the 2 points and got the radius and called it a day
past sand
I mean that only works if the 2 points form a diameter
obtuse pebbleBOT
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visual geyser
You have a 10% HCL solution and 60% HCL solution. How many of each should you mix together to form a 100ml of 25 solution?
obtuse pebbleBOT
You have a 10% HCL solution and 60% HCL solution. How many of each should you mi...
visual geyser
this is solving problems involving linear equation.
obtuse pebbleBOT
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wary badger
obtuse pebbleBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #āhow-to-get-help for instructions.
vital imp
I am attempting to create a formula to determine the level (this is regarding an idle video game) I need to get my transport speed and cargo volume to in order to carry all the ore being mined. I have already set up my spreadsheet to determine the mine rate. and I know that "(1/750)x^4+(31/750)x^3+(326/750)x^2+(1501/750)x+1891/750=y" where x is the level of both cargo and speed, while y is the volume transported per second. I do not know how to invert this formula to solve for x, and my online search has not yeilded results. I thought I would bring it to other people and see if they could help me figure out what to do.
obtuse pebbleBOT
mortal blade
I am attempting to create a formula to determine the level (this is regarding an...
Please claim a new channel, and don't delete your first message this time
vital imp
Please claim a new channel, and don't delete your first message this time
I didn't delete my message the server closed the original channel
vital imp
Your first message was !help I imagine
Oh
mortal blade
Anyway, claim a new channel cuz this one might close on your face
vital imp
how do I close this channel now
austere shard
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eternal berry
Show that the sine or cosine value of an angle measuring 48Ā° is equivalent to the sine or cosine value of that same angle measured in radians and state the value of the function.
obtuse pebbleBOT
Show that the sine or cosine value of an angle measuring 48Ā° is equivalent to th...
mortal blade
What
eternal berry
Bro trust me i dont know either
zenith raft
mortal blade
Bro trust me i dont know either
Show us the original question lol
zenith raft
crazy question
oak bolt
sine or cosine?
which one do they want you to find? is there a different function not mentioned here?
oak bolt
i think maybe you can do something with a pentagon
eternal berry
to the question
zenith raft
it probably wants you to do something with both
oak bolt
because 48 degrees is 3pi/5 - pi/3
zenith raft
i don't really know what it is expecting though
oak bolt
and 3pi / 5 is in a regular pentagon
eternal berry
should i just put im very unsure what this question is asking and not sure how to respond
and wait for the teacher to email
oak bolt
did they teach the angle sum formulas?
pallid willow
I had a stroke reading the question, and all I can think of is "same angle = same value duh" ngl
oak bolt
yeah i think the question is more about finding sin(48) and cos(48)
well, idk. it is confusing
zenith raft
what does it even want you to demonstrate
putting it into the calculator in degrees and radians?
how do you demonstrate that
oak bolt
well pi/3 is a special value
so i'm just wondering if you can do something with a pentagon because it has a lot of golden ratio stuff
zenith raft
i imagine this being a very basic high school trig question
pallid willow
I suppose right, that this is lowkey testing to see if you know how to convert radians to degrees, whether you know that trig functions don't care about the unit so long as they represent the same angle, and... not much else I guess
zenith raft
could be but i still don't know what it's actually asking you to do
eternal berry
what does it even want you to demonstrate
You can't really demonstrate anything, it wants a computer written response
pallid willow
or perhaps it is a trap to those who set their calculators in the wrong mode
eternal berry
this is what
im answering with
Since 48 degrees = 4pi/15 radians, both measurements talk about the same exact angle. Since only the angle matters, the value of sin and cosine will be the same in either radians or degrees.
sin(48degrees) = sin(4pi/15) = 0.743
cos(48degrees) = cos(4pi/15) = 0.669
if its inocrrect im taking the L genuinely what the fuck
night thorn
how is this a kite not a rectangle?
obtuse pebbleBOT
how is this a kite not a rectangle?
worn yoke
in your flowchart it says that rectangles have adjacent sides perpendicular
high lily
wouldn't be a kite either
obtuse pebbleBOT
@night thorn Has your question been resolved?
lunar sparrow
How can I score more marks?
obtuse pebbleBOT
How can I score more marks?
lunar sparrow
I passed but I got 41 for 100 but i want to score 60 marks for 100
gilded needle
answer more things correctly? what feedback are you looking for?
if you have questions that you did not get fully correct, you can show them here
spice inlet
and in general ig practice more questions
obtuse pebbleBOT
@lunar sparrow Has your question been resolved?
night thorn
in your flowchart it says that rectangles have adjacent sides perpendicular
yea i ended up figuring it out thxs
obtuse pebbleBOT
frail latch
Hello
obtuse pebbleBOT
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heady wadi
Hey guys, year 11 VCE student here, is there some sort of collection of Unit 1+2 specialist mathematics resources? I'm looking for practice tests, hard questions, and anythign else that might be handy.
obtuse pebbleBOT
Hey guys, year 11 VCE student here, is there some sort of collection of Unit 1+2...
@heady wadi Has your question been resolved?
vale thunder
Geometric series, half-life.
I have trouble believing that "the minimum concentration is exactly D at 12 hours", since, if injected at t=0, and if the half time is 12 hours, then there would be only D/2 concentration by t=12. This feels like an oversight or misinterpretation because of discrete time intervals
obtuse pebbleBOT
Geometric series, half-life.
I have trouble believing that "the minimum concentr...
vale thunder
The long-term stable concentration being 2D makes perfect sense to me.
manic sonnet
doesnt at steady state mean its not ur first time taking the drug
vale thunder
I'm assuming t=0 is the first time it is ever injected
I guess it is asking for steady state minimum
where, if continously injecting at 12 hour intervals, it will never drop below D again
yeah that makes sense
alright that was silly, thank you
.close
obtuse pebbleBOT
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jade path
obtuse pebbleBOT
jade path
can someone help me with this pls
zenith raft
the points you should calculate the distance between are (0, 0) and (x, sqrt(2x+1))
jade path
ah os it will be b
zenith raft
we should have $d = \sqrt{x^2 + \sqrt{2x+1}^2}$
warm shaleBOT
slayla
jade path
oh:<
vale thunder
we should have $d = \sqrt{x^2 + \sqrt{2x+1}^2}$
can simplify to $d=\sqrt{x^2 + 2x + 1} = \sqrt{(x+1)^2} = x+1$
warm shaleBOT
issy ā¬
zenith raft
thanks, i was wondering about that
viral blade
"shortest distance" when they just mean distance š
zenith raft
school is always out to torture you
viral blade
true
vale thunder
"shortest distance" gets more value when you start trying to find the distance between lines/planes
viral blade
I think they just write shortest because whoever is writing these doesn't know what they're talking about lol
delicate cradle
"shortest distance" gets more value when you start trying to find the distance b...
its more fun while finding distance between 2 invisible points
zenith raft
amen dreyuk
viral blade
"shortest distance" gets more value when you start trying to find the distance b...
I could see this because it's the shortest d(x,y) for y on your line/plane
but there's only one distance between two points
might as well ask you to find the longest distance
delicate cradle
but there's only one distance between two points
infinite distances
obtuse pebbleBOT
@jade path Has your question been resolved?
twin compass
I need help, I have an equation 35y^2+13y-12 and I need to factorise it, the way taught to us in class is to split the middle into 2 numbers so that when you multiply them you get 35 x 12 and when you add them you get 13, with small equations this is easy but with this it's quite hard so can anyone give me an easier trick to do this
obtuse pebbleBOT
I need help, I have an equation 35y^2+13y-12 and I need to factorise it, the way...
ornate sable
Use quadratic formula and find the roots
twin compass
Use quadratic formula and find the roots
Idk what that is
ornate sable
Also what so said is incorrect. You need to find two numbers that sum to -13/35 and product to -12/35
Not multiplication
twin compass
That's not what's in my book
twin compass
Ok ig, thanks anyway
ornate sable
So in this case, you can eyeball that 35 = 7x5 and 12 = 4x3
So your numbers should be a combination of 7 5 4 3
Note that you can have 12 = 2x6 but Iām thinking of this first, we can take that case later if this fails
Now the brilliant observation $\dfrac{x}{7} + \dfrac{y}{5} = \dfrac{5x+7y}{35}$
warm shaleBOT
robin.dabanc_
ornate sable
And $\dfrac{x}{7} \times \dfrac{y}{5} = \dfrac{xy}{35}$
abstract vortex
don't ignore 1x35 and 1x12, and this is still requires even more complicated educated guess
warm shaleBOT
robin.dabanc_
ornate sable
One can see that x= 3, y= -4 solves the system
twin compass
Oh ummm this is sum high level stuff
ornate sable
No itās not trust me
Youāre jsut taking x and y as something you want to solve for
Let the required numbers be x/7 and y/5
They have to sum up to -13/35 and multiply to -12/35, thatās what I wrote in the two equations and then guessed it
twin compass
Oh ok
ornate sable
5x+7y = -13 and xy = -12
ornate sable
š
obtuse pebbleBOT
@twin compass Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
steel night
how do we solve this?
obtuse pebbleBOT
how do we solve this?
quick nova
how do we solve this?
Do you know suvat?
steel night
No i dont
quick nova
No i dont
It's these, they're the equations that you can derive when you have constant acceleration
pallid willow
ack suvat
drifting wraith
you can derive them yeah
pallid willow
how are you asked to do this then
quick nova
Maybe you call them differently
pallid willow
equations of motion maybe?
quick nova
I know there's different ways to name it, but here we call them suvat
pallid willow
(also a detour to say hi to mxr, even though mxr might not know who I am 
)
steel night
so they all can be derived from the basic constant acceleration formula "m/s/s"
quick nova
(also a detour to say hi to mxr, even though mxr might not know who I am <:catlo...
I'm going to guess you're another one of her students 
Anyways hi
pallid willow
well we can cont. in bots if necessary but no to OP
steel night
It's these, they're the equations that you can derive when you have constant acc...
do i need to know this?
how do we use them
quick nova
do i need to know this?
Probably
quick nova
how do we use them
Well let's first identify our variables we are using and what we want to find
As well as the equation
steel night
Well let's first identify our variables we are using and what we want to find
we are given acceleration
we want to find time it takes to acceleratore when t=0 to when acceleration reaches 149.76km/h
deep kraken
Or use deriative
steel night
tell me the best easy mehod
deep kraken
Depends on what your teacher teaching about
deep kraken
Then SUVAT is the best here
deep kraken
Just use v=u+at
steel night
what is u?
quick nova
Well it's in rest at the start and the u is the initial velocity
deep kraken
Yay still rememberāŗ
pallid willow
(some places call it v_0 if you're ever required to use that)
deep kraken
Just turn them all into m/s
steel night
ohh i see
steel night
acceleration should be in m/s/s
pallid willow
you're multiplying acceleration by time mate
deep kraken
If time in second then turn km/h into m/s
Or you can change acceleration unit and nasty
steel night
okok but
how are we
meant to remember the suvat equations
I think i know how to use them now
pallid willow
understand how they come about rather than bruteforce memorization
steel night
I see
quick nova
If you want to derive them yourself, draw a velocity time graph with constant acceleration
steel night
how do they come about?
quick nova
If you want to derive them yourself, draw a velocity time graph with constant ac...
Like this for example
deep kraken
Hmm arent the equations given on exam or on the referenced sheet?
steel night
Like this for example
oh ok and then?
steel night
Hmm arent the equations given on exam or on the referenced sheet?
im not sure on the normal tests but most likely in the final exam
deep kraken
Surely they will be given since they are fundamental equations on velo dista and time
deep kraken
Kin Formula to calculate the motions of points or objects
steel night
ahh right
steel night
Kin Formula to calculate the motions of points or objects
also
if we take the rise/run, it gives the average velocity right?
no matter what type of motion graph or whatever graph it is
steel night
It's these, they're the equations that you can derive when you have constant acc...
also why do we use suvat when we already have the standard accelatartion, displaement, velocity formula
quick nova
also why do we use suvat when we already have the standard accelatartion, displa...
What formula?
As in using calculus
quick nova
oh ok and then?
For starters try to find the acceleration (rate of change of velocity) and the area (displacement) of the graph
obtuse pebbleBOT
@steel night Has your question been resolved?
steel night
What formula?
the v^-> = s^->/t, etc
solar stump
also why do we use suvat when we already have the standard accelatartion, displa...
Ideally you should have been taught this from the outset, but suvat equations are for when, in a modelling question with constant acceleration, you have three variables and you want to find one of the other two
steel night
my prof said this finds the instataneous velocity but it should be average velocity since ur using rise over run
solar stump
For each of s, u, v, a and t, if you remove one of those variables, there exists an equation that relates the other four
solar stump
my prof said this finds the instataneous velocity but it should be average veloc...
For a straight line graph, those are synonymous
steel night
how?
steel night
For a straight line graph, those are synonymous
for any motion graph or just position time graph?
solar stump
Because the instantaneous velocity refers to the gradient of the graph
Position/time
But the gradient of a straight-line is definitionally constant
After all, if the gradient keeps changing... well, it's not a straight line anymore, is it
steel night
Because the instantaneous velocity refers to the gradient of the graph
so we could find tangent on a curve on a position time graph and it would give same answer when using rise/run
solar stump
yes
This is what we mean by "instantaneous (rate of change)"
As opposed to "average (rate of change)", which as you've mentioned is just the rise over run
steel night
This is what we mean by "instantaneous (rate of change)"
im still trying to figure out why they refer to the same thing
obtuse pebbleBOT
@steel night Has your question been resolved?
steel night
Because velocity is just the _gradient_ on a position/time graph
ohh right ok I get it now
one more question
steel night
how do we tell if this graph is a vector or a scalar because they labelled y axis as "position (m) "
what im thinking, the graphing is referring in displacement because it has forward included
but im guessing we can conclude speed and velocity from the same graph
solar stump
...yes
split yew
speed = |velocity| (note the bars)
steel night
yepp got it now thanks
what does it mean
by
"were not havving acceleration vary by time in this course, we are keeping it as a constant"
but acceleration acts like an exponential
at some sense
so it cant be a constant
split yew
acceleration acts like an exponential? that sounds like its effects on position
that has nothing to do with keeping acceleration itself constant
steel night
that has nothing to do with keeping acceleration itself constant
wdym?
split yew
I mean what I said. if you want to ask for clarification, I'd appreciate if you point out what was misleading or confusing
steel night
Im confused on what it means by keeping acceleration constant
solar stump
yes
solar stump
"were not havving acceleration vary by time in this course, we are keeping it as...
Which is literally what this line says already
steel night
and when its not constant, it means it shifts acceleration throughout time
solar stump
-# At the risk of me sounding like a cock, this is more a matter of comprehension š
solar stump
and when its not constant, it means it shifts acceleration throughout time
yes, and that's a separate topic in most high-school textbooks; suffice it to say you'll encounter it at some other moment
pallid willow
differential eq- ok not here so you don't need to worry
obtuse pebbleBOT
@steel night Has your question been resolved?
plush hornet
obtuse pebbleBOT
torn flower
plush hornet
š
obtuse pebbleBOT
@plush hornet Has your question been resolved?
tacit plank
Iām a little confused by this question
obtuse pebbleBOT
Iām a little confused by this question
opaque mesa
what's confusing?
tacit plank
what's confusing?
Idk what Iām doing wrong
The acceleration being 14.7 m/sĀ² doesnāt make sense
opaque mesa
you didnt use total mass
tacit plank
What do you mean
obtuse pebbleBOT
@tacit plank Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
Available help channel!
wind lark
So Iconverted the integral into polar coordinates and obtained
ī \frac{32}{3}\int_0^{2\pi}(1+\sin\theta)^6 \cos^2\theta \sin^2\theta , d\theta. ī Iām not sure how to evaluate the trigonometric Integral efficently.
Is there a way semplify It?
obtuse pebbleBOT
So Iconverted the integral into polar coordinates and obtained
ī \frac{32}{3}\in...
@wind lark Has your question been resolved?
obtuse pebbleBOT
@wind lark Has your question been resolved?
frank arrow
obtuse pebbleBOT
frank arrow
Am I doing problem 45 right so far?
midnight igloo
I mean in the beginning only you could write tanĀ²x as sinĀ²x/cosĀ²x
so cosĀ²x would cancel
frank arrow
Oh š
rose scroll
you could have effectively reduced this to 41
midnight igloo
only sinĀ²x left
frank arrow
you could have effectively reduced this to 41
To 41?
rose scroll
yea, sin^2(x) is not that different from sin^2(2x) as far as this question goes
midnight igloo
hmm
rose scroll
I mean in the beginning only you could write tanĀ²x as sinĀ²x/cosĀ²x
I was trying to hint towards what this guy said
rose scroll
Wait so if I continue my long butthurting method, will I be correct anyway
if you do the steps right, I dont see any reason for that to not work out
frozen wing
okay
can you write tanx as any other form?
frank arrow
I mean in the beginning only you could write tanĀ²x as sinĀ²x/cosĀ²x
i think you are trying to show me what this guy was saying
frank arrow
but i was wondering if i continue with my method, what is my next step
i factored out 1/4
now idk what to do
frozen wing
ok lemme see
midnight igloo
you have wrongly written the numerator here
frozen wing
yes
midnight igloo
1- cos(4x) = 2 sinĀ²(2x)
1+ cos(2x) = 2 cosĀ²(x)
after this open the sin (2x) in numerator it should work
using sin(2x) = 2sinxcosx
it will come out to be sinĀ²x only
@frank arrow where u went
frank arrow
sorry i had to go afk for a bit
frank arrow
1- cos(4x) = 2 sinĀ²(2x)
1+ cos(2x) = 2 cosĀ²(x)
so the 2 and the 2 can cancel, right?
midnight igloo
yes
frank arrow
after this open the sin (2x) in numerator it should work
what does this step mean?
like split the sin^2(2x) into sin(2x)sin(2x) ?
midnight igloo
sinĀ² (2x) = (sin(2x))^2
(2sinxcosx)^Ā²
4sinĀ²xcosĀ²x/4cosĀ²x
Should i write it on paper
midnight igloo
like split the sin^2(2x) into sin(2x)sin(2x) ?
Ya basically same thing
And just apply the formula of sin(2x) then
midnight igloo
and do i do a similar identity for the cos^2(x) on the bottom orrrrrrrr ?
In the bottom just use
1 + cos(2x) = 2cosĀ²(x)
if you want i will write on paper and send
obtuse pebbleBOT
@frank arrow Has your question been resolved?
midnight igloo
Ok i am back
frank arrow
Yay
frank arrow
Thank u
I will read over it in the morning
About 4-5 hours from now
Thanks for ur helppppp
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fresh slate
obtuse pebbleBOT
fresh slate
Take 2^r as 2 x 2^r-1
Cant find the Vn
covert kettle
Cos3t/cos2t
fresh slate
Cos3t/cos2t
Then what?
fresh slate
Write cos3x expansion
Already did that
covert kettle
U get cosx(4cos^2 x - 3)
fresh slate
What to do next?
covert kettle
covert kettle
I can tell you without using complex numbers
fresh slate
Wait have I did something wrong
covert kettle
Wait have I did something wrong
No it's correct
But that will go lengthy
Or sometimes you might get stuck with long calculation
fresh slate
But what do using this
fresh slate
Ok
fresh slate
Yes
covert kettle
2sin^2 x can be written as 1-cos2x
fresh slate
Yes
covert kettle
Then take lcm
fresh slate
Yes
covert kettle
fresh slate
covert kettle
Factorise it like this
fresh slate
Factorise it like this
Ok
fresh slate
2cos2x-1 = cos4x
??
fresh slate
U know this identity right?
Yes but it must be square
fresh slate
I dont know but how
fresh slate
Yes
covert kettle
Ok wait for 5 mins
fresh slate
Are you there?
fresh slate
I think this might not be correct
fresh slate
Man my paper is near and my algebra is almost trash
ancient berry
Hm.. i am unable to think beyond this as well
covert kettle
check this out
fresh slate
Hm.. i am unable to think beyond this as well
I forgot multiplying factor of 2
ancient berry
I forgot multiplying factor of 2
Yh
covert kettle
Did you get it?
fresh slate
check this out
But P(n) is the complete summation
covert kettle
Man my paper is near and my algebra is almost trash
Are you an engineering student?
covert kettle
But P(n) is the complete summation
Yea the terms will get cancelled
fresh slate
Are you an engineering student?
In 12th standard, almost leaving school
covert kettle
In 12th standard, almost leaving school
Oh nice
I am 11th
covert kettle
But P(n) is the complete summation
With this answer trying checking some value of n and beta
and check with the answer
U will get it same
fresh slate
Yea the terms will get cancelled
But there is no cancellation?
ancient berry
check this out
What after step 4
fresh slate
You gave general term
covert kettle
so u want a value?
fresh slate
so u want a value?
It asked for expression for P(n)
ancient berry
so u want a value?
Question asks for a simplified expression of P(n)
fresh slate
Do you think its possible?
covert kettle
Do you think its possible?
no i don't think so
ancient berry
Do you think its possible?
Maybe just we can't see it
fresh slate
Maybe just we can't see it
Maybe....
fresh slate
Do you have a solution?
fresh slate
u get s(2011)=2010
I found the S(n) expression
covert kettle
then u are facing prob in p(n)?
fresh slate
Listen to me ,in the telescoping step there is something very wrong ,can you explain that step in detail
fresh slate
then u are facing prob in p(n)?
Yes
covert kettle
okay wait
fresh slate
Do you have a solution?
I have answer to the problem but no solution
chrome walrus
I have answer to the problem but no solution
is the answer b?
covert kettle
is it D?
fresh slate
A and D both are correct
covert kettle
okay i got the answer
lemme explain it to you
fresh slate
Hello?
covert kettle
Bro
timid silo
I found the S(n) expression
what expression did you get
covert kettle
you know
cos2x/sin3x = cot x - cot3x?
fresh slate
you know
cos2x/sin3x = cot x - cot3x?
Yes
fresh slate
you know
cos2x/sin3x = cot x - cot3x?
This one @timid silo
As I said i have problem in the P(n) portion
timid silo
this looks ai 
fresh slate
Bro are you not listening to me i have problem in P(n) one can you resolve it?
covert kettle
Bro are you not listening to me i have problem in P(n) one can you resolve it?
yeah wait i am sending that also
fresh slate
this looks ai <:thonk:406575732563902485>
Who cares ,if someone explains
timid silo
you cant just divide by sinx can you ?
timid silo
Who cares ,if someone explains
it is not advised to use ai for helping
covert kettle
it is not advised to use ai for helping
who said it's ai bro?
fresh slate
it is not advised to use ai for helping
I didn't knew that
covert kettle
you cant just divide by sinx can you ?
we can for making the identity
fresh slate
Elaborate the steps??
timid silo
if someone needs ai, then theycan directly use that
timid silo
I didn't knew that
nah no deal mate just that ai can be verywrong in mathssometimes
fresh slate
if someone needs ai, then theycan directly use that
Mine one does not works that well and I am very annoyed by its language
timid silo
we can for making the identity
which identity?
covert kettle
cos3x/cos2x = tan2x- tanx
fresh slate
cos3x/cos2x = tan2x- tanx
Proof?
timid silo
also tan2y - tany also seem incorrect
fresh slate
also tan2y - tany also seem incorrect
Yes I think
timid silo
Mine one does not works that well and I am very annoyed by its language
fr they just gaslight you into thinking you have arrived at the answer
covert kettle
no it's write
fresh slate
fr they just gaslight you into thinking you have arrived at the answer
š„
covert kettle
Bro i am fasting
I need to go to prayer
I will be right back
fresh slate
Can I swear?
fresh slate
Bro i am fasting
I need to go to prayer
I will be right back
Okay
timid silo
i dont think you achieve a good expression for S(n) or P(n)
timid silo
however if you calculate first few terms for S(n) they are +1 -1... ( ig or they follow a pattern)
fresh slate
timid silo
,rccw
warm shaleBOT
chrome walrus
@fresh slate could you please explain how cos2x/sin3x is equal to cot x - cot3x
fresh slate
however if you calculate first few terms for S(n) they are +1 -1... ( ig or they...
Whattttttt
fresh slate
<@842304920236457994> could you please explain how cos2x/sin3x is equal to cot x...
Replace cot with cosec
And half it
timid silo
Is this correct?
how did you reach there?
fresh slate
My brain is not braining that well
timid silo
Replace cot with cosec
?
timid silo
,rccw
warm shaleBOT
fresh slate
<@842304920236457994> could you please explain how cos2x/sin3x is equal to cot x...
.
@timid silo ??