knief
#help-43
boreal girderBOT
next latch
Since they're the same number?
native shard
so ln(x) tells you what you need to raise e to to get x
next latch
**knief**
So we would have e^2 = e^1
According to same base, you can cancel the two es, and then you're left with ... 2 = 1??
next latch
so ln(x) tells you what you need to raise e to to get x
I see
native shard
So we would have e^2 = e^1
According to same base, you can cancel the two es, an...
no...
native shard
So we would have e^2 = e^1
According to same base, you can cancel the two es, an...
ln(e^2) = y means e^y = e^2
y = 2
next latch
ok thank you
compact pewterBOT
Available help channel!
eternal pulsar
$\sum_{n=1}^{\infty}\frac{n^2}{n^4+1}$.
compact pewterBOT
$\sum_{n=1}^{\infty}\frac{n^2}{n^4+1}$.
boreal girderBOT
;(
eternal pulsar
How do I do this?
eternal pulsar
Seen that before.
bright pecan
yep
bright pecan
use : x/(1+x²) = Re{1/(x+i)}
.
bright pecan
How would you prove it?
it can be proved by the digamma function
- Euler reflexion formula
eternal pulsar
use : x/(1+x²) = Re{1/(x+i)}
So it becomes $\Im\qty(\sum_{n=1}^{\infty}\frac{1}{1-in^2})$?
boreal girderBOT
;(
eternal pulsar
Wtf...
eternal pulsar
So $\Re\qty(\sum_{n=1}^{\infty}\frac{1}{n^2+i})$
bright pecan
yep
boreal girderBOT
;(
bright pecan
yep
eternal pulsar
Stop tricking me bro 😭
bright pecan
Stop tricking me bro 😭
its just the same but i am fixing to make it easier
sry
you can put t = sqrt(i)
bright pecan
.
eternal pulsar
$\Re\qty(\frac{\pi\coth(\pi\cdot e^{\frac{i\pi}{4}})}{2e^{\frac{i\pi}{4}}}+\frac{1}{2i})$
Fucker
bright pecan
so only what you have to do is to find the Real part of that coth thing and the other things
boreal girderBOT
;(
eternal pulsar
$\coth(x)=i\cot(ix)$?
eternal pulsar
,w is coth(x)=icot(ix)
boreal girderBOT
boreal girderBOT
;(
bright pecan
so i think you can do it
eternal pulsar
K
bright pecan
good luck
btw , take care of the bounds
of the sum
you are summing from n =0 now
your question is n from 1 to infinity
eternal pulsar
That’s so fucked though 😭
eternal pulsar
your question is n from 1 to infinity
I can include n=0 regardless
It’s the same thing
bright pecan
yep
boreal girderBOT
;(
bright pecan
cool
compact pewterBOT
@eternal pulsar Has your question been resolved?
vivid siren
floor (xsinpix)
compact pewterBOT
floor (xsinpix)
vivid siren
how to draw this?
kind viper
$\floor{x\sin(\pi x)}$
boreal girderBOT
Ann
vivid siren
yes maam
kind viper
and you're having to draw this by HAND??
kind viper
what are you actually looking for
native shard
desmos
native shard
why do you want to draw this by hand
vivid siren
time to reveal original question
native shard
its going to look like shit
vivid siren
native shard
you don't need to draw that much
native shard
some of these should be pretty obvious
regal storm
This looks more like $\floor{x^2 \sin(\pi)}$ anyway
boreal girderBOT
Oliver
vivid siren
This looks more like $\floor{x^2 \sin(\pi)}$ anyway
but how you thought automatically?
regal storm
thats just 0 mate
Yeah obviously
regal storm
which would be an easy question if it's a textbook instructing people to draw graphs to identify continuity of functions
native shard
yea i usually write x^2 sin(pi) as x sin(pi) x
kind viper
vivid siren
but i need clear vision
kind viper
the best you can say is that this function is equal to 0 in some nbhd of x=0
native shard
waiting..
kind viper
so only the continuity at 0 thing looks true
vivid siren
the best you can say is that this function is equal to 0 in some nbhd of x=0
but the floor?
kind viper
what about the floor
i mean this part right here
where x sin(pi x) is between 0 and 1 so its floor is 0
kind viper
also im just gonna go and say it, this book's typesetting is complete dogshit
vivid siren
thanks everyone
native shard
$f(x) ,, = ,,[x,,\sin \pi \quad x]$
boreal girderBOT
knief
eternal pulsar
@vivid siren Indian textbook?
native shard
probably
eternal pulsar
also im just gonna go and say it, this book's typesetting is complete dogshit
So yeah, completely expected
compact pewterBOT
kind viper
So yeah, completely expected
i said nothing about where this textbook came from
only that it is just dogshit
vivid siren
yes ma'am
compact pewterBOT
Available help channel!
strange pendant
compact pewterBOT
forest token
pls translate
strange pendant
forest token
for a, pressure at q = p0 + rho g h
forest token
yes
but they are asking by how much it is greater than atmospheric pressure
so q = p0 + rho g h - p0
q= rho g h
strange pendant
q= rho g h
now what?
strange pendant
whats h
strange pendant
,w 3/4 * 2cm
boreal girderBOT
gleaming latch
how much time did you spend on the problem before asking renato?
pine osprey
Im pretty sure you didn't need wa for this
strange pendant
I dont really understand any of this problems tbh
its all so complicated
maybe I need to read up more theory because
gleaming latch
take some more time to think about the problems
step away from this channel for 10 minutes
and then come back after perhaps thinking some more about it, rereading your notes, looking back at the lectures, etc
strange pendant
yoda helped a lot for a)
I think its just plugging the density of the oil and the height being 3/4 of 2cm and gravity being 9.8 m/s^2
forest token
yes correct
strange pendant
about the density of the plastic cube
forest token
that we do by force equilibrium
upthrust = weight of body since it is floating
upthrust = density of liquid x g x volume submerged
strange pendant
Fb = (density of water) x (Volume of cube) x gravity
forest token
weight of body = mg which we write as volume of body x density of cube x g
strange pendant
yep, the buoyancy
forest token
Fb = (density of water) x (Volume of cube) x gravity
VOLUME SUBMERGED
not whole volume
strange pendant
we dont know mass of cube
mass of cube = (density of oil) x (volume of submerged)
forest token
why would mass of cube require density of oil
;/
and why would it be the volume submerged
dude are u listening
strange pendant
and write mass as volume of body into density of body
wdym?
compact pewterBOT
@strange pendant Has your question been resolved?
compact pewterBOT
@strange pendant Has your question been resolved?
compact pewterBOT
@strange pendant Has your question been resolved?
compact pewterBOT
@strange pendant Has your question been resolved?
foggy vapor
@strange pendant What part do you have a problem with?
Largely, the theory is simply that a floating body is in equilibrium, i.e. net force (as well as torque) is 0.
Gravity exerts a downward force on the block. There exists air pressure from the top. Water exerts a buoyant force equal to ρgh. An FBD will help.
strange pendant
can you help me with the FBD
foggy vapor
Water exerts a buoyant force equal to the weight of the water displaced by the block
strange pendant
like I dont have paper rn for drawing a fbd
strange pendant
Water exerts a buoyant force equal to the *weight of the water displaced by the ...
fr
foggy vapor
like I dont have paper rn for drawing a fbd
Me neither ._.
compact pewterBOT
@strange pendant Has your question been resolved?
acoustic solstice
In the solution why did they use sqrt(n-1) for f(x)?
compact pewterBOT
In the solution why did they use sqrt(n-1) for f(x)?
acoustic solstice
.close
compact pewterBOT
carmine garden
In the solution why did they use sqrt(n-1) for f(x)?
Is this a JEE adv question
compact pewterBOT
Available help channel!
rigid thunder
I don't know how to do the question 2
compact pewterBOT
I don't know how to do the question 2
rigid thunder
Can't even find an approach
short ferry
what'd be the other factor of ax^3 + bx + c?
in its general form
would it be linear, quadratic
or what
rigid thunder
Oh if one factor of the cubic is a quadratic then the reminder will be linear
short ferry
not the remainder, but the second factor, yeah
rigid thunder
Yeah I got this
short ferry
now expand it and compare the coefficients
short ferry
correct
short ferry
ye
short ferry
Comparing the quadratic and linear (x^2 and x) terms should now get you the 2 conditions
short ferry
(x²+ax+1)(ax+c)
(x²+ax+1)(ax+c) = ax^3 + bx + c
short ferry
yep, exactly like that
rigid thunder
I need to find that something
rigid thunder
Coe of x=b
coe of x²=0
short ferry
if you compare that as well, youll get the second eq
short ferry
np
forest token
I don't know how to do the question 2
btw for the first one is the answer 2?
rigid thunder
btw for the first one is the answer 2?
Yeah
eager wasp
I don't know how to do the question 2
ever heard of long division method?
rigid thunder
The answers are written below question no 3
rigid thunder
ever heard of long division method?
I think long division isn't gonna be that good here
rigid thunder
oh didnt see mb, but just to ask how did you do it
Coe of x²=0
Coe of x=0
Coe of const =0
eager wasp
I think long division isn't gonna be that good here
so u need an intuitive answer
try remainder theorem
forest token
Coe of x²=0
Coe of x=0
Coe of const =0
ohk yeah nice
short ferry
try remainder theorem
that could work after you find what the linear factor is
rigid thunder
Coe of x=b
coe of x²=0
I think I just tied it but the thing is you will eventually come up with the method that we got here
short ferry
that could work after you find what the linear factor is
but it would get you just one eq anyway
eager wasp
that could work after you find what the linear factor is
no need for that we can define a linear factor
short ferry
oh i see what you mean
rigid thunder
let say ax+d
Yeah
short ferry
i dont see how you could apply the remainder theorem though
short ferry
that ax + b must be 0
eager wasp
i dont see how you could apply the remainder theorem though
ok lemme show u
ax^3+bx+c = ax+d(x^2+bx+c)
=> ax^3+bx+c = ax^3+(ab+d)x^2+(ac+bd)x+cd
rigid thunder
Book's solution
short ferry
ok lemme show u
ax^3+bx+c = ax+d(x^2+bx+c)
=> ax^3+bx+c = ax^3+(ab+d)x^2+(ac+bd...
ax^3+bx+c = (ax+d)(x^2+bx+c)
did you mean this?
rigid thunder
d?
eager wasp
ax^3+bx+c = (ax+d)(x^2+bx+c)
yep
rigid thunder
Oh
rigid thunder
we are assuming a linear factor at the start
Ha
eager wasp
Yeah, thats essentially the method we used
that called is remainder theorem
short ferry
Book's solution
this also works, but you have to go through the long division which I'd be too lazy to do
rigid thunder
this also works, but you have to go through the long division which I'd be too l...
Me too
short ferry
that called is remainder theorem
isnt the remainder theorem something along the lines that f(a) = the remainder after division by x-a
eager wasp
isnt the remainder theorem something along the lines that f(a) = the remainder a...
nope
short ferry
,w remainder theorem
boreal girderBOT
eager wasp
,w remainder theorem
remainder theorem also works as factor theorem too
eager wasp
because remainder is zero]
short ferry
i mean yeah, its kind of the special case
rigid thunder
that called is remainder theorem
short ferry
somewhat fancy to call it remainder theorem though lol
rigid thunder
remainder theorem also works as factor theorem too
Yeah but I think the reminder theorem would take you to the same method
We used the factor theorem here
short ferry
Yeah, it's exactly the same
eager wasp
Yeah but I think the reminder theorem would take you to the same method
remainder theorem is fancy
short ferry
factor theorem is a specific case of remaidner theorem
rigid thunder
(x²+ax+1)(ax+c) = ax^3 + bx + c
Eventually its factor theorem is a special case of reminder theorem where R=0
short ferry
yeah
rigid thunder
We used it without mentioning it
eager wasp
factor theorem is a specific case of remaidner theorem
but u don't have to remember it remainder theorem should be enough
nvm
short ferry
but u don't have to remember it remainder theorem should be enough
i dont remember it, i had to look it up to see which one it was lol
eager wasp
next question
rigid thunder
but u don't have to remember it remainder theorem should be enough
Reminder theorem R is a polynomial
Factor theorem R=0
short ferry
factoring is so obvious that i dont even need a name for it
rigid thunder
factoring is so obvious that i dont even need a name for it
Yeah
eager wasp
factoring is so obvious that i dont even need a name for it
yes
short ferry
Do you know how to do 3 or do you also need help with that?
rigid thunder
Do you know how to do 3 or do you also need help with that?
Yeah I did the 3
forest token
is this cengage?
eager wasp
Yeah I did the 3
which grade
rigid thunder
I have a doubt with complex numbers
rigid thunder
is this cengage?
Yeah
eager wasp
I have a doubt with complex numbers
ask
rigid thunder
which grade
Grade 11
eager wasp
ok
rigid thunder
rigid thunder
rigid thunder
going to 11th or going to 12th?
Going to 12
I don't know how to do this I'm struggling with it for days
rigid thunder
Brain teaser
eager wasp
do u know rotation theorem
eager wasp
ok cool
rigid thunder
The problem is I can't even find a solution on the internet
eager wasp
ur approach is correct complete the answer dude u r just slacking rn
short ferry
cant you divide both sides of the wanted equation by z4 - z1 twice
then use the rotation theorem or whatever is it called
rewrite everything as trig equation
and prove it
and ofc the real proof would then be all the steps in reverse
I'd definitely work backwards here
rigid thunder
Okay trying to work backwards
Leave it 😭 I would rather do other questions than doing this
This is too much hard
Thanks guys
🫂🫂🫂🫂
.close
compact pewterBOT
short ferry
$\left|\frac{z_{2}-z_{1}}{z_{4}-z_{1}}\right|e^{\frac{i\theta}{2}}\cdot\left|\frac{z_{3}-z_{1}}{z_{4}-z_{1}}\right|e^{\frac{i\theta}{2}}=\sec\left(\theta\right)+1$
boreal girderBOT
MathIsAlwaysRight
short ferry
after giving it a go, i simplified the wanted equation to this
it can be simplfied way more by noting that those 2 magnitudes are equal
and those e's combine
compact pewterBOT
✅
short ferry
it can be simplfied way more by noting that those 2 magnitudes are equal
oh whoops, they're not equal, i forgot about which sides are equal
rigid thunder
oh whoops, they're not equal, i forgot about which sides are equal
I was also thinking how you got that
small tangle
Arnab
rigid thunder
Yeah
small tangle
Jee aspirant
rigid thunder
Yeah
small tangle
My competition
rigid thunder
💀💀💀
rigid thunder
26
small tangle
Same
rigid thunder
Yeah
small tangle
All the best
rigid thunder
You too
rigid thunder
I just can't find any other way
short ferry
the equation itself looks weirdly assymetric
rigid thunder
Yeah 🥹
I think I should just leave it , this is too hard and it's that relevant for what I'm preparing for , i should rather do some questions which are not this hard 🥲
Yeah
.close
compact pewterBOT
short ferry
**MathIsAlwaysRight**
Oh i made a mistake, one of the angles is negative resulting in total cancellation of the e^itheta terms
compact pewterBOT
Available help channel!
opal stirrup
3(x+2)-7 = 2x+8
compact pewterBOT
3(x+2)-7 = 2x+8
opal stirrup
3x+6-7 = 2x+8
II+1 both sides
3x=2x+9 II -2x both sides
x=9
what went wrong here
thorny urchin
nothing
thorny urchin
if you want to check,
sub the value back into the original equation
opal stirrup
3 times 9+2-7 = 2 times 9+8is diff
thorny urchin
its different because in the process of subbing in x=9, you removed those () on the left side
thorny urchin
you did that already
opal stirrup
bverify i mean
thorny urchin
sub it into your actual equation, making no unjustified modifications
3 times (9+2)-7 = 2 times 9+8
your () disappeared
compact pewterBOT
compact pewterBOT
Available help channel!
grave acorn
Step
Amount
List purchase price
210.00
– Supplier discount (15%)
–31.50
= Target purchase price
178.50
– Supplier cash discount (2%)
–3.57
= Net purchase price
174.93
- Overhead costs (16%)
+27.99
= Cost price
202.92 - Profit margin (12%)
+24.35
= Net selling price
227.27 - Customer cash discount (3%)
+6.82
= Target selling price
234.09 - Customer discount (10%)
+23.41
= List selling price
257.50
How can i get the minimum profit margin for a list selling price below 250?
compact pewterBOT
Step
Amount
List purchase price
210.00
– Supplier discount (15%)
–31.50
= Targe...
@grave acorn Has your question been resolved?
grave acorn
The minimum profit margin would be 8.73% or 17.71 Currency. I solved it with a program but i still dont know how to solve it without guessing the margin
Problem is that the customer cash discount and customer discount act like a compound iterest on the previous product
<@&286206848099549185>
*I honestly dont know if i asked right or if this question is appropriate for this discord. *
.close
analog sleet
Hi for part iii can someone explain how to construct the perpendicular distance with vectors
compact pewterBOT
Hi for part iii can someone explain how to construct the perpendicular distance ...
forest token
Hi for part iii can someone explain how to construct the perpendicular distance ...
plot the points (7,-1) and (-1,-5) on graph
connect the 2 pts and then draw a line connecting the origin to the pt on the line which looks closest to origin
the construction need not be that precise as we just need the value of t
analog sleet
connect the 2 pts and then draw a line connecting the origin to the pt on the li...
done
forest token
could you send a pic if possible
analog sleet
one sec
analog sleet
could you send a pic if possible
forest token
yeah ok also name the points 7,-1 and -1,-5
analog sleet
oh k
forest token
so that it feels like a question more about coordinate geometry
analog sleet
ok done
forest token
so now that we have this, find the equation of the line joining the points 7,-1 and -1,-5
analog sleet
so now that we have this, find the equation of the line joining the points 7,-1 ...
general form?
forest token
yes general form
analog sleet
4y-3x+17=0
forest token
ok so now use foot of perpendicular formula to find this point
after you find that point use distance formula from 7,-1 to that point
and now that u have the distance,
time = distance/speed
analog sleet
ok so now use foot of perpendicular formula to find this point
Wait how?
forest token
oh you dont know foot of perpendicular?
analog sleet
nope
forest token
if you are talking about perpendicular distance, no it is not
analog sleet
if you are talking about perpendicular distance, no it is not
ok nvm
analog sleet
yep
forest token
ax+by+c = 0 is the line that we have
and we need to fine h,k
(h-p)/a = (k-q)/b = -(ap + bq + c)/a^2 + b^2
@analog sleet can you use this to find p and q
i mean h,k
analog sleet
oh
ok sure
wait i just found the solutions and they did smth different
but i dont get what they did
forest token
wait i just found the solutions and they did smth different
they took dot product
since the angle = 90 degrees, cos theta = 0
analog sleet
but like i dont get where the (-4,-2) came from
forest token
oh so they wrote the point we are trying to find in terms of time
analog sleet
oh so they wrote the point we are trying to find in terms of time
oh
forest token
but like i dont get where the (-4,-2) came from
me neither, but possibly that is the point we are trying to find by foot of perpendicular?
analog sleet
oh yeah could be
forest token
but whatever it is did you understand one of the methods atleast?
analog sleet
but whatever it is did you understand one of the methods atleast?
yeah i think so
forest token
ok good 👍
analog sleet
the thing is i dont think my school taught me foot by perpendicular so idk if im allowed to use it (in an exam)
forest token
oh xd u gave a physics question in a math server thats why i solved it using coordinate geometry
analog sleet
oh xd u gave a physics question in a math server thats why i solved it using coo...
ohh lol thats fair
forest token
wait i just found the solutions and they did smth different
OH WAIT
forest token
XD
analog sleet
lol
analog sleet
rip ok fair enough
forest token
wait i just found the solutions and they did smth different
im not used to this kind of notation sorry
compact pewterBOT
compact pewterBOT
knotty basin
,w 1/2 integral of (1+2cos(x))^2-4
boreal girderBOT
compact pewterBOT
Available help channel!
past coral
Prove that 10! + 1 is not prime.
compact pewterBOT
Prove that 10! + 1 is not prime.
carmine garden
,w factorise 10!+1
boreal girderBOT
carmine garden
There you go
past coral
Without using an AI.
past coral
Without using a calculator.
hushed magnet
wilsons theorem
compact pewterBOT
compact pewterBOT
Available help channel!
woeful fable
compact pewterBOT
woeful fable
Idk why i'm getting some factor when i integrate that depends on f(x) and f(y) when i only want to find value that can be describe as y
The red thing is where the problem start and they ask us to use the property "of homogeneous ODE" but idk what will we different from that
compact pewterBOT
@woeful fable Has your question been resolved?
compact pewterBOT
@woeful fable Has your question been resolved?
stoic dove
The red thing is where the problem start and they ask us to use the property "of...
Im not sure what you mean by property but I would assume y=vx=>y’=v+xdv/dx
Then v +xdv/dx=1/(2v+1/v)
Then I think this should be solvable?
xdv/dx=(v-2v^3-v)/(2v^2+1)
(2v^2+1)dv/2v^3 =-dx/x
Yeah now you can integrate and out back v=y/x
@woeful fable does that make sense?
compact pewterBOT
@woeful fable Has your question been resolved?
undone maple
Why is it wrong? The answer is ln|x/(sqrt(x^2+1))|
compact pewterBOT
Why is it wrong? The answer is ln|x/(sqrt(x^2+1))|
rotund sphinx
Why is it wrong? The answer is ln|x/(sqrt(x^2+1))|
How did you get between these two steps?
$\ln|x|-\ln \left(\sqrt{x^2+1} \right)=\ln \left(\frac{|x|}{\sqrt{x^2+1}} \right)=\ln \left| \frac{x}{\sqrt{x^2+1}} \right|$
boreal girderBOT
Civil Service Pigeon
undone maple
How did you get between these two steps?
Rule of logarithms
Nvm i understood
The 1/2 with the rule becomes an exponent
compact pewterBOT
If you are done with this channel, please mark your problem as solved by typing .close
undone maple
How do i go from theta to x for the sin2x/2
compact pewterBOT
How do i go from theta to x for the sin2x/2
native shard
dx ≠ dtheta
undone maple
👍
native shard
your first line was a mistake
undone maple
How
native shard
dx ≠ dtheta
^
undone maple
Dtheta is 5costheta?
native shard
no
undone maple
So dtheta is dx/5costheta?
native shard
why
you have dx in your integral already
just put 5cos theta dtheta in place of dx
dx = 5cos theta dtheta
why are you solving for dtheta
we want to solve for dx
to replace it with our new variable
compact pewterBOT
undone maple
.reopen
compact pewterBOT
✅
rigid perch
use the double angle identity to express it in terms of sin(theta) and cos(theta)
rigid perch
,w double angle identity
boreal girderBOT
rigid perch
just use theta instead of x
compact pewterBOT
compact pewterBOT
Available help channel!
umbral grove
I need help on b
compact pewterBOT
I need help on b
hearty lake
I need help on b
!status
compact pewterBOT
I need help on b
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
OK, so do you know what complement means?
hearty lake
OK, so with things like this, complement means "everything else".
umbral grove
So you subtract everything other than what it wants?
hearty lake
Like if there are three colors, red, green, and blue, and I ask what the complement of blue is, it's red or green.
Well, you take everything else, get its probability, and subtract it from 1.
So, the first question is what the complement is.
umbral grove
Ok so subtract cracker a and under 20?
wooden lark
@umbral grove give me three numbers:
- number of people under 20
- number of people who chose craker A
- intersection of. the last two sets
hearty lake
What's the complement of that?
umbral grove
Cracker b c and over 20
hearty lake
What does b c mean?
umbral grove
Complement of a
hearty lake
OK, so let's go over all the possibilities.
There are people who:
- choose A and are under 20
- choose B or C and are under 20
- choose A and are 20 or over
- choose B or C and are 20 or over.
umbral grove
So we subtract prob of cracker a and under 20 to get the conpliment of it?
hearty lake
No.
umbral grove
From 1
hearty lake
Do you see how the four categories I gave cover everyone?
umbral grove
Yes
hearty lake
OK, which one are you taking the complement of?
umbral grove
Cracker a?
hearty lake
Or ones.
No, of the four choices I gave.
Oh, wait.
What are you taking the complement of?
Like quote the text.
umbral grove
From the ones you said?
hearty lake
No, quote from the text of the question.
umbral grove
Compliment of under 20 and not a
umbral grove
What is the prob that a participant did not choose cracker a and was over 20 years old
hearty lake
OK.
So, let me bring up my four choices again.
There are people who:
- choose A and are under 20
- choose B or C and are under 20
- choose A and are 20 or over
- choose B or C and are 20 or over.
Which choice or choices are covered under the text of the question?
umbral grove
The third one
hearty lake
OK, check that against the text of the question.
Does the question say that they choose A and are 20 or over?
umbral grove
Its not choose a and was over
hearty lake
OK, so which choice?
hearty lake
OK, so the complement means "everything else", so the three other choices are the complement, since the choices cover all possibilities.
So, these:
- choose A and are under 20
- choose B or C and are under 20
- choose A and are 20 or over
umbral grove
So it means everything other than over 20 and not a?
umbral grove
So its under and a
hearty lake
When you complement something, you subtract it from all the possibilities. Whatever's left is the complement.
No, it's not under and a.
That's only one of the remaining choices.
You need to cover all three.
That's because the complement is everything that's left.
umbral grove
Wait im confused
When you compliment something its everything that is not what it asks?
hearty lake
Right.
You get all the possibilities.
You subtract the ones you're complementing.
All of whatever's left is the complement.
Like, let's say there are six colors possible for a particular brand of shirt:
- Red
- Orange
- Yellow
- Green
- Blue
- Purple
What's the complement of green?
umbral grove
Everything other than green
umbral grove
Nope
hearty lake
OK, so there are two parts to it.
- not (A and B) = not A or not B
- not (A or B) = not A and not B
So, if you're taking the complement of A and B, you get not A or not B.
Let's see how that applies to your question.
There are people who:
- choose A and are under 20
- choose B or C and are under 20
- choose A and are 20 or over
choose B or C and are 20 or over.
umbral grove
So the conpliment is a and under 20?
hearty lake
So, the complement of choose B or C and are 20 or over is choose A or under 20.
Not and.
If you do and, that's the first choice.
But you're leaving out the second and third choice.
Notice how all three choices left fit with choose A or under 20.
umbral grove
So do i find the probability of a and under and subtract from 1?
umbral grove
This is like a whole tongue twister
hearty lake
Let's go over it again.
umbral grove
How is it not and is it because compliment also changes and too?
hearty lake
Yes.
We can see why.
These choices cover everything:
- choose A and are under 20
- choose B or C and are under 20
- choose A and are 20 or over
- choose B or C and are 20 or over.
We're getting the complement of the fourth choice.
umbral grove
Ohhhh you never told me compliment changes and to or / or to and
hearty lake
These choices cover everything:
- choose A and are under 20
- choose B or C and are under 20
- choose A and are 20 or over
choose B or C and are 20 or over.
Now, the complement is everything left over after subtracting what you're taking the complement of.
So, it's the first three choices.
Now if you say the complement of not A and 20 or over is A and under 20, that's only the first choice.
You're leaving out two choices.
If you say that the complement of not A and 20 or over is A or under 20, let's see if that covers what's left.
umbral grove
Wait but is it true compliment changes or to and / and to or?
hearty lake
Yes.
umbral grove
Ok
hearty lake
- choose A and are under 20
This fits both parts of A or under 20.
- choose B or C and are under 20
This fits the under 20 part of A or under 20.
- choose A and are 20 or over
This fits the A part of A or under 20.
So, A or under 20 fits everything else.
And it leaves out the one we want to get rid of.
- choose B or C and are 20 or over
umbral grove
So a or ubder 20 is the compliment?
hearty lake
This doesn't fit the A part. It also doesn't fit the under 20 part.
Yes, that's right.
This last part of my explanation was just an example of why that works in this problem.
It covers everything except the thing we're trying to get rid of.
So, look back at part A.
What did that ask you to find the probability of?
umbral grove
The opposite of our compliment
hearty lake
Well, opposite is wrong.
Opposite is usually only part of a complement.
Like the opposite of cold is hot.
But that leaves out lukewarm, for example.
The complement of cold is hot or lukewarm or whatever other temperatures that fit.
umbral grove
Ok makes sense
hearty lake
But the complement of part B is part A.
umbral grove
Ok and we have the probability for that
hearty lake
Right.
umbral grove
So now we just subtravt that from one
hearty lake
Correct.
umbral grove
This is because it was asking for something and we had the compliment which is everything but that
And if we subtract that conpliment its gets us the rest which is that
hearty lake
Right.
hearty lake
OK, so they want you to use a complement again.
So, what's the complement of what they're asking you to measure?
umbral grove
Under 20
hearty lake
OK, what's the probability of being under 20?
(this is also one case where the complement is the opposite)
umbral grove
1/4
hearty lake
(that happens when there are only two possible mutually exclusive choices)
OK, so what's the answer to part C?
umbral grove
3/4?
hearty lake
Right.
umbral grove
Last one part d
hearty lake
OK, so the participant said they're 15.
Do you know what a universe is in probability or sets?
umbral grove
No
hearty lake
OK, a universe is basically "all the items you're allowed to look at".
So, all 1000 people in this problem.
umbral grove
So the whole? Or whats given?
hearty lake
Right.
Now we're going to restrict the universe a bit.
The person is 15.
So, they're in the under 20 group.
So, our universe for this problem is the under 20 group.
umbral grove
Which is 250 right?
umbral grove
So out of the under 20 kids which is 250 what is the probability he chose a?
hearty lake
Right.
umbral grove
152 out of 250?
hearty lake
Yes, just reduce that to lowest terms.
umbral grove
k
hearty lake
Have you done conditional probability yet?
umbral grove
60.8%?
hearty lake
Like P(A | B) with the | symbol?
umbral grove
Uhhh i have months ago but i forgot everything
boreal girderBOT
Result:
0.608
Yes, looks good.
This problem is P(chose cracker A | under 20).
The probability that they chose cracker A given that they were under 20.
umbral grove
How do you determine what to use or what ot is?
hearty lake
What do you mean in particular?
umbral grove
So like when do you know its conditional prob or compliment or independent ect
hearty lake
For complement, we only used it because they asked.
But you usually use that when the complement is easier to calculate.
Like for part B, the complement was the answer to part A, which you'd already calculated.
So, you would just use A's answer by doing 1 - part A.
umbral grove
I have a super hard time remembering this stuff
Like how do you remeber what does what
hearty lake
Not sure.
Practice problems help you to learn when they apply, but I don't know how to help memory other than repetition.
Conditional probability is when you're asking only about a part of the sample set.
Like with the question about the 15-year-old.
You would only look at the under 20 group and ignore the rest.
Ignoring parts is where conditional probability is used.
P(A | B) means find the probability of A but only pay attention to cases where B is true.
So, it's useful when you have to or want to ignore things.
Independence is used when some probability is the same in some groups.
ruby glade
-eigen victor and eigen value
-Linear transformation and the standard matrix
-linear combination
-relations and their priorities
-equivalent
kernel, rank, nullity
can any one help me in those i have exam after 4 hours and i dont know thing
hearty lake
-eigen victor and eigen value
-Linear transformation and the standard matrix
-l...
!occupied
compact pewterBOT
-eigen victor and eigen value
-Linear transformation and the standard matrix
-l...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
hearty lake
For example, let's say the probability of liking cracker A was the same in all groups.
You could then say that liking cracker A was independent of the groups.
umbral grove
So it doesnt change based on the group?
hearty lake
And that would allow you to use facts about independence to simplify your work or to make your work possible.
Right.
Independence means that something is the same no matter what group you look at.
hearty lake
PLZ bro
That shows you how to get help.
Like for example, flipping a coin is independent of the time of day.
A fair coin, I mean.
umbral grove
And what if its not the same and not independent?
hearty lake
Then you can't use things that require independence.
Like if two events are independent, that allows you to use P(A and B) = P(A) * P(B).
Like in coin tosses.
What's the probability you get a heads then a tails.
Well, P(heads first and tails second) = P(heads first) * P(tails second).
And that's easy because it's just 1/2 * 1/2.
But without independence, you can't use that.
umbral grove
Im confused
hearty lake
About what?
umbral grove
Like ondependence and of you dont have kt
umbral grove
You don't know when you have independence?
Sorry my phone died
Uhhh im just confused about that and dependence
hearty lake
It's OK.
compact pewterBOT
Available help channel!
hearty lake
Independence basically means you have two probabilities and they don't affect each other.
compact pewterBOT
Independence basically means you have two probabilities and they don't affect ea...
hearty lake
Like in your problem above, you can't say that liking A is independent of what group they're in.
What age group they're in changes how likely they are to like A.
umbral grove
So it depends on the age group
hearty lake
But when you toss a coin twice, the two tosses are independent because one doesn't depend on the other.
Same probability in the first toss as in the second.
Right, in that case, it depends on the age group.
But in the coins, the first doesn't depend on the second.
umbral grove
Ahhh ok that makes sense
hearty lake
Independence allows you to say that P(first thing AND second thing) = P(first thing)* P(second thing), which can be pretty easy to calculate.
Like two coin tosses can use that.
But you can't do P(under 20 AND likes A) = P(under 20) * P(likes A).
umbral grove
But you can't do P(under 20 AND likes A) = P(under 20) * P(likes A).
You cant do this because it has nothing to do woth eachother
hearty lake
Well, no.
You can't do it because they DO have something to do with each other.
At least as far as probabilities.
Fair coin tosses don't have anything to do with each other.
umbral grove
Ok that makes sense
hearty lake
One toss doesn't affect the other in any way.
umbral grove
Ok that makes sense
hearty lake
Wikipedia says:
Two events are independent ... if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
umbral grove
Ahhh ok
hearty lake
Which age group you're in definitely affects whether you like A best or not.
Different odds for each age group.
umbral grove
It does depend ok
hearty lake
Yeah.
umbral grove
Alr tysm
hearty lake
No problem.
umbral grove
Hey for a constant function does it mean if you input three you get three? Inpit 4 you get 4?
hearty lake
No, that's an identity function (output is identical to input).
Constant means the answer doesn't change no matter the input.
f(2) = 3, f(3) = 3, f(1000000) = 3.
hearty lake
Right.
umbral grove
Alr tysm
hearty lake
No problem.
odd bolt
Hello, would such an integral be possible?
compact pewterBOT
Hello, would such an integral be possible?
timid dune
Quite trivial ngl
odd bolt
Soo I can assume that it's not solvable riiight?
compact pewterBOT
@odd bolt Has your question been resolved?
compact pewterBOT
compact pewterBOT
Available help channel!
vale perch
Hello
chilly basalt
compact pewterBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
quartz yoke
think
56+45
what do you get?
first, add the ones digit
6+5 which is 11
but we need only the ones
so the tens are carried
the resulting tens are 1+5+4
kind viper
Why do we carry nos. while performing addition?
ten units of one place equal one unit of the place to its left
what is the currency called where you are? i can try to explain it with money
kind viper
yes
quartz yoke
yea
vale perch
It's Indian rupees ₹
quartz yoke
ooh
kind viper
ok excellent
quartz yoke
same
kind viper
so
quartz yoke
yea?
kind viper
imagine for a moment that money only came in denominations of 1 INR, 10 INR, 100 INR, 1000 INR etc
vale perch
Okay
kind viper
a number's decimal representation is like an instruction for how many of each coin/bill you need to use to pay that sum
vale perch
imagine for a moment that money only came in denominations of 1 INR, 10 INR, 100...
Some of them are still used lol
kind viper
for example, 472 means 4 hundreds, 7 tens and 2 singles
vale perch
a number's decimal representation is like an instruction for how many of each co...
decimal representation is not included in the denominations like 1₹,100₹ etc
or do u mean smh else by decimal representation
kind viper
the rightmost digit (or the one immediately before the decimal point if there is one) tells you the number of 1-coins that you need
kind viper
or do u mean smh else by decimal representation
i mean just the normal way we write numbers in base ten
if you want to introduce a decimal point into this analogy, that would be paisa
but we don't need to worry about that at the moment
vale perch
Like 100.5₹ 100 rupees and 5 paisa
kind viper
for example, 472 means 4 hundreds, 7 tens and 2 singles
do you understand this here?
vale perch
Yes i understood that
kind viper
Like 100.5₹ 100 rupees and 5 paisa
50 paisa actually. there are 100 paisa in one rupee
but anyway
kind viper
Yes i understood that
yeah ok so
vale perch
Yes
kind viper
there's also a restriction: you can't have more than 9 bills of the same type
if you have ten of the same type of bill you have to swap them for one of the next higher bill
so ten singles become one 10
ten 10s become one 100
ten 100s become one thousand
vale perch
if you have ten of the same type of bill you have to swap them for one of the ne...
swap with which thing?
kind viper
just explained it
vale perch
lemme grasp it
vale perch
so ten singles become one 10
10 -> 10
10x10 -> 100
And 100s -> 1000
1000s -> 10000
Do u mean this?
kind viper
yes exactly
in English we don't have a commonly used single word for 10000 but in China and Japan they do (it's called "wan"/"man")
in English there's a rare word for it taken from Greek: myriad
kind viper
the next higher place is 100000, and in the west they don't have a word for it either (it's just called "hundred thousand") but in India you call it Lakh
vale perch
So they call 10 wan
vale perch
the next higher place is 100000, and in the west they don't have a word for it e...
ur correct
kind viper
after that it's called million, or ten lakh
vale perch
Yes
vale perch
c sharp
vale perch
Lol
kind viper
finger slip
anyway
when you add two numbers
every carry means replacing ten identical bills by one bill of the next denomination up
carrying from the tens place into the hundreds place means replacing ten 10s with one 100
and so on
vale perch
So we add that extra bill to other 9 bills?
vale perch
Yes
vale perch
Alright
kind viper
no no hold on let me explain
vale perch
mb
kind viper
we have 4 hundreds, 1 ten, 7 singles, then 2 more hundreds, 4 more tens and 9 more singles
vale perch
Got it
kind viper
grouping them by denomination, we have in total:
- 4+2 = 6 hundreds
- 1+4 = 5 tens
- 7+9 = sixteen singles...
vale perch
Yups
kind viper
but we don't have a single digit for sixteen
so we take ten of these sixteen singles and replace them with a ten!
vale perch
single digit like?
kind viper
single digit like?
the digits go up to 9 only
vale perch
16 = 10 + 6
kind viper
yes
kind viper
now my point is
to make ourselves not have too many singles (1 rupee coins)
we take ten such coins
and make them into one 10 INR coin
vale perch
We have singles till 9 only
vale perch
hm
kind viper
wait btw is Rs 10 a coin or a note
vale perch
Note
kind viper
ok
vale perch
And coin both are used
kind viper
ah.
vale perch
Similarly for 20₹
vale perch
Alright
vale perch
so we take ten of these sixteen singles and replace them with a ten!
we don't have a single digit to represent 16 such as 5,8,7etc. We take 10 sixteen and replace with 10
But if we take 16 singles 10 times it would be 160
strange ermine
potent berry
you have nice writing btw
kind viper
thank you