1/sqrroot(2)
#help-13
cerulean bridge
vernal shell
1/sqrroot(2)
Yess 👍🏽
cerulean bridge
i cant really understand why this worked🤔
i take the lower bound for z to get the upper bound for r🤔
vernal shell
i cant really understand why this worked🤔
neither do I for real 😵💫 , you found your own method
ahh I see
cerulean bridge
hahaha but how did you reason ur way to the bounderies??
i cant really understand the 2d thing u talked about
vernal shell
You solved for r considering z = r and r^2 + z^2 = 1
which is the same as finding the value of r of the intersection of both surfaces
in a similar way to when you find the intersection of two lines, you use both equations
cerulean bridge
aha i think i know
if i take the lowest value of z which is r, then r should be maximizied because of the lower z is the higher r is
which is stated: z^2+r^2<1
i get it!!!🥳
and with that upperlimit i get the right answer for the tripleintergral😄
Thanks alot @vernal shell !!
.close
austere iron
cedar kilnBOT
weary fulcrum
<@&286206848099549185>
do you know the angle of the triangle? something
cedar kilnBOT
@austere iron Has your question been resolved?
cedar kilnBOT
austere iron
.reopen
cedar kilnBOT
✅
muted bear
do you know what a median is?
narrow stone
If you dont know where to start you could plot the points on a graph like desmos
cedar kilnBOT
@austere iron Has your question been resolved?
austere iron
do you know what a median is?
Yes
cedar kilnBOT
@austere iron Has your question been resolved?
austere iron
Whatre extreme points
cedar kilnBOT
@austere iron Has your question been resolved?
vernal shell
Whatre extreme points
The median is a segment, so it has extreme points
You said you know what a median is, what is the concept you have for median?
cedar kilnBOT
@austere iron Has your question been resolved?
distant cedar
@austere iron Are you perhaps confusing median in the sense of a line segment with median of a given set of data? If yes, it's the former that your question is referring to here
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
crimson sedge
Do you understand what median is
cedar kilnBOT
@austere iron Has your question been resolved?
broken knoll
yo
broken knoll
need abit help here
ik for one one y should be equate to the f(x)
sorry for onto
but how to approach it
flint plinth
hint: $(x-1)^2 \geq 0$
wraith daggerBOT
Bungo
burnt vapor
but how to approach it
You should find a real number y such that the equation x/(x^2+1) = y has no real solutions
broken knoll
ok
so xsquare + 1 is greater then or equal to 0 but no 0
therefore it has no 0 so it cant be onto
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
minor bear
hey uh
minor bear
how do i do this?
i dont understand the question or the answer
oh @digital cliff what's up man you got time?
limpid plume
Remember the principle - if you need to keep a fraction unchanged while changing the numerator and denominator - you must always multiply or divide the same number on both sides.
So if 3xy^3 has changed to 15xy^7, then something has been multiplied. Find it, multiply it to the existing numerator. Compare that with ky^n.
cedar kilnBOT
@minor bear Has your question been resolved?
heady cypress
cedar kilnBOT
green grove
im trying to find the covariance of 3 random variables each with expected value of 1
green grove
$cov(X,Y)=\mathrm{E}((X-\mu_1)(Y-\mu_2))$
wraith daggerBOT
metnal
green grove
but how do i find the expected value of two random variables multiplied?
E(XY-XE(Y)-E(X)Y+E(X)E(Y))
E(XY) how do i find that
or do i just use this
[
cov(X,Y)=\sum_{x}\sum_{y}((x-\mathrm{E}(X))(y-\mathrm{E}(Y))P(X=x,Y=y)
]
wraith daggerBOT
metnal
turbid bone
E(XY-XE(Y)-E(X)Y+E(X)E(Y))
You need some more information. If you expand out RHS of the covariance definition, you should get $cov(X, Y) = E(XY) - E(X)E(Y)$.
wraith daggerBOT
11de784a
green grove
You need some more information. If you expand out RHS of the covariance definiti...
what information do i need
turbid bone
You have to know one of $cov(X, Y)$ or $E(XY)$ to find the other.
wraith daggerBOT
11de784a
green grove
\begin{tabular}{rllrrl}
X $\backslash$ Y & 0 & 1 & 2 & 3 & P(X=x)\
\hline
0 & 1/10 & 1/10 & 1/10 & 1/10 & 4/10\
1 & 1/10 & 1/10 & 1/10 & 0 & 3/10\
2 & 1/10 & 1/10 & 0 & 0 & 2/10\
3 & 1/10 & 0 & 0 & 0 & 1/10\
P(Y=y) & 4/10 & 3/10 & 2/10 & 1/10 & 1\
\end{tabular}
wraith daggerBOT
metnal
green grove
isnt this table sufficient for use with the following formula though
[
cov(X,Y)=\sum_{x}\sum_{y}((x-\mathrm{E}(X))(y-\mathrm{E}(Y))P(X=x,Y=y)
]
wraith daggerBOT
metnal
turbid bone
Ah, I see.
crimson sedge
I've gotten the answer 5 (+ or - symbol) sqrt 105. However, deltamath say that is wrong. Here are my steps but I don't know where I am wrong -
4x^2 - 10x = 5
firstly, I identified that - 10 could be (x-5)(x-5)
Then, I got -5 * -5 = 25 and mulitplied it by 4 to get the value i needed to add to both sides
Therefore, I got 4x^2 - 10x + 100 = 5 + 100
Then, I got (x-5)^2 = 105
After that, I square rooted it to get x-5 = sqrt(+ or - symbol) sqrt 105 105
Then, I moved the 5 to get the final answer of x = 5(+ or - symbol) sqrt 105
austere sierra
Just use quadratic formula.
crimson sedge
?
livid hound
you forgot about the factor of 4
tropic oxide
Just use quadratic formula.
literally goes against the instructions but ok
crimson sedge
literally goes against the instructions but ok
true
livid hound
Just use quadratic formula.
if you're being asked to use one specific method and you use another, you won't get full marks and potentially get 0
austere sierra
Oops I just read equation. Sorry.
buoyant latch
I've gotten the answer 5 (+ or - symbol) sqrt 105. However, deltamath say that i...
(x-5)² doesn’t even get you 4x²
crimson sedge
(x-5)² doesn’t even get you 4x²
that's not what I meant
buoyant latch
Your idea of completing the square is not complete
crimson sedge
it's a method my teacher taught me
it said it was correct for all the other responses
buoyant latch
Yeah I don’t think you understood the method
buoyant latch
it said it was correct for all the other responses
That’s unlikely
crimson sedge
I did...
crimson sedge
That’s unlikely
No it did
buoyant latch
The first step to completing the square is factoring until the coefficient of x² is 1
livid hound
you were doing most of the calculations based on the leading coefficient being 1,
when it isn't
crimson sedge
you forgot about the factor of 4
So I added the factor of 4 but I got 10(+ or - symbol) sqrt 105 with the whole thing over 2
crimson sedge
you were doing most of the calculations based on the leading coefficient being 1...
wait so what do I change
buoyant latch
The first step to completing the square is factoring until the coefficient of x²...
.
Do this first
livid hound
The first step to completing the square is factoring until the coefficient of x²...
technically unnecessary, its more convenient to many but you don't have to if you know how to account for it
buoyant latch
Lol at that point you could say first step is to put it in vertex form
crimson sedge
wait but if I factor left side do I have to factor right side as well?
buoyant latch
Not very helpful for learning an algorithmic way to complete the square
livid hound
i'd recommend first dividing both sides of the equation by 4
crimson sedge
cuz 4 and 10 have a different gcf than 5
crimson sedge
i'd recommend first dividing both sides of the equation by 4
ok
bro what
I got x = 0 and x = 10/4
crimson sedge
I did this:
4x^2 - 10x = 5 with the entire thing divided by 4
Then I got x^2 -10/4x = 5/4
(x-5/4)(x-5/4) for the -10/4
- 5/4 * -5/4 = 25/16
Then I add 25/16 to 5/4 which is 25/16 + 25/16 which is 50/32 which is again 25/16 if u simplify it
After that I put the equation together as (x-5/4)^2 = 25/16
Then I square rooted it to get x - 5/4 = (+ or - symbol) 5/4
this lead me to get two different possibilities: x - 5/4 = 5/4 and x - 5/4 = - 5/4
In the first case, it is 10/4 when u combine 5/4 and 5/4, in the second case, the 5/4 and - 5/4 cancel out to equal 0
lyric narwhal
your addition is wrong
25/16+25/16 != 50/32
you just said 25/16 + 25/16 = 25/16...
that makes no sense
crimson sedge
oh wait
frick nvm
now I got x = 10 sqrt2 entire thing voer 4 and x = sqrt 2 over 4
lyric narwhal
I did this:
4x^2 - 10x = 5 with the entire thing divided by 4
Then I got x^2 -10...
also
5/4 != 25/16
you said "I add 25/16 to 5/4 which is 25/16 + 25/16"
crimson sedge
I did this:
starting from the place where I did the addition wrong
(x-5/4)^2 = 25/16 + 25/16
(x-5/4)^2 = 50/16
(x-5/4)^2 = 25/8
x - 5/4 = 5/2 sqrt 2
x - 5/4 = +- 5 sqrt 2 entire thing over 4 after u rationalize the denominator
two different possibilities: x-5/4 = 5sqrt/4 and x - 5/4 = 5 sqrt 2 over 4
This leaves me with the values x = 10 sqrt 2 entire thing over 4 and x = sqrt2 over 4
lyric narwhal
did you read what I wrote?
lyric narwhal
factorials?
do you mean fractions?
you have to add 5/4 and 25/16
so when you get a common denominator
5/4 = 20/16
NOT 25/16
since you multiply both numerator and denominator by 4
placid portal
hi how do you convert x and y coordinates to a 360 degree angle, im trying a coding and the function im supposed to use is some arctan thing, but id like to know how to actually do that calculation if its not too complicated
fair geyser
atan2(y,x)
placid portal
yes
fair geyser
that's the entire calculation
placid portal
yeah i wanna know how atan2 works tho
lyric narwhal
yeah i wanna know how atan2 works tho
probably some form of taylor series
fair geyser
fixed
lyric narwhal
ya
placid portal
is this the simplest calculation for getting an angle out of coordinates?
💀
is this the same thing?
or a different thing
fair geyser
same
placid portal
so tan^-1 y÷x does the angle?
fair geyser
yes except you can't tell it if y or x is negative
so it doesn't have 360 degree range, it has to assume
fair geyser
i tried to do what i said and it works if y < x, but not otherwise
where's the mistake
placid portal
uhh
fair geyser
ok there's something caleld interval of convergence apparently
and it's -1 to 1
fair enough
placid portal
im not good enough at trig to get atan2
im a highschool dropout
well i did the calculation wrong tho in my coding attempt
idk if u can read the code or if u want to
fair geyser
yeah let me see
placid portal
transform.rotation = Quaternion.Euler(0, 0, Mathf.Atan2(characterPosition.x - Input.mousePosition.x, characterPosition.y - Input.mousePosition.y) * Mathf.Rad2Deg);
i prolly just missed something
fair geyser
it should be mouse − player
fair geyser
you have x then y
this makes it start at 12 o clock and go clockwise
and the range is −180 to 180
many things to check what exactly doesn't work?
and it's mildly weird that you convert to degrees at all
fair geyser
it opens fine
fair geyser
are you sure you want degrees?
placid portal
i tried copying code from a solution i found online
fair geyser
that's the sussiest part
placid portal
and that had the degrees thing
and unity does use degrees for rotating
im pretty sure
yes it does
fair geyser
very mysterious
placid portal
you have x then y
i fixed this now btw
placid portal
very mysterious
yeah
maybe i need to ask in for unity help this may not be a calculation mistake
oh yeah
mouse position prolly has a different frame of reference than the object coordinates
is why
i need to shift that
fair geyser
that may be right
placid portal
it uses the very bottom left as zero and not the object position
i want it to use the object position as zero
hmmmmmm
oblique helm
hey , i have been wondering if the Constant of integrating have units ?
oblique helm
integral of dx = x + c
if it has no units (since it is a constant)
integral of dx/sqrt(a^ 2- x^2 ) = integral Wdt
where W is constant
so integrating
we get Sin inverse x/a = Wt + c
fair geyser
it's the same unit as the rest of the expression
oblique helm
it's the same unit as the rest of the expression
here turns out that the c must be in radians ?
burnt leaf
hey , i have been wondering if the Constant of integrating have units ?
I think it's related to FTC
oblique helm
just don't think about it
what
burnt leaf
Sometimes you'll have things like e^(x+c) but instead of +c you can write Ae^x
oblique helm
I think it's related to FTC
sorry i don't know what that is , i am still learning basic calculus only
burnt leaf
sorry i don't know what that is , i am still learning basic calculus only
Fundamental theorem of calculus
For instance if you ∫velocity dt
You would get ∆position
Which means your + c would be x_0 aka starting position
The purpose of your integral has its reasons
oblique helm
Oh! got it also i have another doubt
integral of dx/sqrt(a^ 2- x^2 ) = integral Wdt
where W is constant
so integrating
we get Sin inverse x/a = Wt + c , From Which side does this c come from , the integral of dt or dx ?
i am still learning so i dont know if that's stupid or not
burnt leaf
It's not a stupid question
Imagine dx and dt are minute changes
The integral is basically adding an infinite amount of rectangles underneath a graph with a width of dx
Obviously the smaller dx, the more accurate
You only need to pick one side of the equation for + c which is good but is there a context?
for arcsin(x/a) + c = ∫ W dt ?
oblique helm
You only need to pick one side of the equation for + c which is good but is ther...
yes , this is a bit related to physics
SHM
the equation is x = a sin (Wt + phi) , location of particle at any time t
where phi is a constant
burnt leaf
phi is a phase shift
burnt leaf
is this a pendulum?
oblique helm
general SHM
burnt leaf
So, both
The starting position shouldn't make a difference with the period so it doesn't have a big effect besides context
At least I believe so
oblique helm
integral of dx/sqrt(a^ 2- x^2 ) = integral Wdt THIS is the original equation
when integrating so integrating
we get Sin inverse x/a = Wt + phi(phase shift)
but why can't we take this constant to left side
burnt leaf
Don't you want an expression for x?
oblique helm
like Sin inverse x/a + phi = wt
burnt leaf
integral of dx/sqrt(a^ 2- x^2 ) = integral Wdt THIS is the original equation
∫ dx/√(a^2 - x^2) = ∫ W dt
Do you know the difference between definite and indefinite integrals?
burnt leaf
Good
I don't recall proving SHM with that integral though
But since the context is dependent on a function x(t), it's usually a sign to apply +c to the other side
oblique helm
so there is no reason for it 
burnt leaf
I mean if w is a constant...
Well it's fine
Did your teacher suggest it?
Or was it just indulging in curiosity?
oblique helm
i dont know tbh
maybe right now
this question came into my mind
@burnt leaf Anyway i will just accept that as a fact
Thank you for your help though !!
.close
turbid mauve
Hi friends, I am looking for some extra guidance on this problem. I know how to represent this as an definite integral, but no clue how to make the jump to a definite integral
clear berry
Hi friends, I am looking for some extra guidance on this problem. I know how to...
I don't understand your question
turbid mauve
like the question provided by the professor, or the question that Im asking (how to take the extra step to represent this as the integral between 0 and 1)
clear berry
as in what you're asking
turbid mauve
do I just plug in 1 for one series and subtract that by the series with 0 plugged into it?
clear berry
You'd need to exchange the summation and integration right?
turbid mauve
wouldn't the series with 0 plugged in just be all 0s? and we would get the series with x=1 as the whole thing?
gritty viper
that step seems to have been done, yes
yes for the 0s part
not exactly sure what the whole thing means
ah
yes, that's correct
turbid mauve
can i try and do the step and send what i mean? just to make sure im going about it the right way - the professor didn't give us any examples of definite integrals and didn't link any in the notes either so this is all a new process :)
gritty viper
Sure
turbid mauve
Like this?
oops i didn't mean to include the integral symbol in the line with the subtraction
cedar kilnBOT
@turbid mauve Has your question been resolved?
turbid mauve
.close
long mauve
help b and c
cedar kilnBOT
help b and c
long mauve
how to b)
c) what is angle between VAB and VAC
untold thorn
I would start by finding the triangle of A, V, and the midpoint of BC
long mauve
I would start by finding the triangle of A, V, and the midpoint of BC
can you show me?😅I don't get it
like this?
untold thorn
yes, but also connect the midpoint of BC to V
long mauve
yes, but also connect the midpoint of BC to V
i see how about (c)
long mauve
i see how about (c)
for c) how to know where is the angle
nvm I found the angle
tytyty ty
.close
north cradle
Anyway to undo something like $2^x * 3^y * 5^z$ to get any of the exponents?
wraith daggerBOT
λemon
wraith daggerBOT
MathIsAlwaysRight
dusk finch
then try to expand the left side
north cradle
$$C = 1563485784343740843750000000000$$
$$\ln(2^x * 3^y * 5^z)= \ln(C)$$
$$x * y * z = \ln(C)$$
like that?
wraith daggerBOT
λemon
burnt vapor
$$C = 1563485784343740843750000000000$$
$$\ln(2^x * 3^y * 5^z)= \ln(C)$$
$$x * y...
That is wrong, $\log (2^x\cdot 3^y \cdot 5^z) = x\log 2 + y\log 3 + z\log 5$
wraith daggerBOT
d឵
north cradle
logs hurt me
I am guessing there's no way to find all of the unknowns because of algebra rules and stuff?
burnt vapor
Anyway to undo something like $2^x * 3^y * 5^z$ to get any of the exponents?
What you mean is that you know C = 15634... (the number before) and want to find the exponents, right?
north cradle
yes
burnt vapor
Then you should use a computer or a calculator
Divide the number by 2 as many times as you can before getting a non-integer number, and count how many times you did it
Then do the same with 3 and 5
Actually with 5 you can use logarithms
burnt vapor
$$C = 1563485784343740843750000000000$$
$$\ln(2^x * 3^y * 5^z)= \ln(C)$$
$$x * y...
Also looking carefully at C it is obvious that x = 10 and z >= 11
north cradle
Also looking carefully at C it is obvious that x = 10 and z >= 11
2^10 * 3^35 * 5^15
yeah I used this
cedar kilnBOT
@north cradle Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
native jolt
2.1 this is my answer is it wrong ?
cedar kilnBOT
2.1 this is my answer is it wrong ?
native jolt
I think it is wrong 😂
turbid bone
The question asked you to integrate $\frac{e^x}{(e^x + 1)\sqrt{e^x - 1}}$, why are you integrating $e^x + 1$?
wraith daggerBOT
11de784a
native jolt
Duuuh cuz am dumb asf
turbid bone
So, do you want help integrating $e^x + 1$?
wraith daggerBOT
11de784a
native jolt
No i do not i want to integrate ex/(exp(x)+1)sqrt…. By substituting the variable to t=sqrt(e^x+1 )
It’s easier if I substitute it to exp(x)+1 but that’s not what he asked
hardy island
Try finding dt using $t^2=e^x-1$
wraith daggerBOT
Meep
hardy island
also labeling what each expression means would be helpful
cedar kilnBOT
@native jolt Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
jolly kernel
I need help for this question: A box contains 10 pins
3 are blue and 7 are green.
Two pins are randomly taken out of the box without replacements.
Workout the probability that both pins are the same colour.
obsidian coral
Didn't you say that you solved this?
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
jolly kernel
ok i will explain
The probability of selecting a blue pin on the first draw is 3/10. If a blue pin is selected on the first draw, then there are 2 blue pins left out of 9 total pins on the second draw. Therefore, the probability of selecting two blue pins in a row is:
P(Blue, Blue) = (3/10) * (2/9) = 1/15
Similarly, the probability of selecting a green pin on the first draw is 7/10. If a green pin is selected on the first draw, then there are 6 green pins left out of 9 total pins on the second draw. Therefore, the probability of selecting two green pins in a row is:
P(Green, Green) = (7/10) * (6/9) = 14/45
The probability of selecting two pins of the same colour is the sum of the probability of selecting two blue pins and the probability of selecting two green pins:
P(Same colour) = P(Blue, Blue) + P(Green, Green)
= 1/15 + 14/45
= 3/45 + 14/45
= 17/45
Therefore, the probability that both pins are the same colour is 17/45.
glad kestrel
seems awfully gpt-y
jolly kernel
yep
dire geode
ok i will explain
soooo you don't know how to do the problem then?
jolly kernel
kinda
cosmic steppe
Chat GPT's more politically incorrect than political subreddits
jolly kernel
fairs
dire geode
write the solution as you understand in your own words
there's no point in explaining a bot response to you
jolly kernel
ye mb lol
dire geode
open a new channel when you do
jolly kernel
?
gritty viper
also the bot is wrong
jolly kernel
but can someone explain to me how thebot is wrong
dire geode
moni got baited into reading chatgpt response
gritty viper
though it gets the ideas involved right
jolly kernel
it looks correct to me
dire geode
there's no point in explaining a bot response to you
.
do your own work and just don't use chatgpt altogether
jolly kernel
but it looks correct no?
gritty viper
there's a mistake
dire geode
do your own work and just don't use chatgpt altogether
.
jolly kernel
can you tell me where
dire geode
mate i know calm down
you're just wasting helpers' time
jolly kernel
ive tried for half an hour i dont know that is why i opened the channel 🤦
excuse me if i came across rude there
gritty viper
Did you try submitting the chatGPT answer and it didn't work
gritty viper
is there a part of the solution that you don't understand the reasoning behind
gritty viper
try doing the solution yourself from memory without looking at the bot output
remember how its done only, rederive everything else
dont memorize numbers
jolly kernel
rederive sorry what does that mean?
gritty viper
build up again from scratch
jolly kernel
sounds good thx
gritty viper
np
gritty viper
you're welcome
cedar kilnBOT
@jolly kernel Has your question been resolved?
indigo marsh
For part b would it matter if I solve using an equality sign or equals sign?
indigo marsh
I feel like cuz they give the diagram u can get the answer either way
Mainly for working out marks
crimson sedge
it is an inequality question
but here, you could use an equality sign first, and be careful about the inequality directions later on
(though its probably the same amount of effort either way)
cedar kilnBOT
@indigo marsh Has your question been resolved?
indigo marsh
it is an inequality question
my thoughts hence why i started with that
fair enough
thanks
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
sick turtle
hello
sick turtle
my question is I'm trying to figure out a shipping pricing. I'm a bit lost with everything. I've set my products for t shirt at .5lb and hoodies at .6lb now I want my pricing starting at $7 and each product that a customer adds has an additional $2.50 per item
from what range should i set the lb condition for it to work as $2.50 per item
@cold briar
cerulean valley
i don't think i understand your question?
cedar kilnBOT
@sick turtle Has your question been resolved?
barren gust
How do you find the radius for this?
My working out so far:
(x^2 - 8x + 16) + (y^2 + 14y + 49) = 35 - 16 - 49
= (x-4)^2 + (y+7)^2 = -30
barren gust
the tb says the radius is 10
gilded elm
you made a huge mistake
if you add 16 and 49
to the left side
you should be adding it to the right side
try again
instead you seem to have subtracted it
barren gust
.close
gray blade
cedar kilnBOT
gray blade
I'm just like confused on how to approach this
like i can guess and check the answer
but
that seems wrong
modern compass
if they're similar, all the sides are proportional
gray blade
right
modern compass
so if the dimensions of A are a,b,c
and the dimensions of B are x,y,z
then x = ma, y = mb, z = mc
gray blade
ohhhhh
so B = m^3 abc
and then
we can really just divide 96/12
and cbrt?
and that's m
modern compass
yep
gray blade
so 2
modern compass
now, you know the proportion. So given the side of A, you can find the side of B
rose flax
cedar kilnBOT
rose flax
I know there are 3 horizontal 3 vertical and 2 diagonal straight lines
And I thought you would do 1/9 x 1/8 x 1/7
Multiply by 8 because of the 8 possibilities but apparently that is not right
What do I do instead?
modern compass
the probability you gave assumes order you fill the dots matters. It does not
rose flax
How so?
modern compass
the order you choose the dots in the top row doesn't matter, if you end up choosing all the dots in the top row it'll be filled. No matter which order you choose them in
that goes for any 3 dots you choose too
rose flax
Ah okay so what do I do instead
modern compass
there's 8 straight lines.
divide by how many ways there are to choose 3 dots from 9
rose flax
I’m still a bit confused
modern compass
do you know combinations and permutations?
modern compass
so you've never seen $_nC_k = \frac{n!}{k!(n-k)!}$?
wraith daggerBOT
Zybikron
modern compass
Can you tell me how many ways you can line up 3 things?
rose flax
8 ways
modern compass
not the dots, just if we have 3 objects, how many ways can I line them up?
rose flax
6
modern compass
good,
So there's 6 ways to choose any 3 dots that end up being the same grid pattern.
So multiply the answer you got by 6
rose flax
Ahh okay thank you I see!But why can’t you multiply by 8
modern compass
your answer before had 8 multiplied already
inland ocean
cedar kilnBOT
inland ocean
How do i determine if they odd?
cedar kilnBOT
@inland ocean Has your question been resolved?
limpid schooner
cedar kilnBOT
limpid schooner
So is the limit should be like -2 right
livid hound
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
hoary spoke
cedar kilnBOT
livid hound
distributive property
hoary spoke
m^3-7m-6
oh hm....
i didn't get it
what does distributive property has to do with it
livid hound
you said you wanted to expand
hoary spoke
and what does that say?
eager panther
Smyle are you ismyle
livid hound
try first looking that up.
hoary spoke
Smyle are you ismyle
s
hoary spoke
ya mauktik
hoary spoke
try first looking that up.
hm...
eager panther
ya mauktik
Yaya
hoary spoke
try first looking that up.
okay i did found a bit
so it has to do with the first and last term of the polynomial?
so can u plz help me with it?
like,
if there is a polynomial with coefficients ai and degrees i
such that I ranges from 0 to n
livid hound
rational root theorem can help you identify candidates for rational roots.
livid hound
its a systematic method of determining nice roots
hoary spoke
okay.....
livid hound
and then you can apply factor theorem / long division
to factorise
hoary spoke
hm...
hoary spoke
m^3-7m-6
so if I have this...
I have to consider coefficient of m^3 and m^0 right?
so what I learnt so far is....
hoary spoke
m^3-7m-6
every single root of this....
should be in the form p/q
where q is factor of a0
livid hound
not every single root
hoary spoke
and p is factor of an
livid hound
if the polynomial has rational roots, they'll be available in that list
hoary spoke
what I meant is...
if x is a root of the given polynomial
then it will be in the form p/q
livid hound
identify the candidates and test which ones are actual roots
hoary spoke
is that right?
livid hound
if x is a rational root
livid hound
p and q don't need to be relatively prime
livid hound
depends on how you define them
livid hound
it just increases efficiency if you consider that
livid hound
if you consider all cases, you'll get duplicates
livid hound
e.g. for
2x^3-x^2 - 13x - 6
hoary spoke
if you consider all cases, you'll get duplicates
what exactly u mean by duplicates?
hoary spoke
p and q don't need to be relatively prime
so this is true...
but why is wiki saying like that?
livid hound
considering the factors of 6 : 1,2,3,6
and factors of 2: 1,2
you'll have +-6/2 as a candidate (where 6 and 2 aren't relatively prime)
but that's the same as +-3/1
livid hound
no
livid hound
yes
livid hound
you seemed to have skipped a lot of steps
livid hound
so roots are
-2
-1/2
and 3
they are correct, but just by stating those, not sure if you did the valid work to reach those,
anyway try applying whatever you did you what you had
livid hound
-2 = -2/1
hoary spoke
hm...
livid hound
and 3 = 3/1
hoary spoke
and -1/2?
hm....
oh
so you can pick any random p and q?
from those factors?
and keep checking
livid hound
usually you'd start small with +-1
hoary spoke
this means there are 4×2×2 possibilities?
16?
like I took all their permutations
and also considered the negative sign so multiplied by 2
livid hound
well after identifying one root, you can do some division making finding the rest easier
livid hound
for which, your question or the one i gave
livid hound
well this would be a good time to actually ask how you got
so roots are
-2
-1/2
and 3
please don't say you chucked it into a calculator
livid hound
knowing that 3 is a root, you can apply factor theorem
hoary spoke
hm...
livid hound
do you know what factor theorem states
hoary spoke
hm....
i am not good in names
but..
i know that is a is a root of f(x)
then f(x)/x-a is also equal to zero
livid hound
no
hoary spoke
then f(x)/x-a is also equal to zero
this will also share the same roots as our f(x)
livid hound
no
livid hound
f(x)/(x-a) doesn't have a as a root
if $\alpha$ is a root of a polynomial $f(x), (x-\alpha)$ is a factor of $f(x)$
wraith daggerBOT
ℝamonov
hoary spoke
will also have the same roots as f(x) right?
livid hound
no
hoary spoke
it may or may not have a now
livid hound
it'll give you the other factor
hoary spoke
like...
livid hound
but its not the same
hoary spoke
if
livid hound
wording is important
livid hound
(x-a)(x-b)(x-c)=0
doesn't have the exact same roots as
(x-b)(x-c)=0
hoary spoke
this will also share the same roots as our f(x)
I said "share"
livid hound
you said have
livid hound
to which i responded
wording is important
livid hound
missing () around the x-a
livid hound
well do the long division
hoary spoke
hm...
livid hound
3 is a root of 2x^3-x^2 - 13x - 6
what will be a factor
(according to factor theorem)
hoary spoke
(x-3)
livid hound
yes
hoary spoke
so I have to do long division
livid hound
or synthetic division if you prefer
hoary spoke
or synthetic division if you prefer
this one seems smaller
livid hound
do whatever valid method you're most comfortable with
hoary spoke
oh
thank you very much
and you are very serious when it comes to wordings tho😅
i really appreciate it
hoary spoke
missing () around the x-a
i would have considered it when I was talking with a noob. but not with a pro
.close
cedar kilnBOT
livid hound
bad wording comes off as misunderstanding
cedar kilnBOT
Available help channel!
restive plover
How many positive integers not exceeding 1000 are divisible by 7 or 11, but not
by 13?
restive plover
I found out the answer to the first part of the question, and that is 220
I do not know about the second part, can someone help me with it?
it is like A union B and minus C if A is the number of integers divisible by 7 and B is the number of integres divisible by 11
dusk finch
Hint: all integers divisible by 7 and 13 are divisible by 7*13
There is actually iff relation, N is divisible by 7 and 13 if and only if N is divisible by 7*13
restive plover
Hint: all integers divisible by 7 and 13 are divisible by 7*13
in the same way I can say all integers divisible by 11 and 13 are divisibly by 11*13
right
crimson sedge
yep
restive plover
thanku for the hints
I will try noe
so I should first find the number of integers that are divisible by 7 or 13, and then take the compliment of it?
do the same for 11 or 13 , and then find the intersection of the above two?
it is quite confusing
@dusk finch
dusk finch
You are trying to find red region
and you found out that red+blue = 220
To find that first subtract this
then this
and then add this
In general
crimson sedge
goddamn how did you do all that
dusk finch
goddamn how did you do all that
Microsoft paint
crimson sedge
impressive
dusk finch
In general
@restive plover using this can you finish it?
You just need to find divisible by 7 and 13, by 11 and 13, by 11 7 and 13
using the product thing 7*13, 11*13, 11*7*13
dusk finch
In general
those are called venn diagrams, they are helpful when you are making intersections, unions etc
restive plover
Here does the 13 in the venn diagram represent that it is the set of numbers divisible by 13 or not divisible by 13
@dusk finch
dusk finch
Here does the 13 in the venn diagram represent that it is the set of numbers div...
divisible
You are trying to find this which is set of all numbers divisible by 7, 11 but not by 13
cedar kilnBOT
@restive plover Has your question been resolved?
wind glade
there is a useful set formula useful for a problem like this
$|A\cup B\cup C| = |A| + |B| + |C| - (|A\cap B| + |A\cap C| + |B\cap C|) + |A\cap B\cap C|$
wraith daggerBOT
please request a new nickname
echo jasper
I've solved for col A, nul A, and row A for the matrix, and have found all three to be existent, but I'm not sure what the question means by "Which of the following vector spaces ColA, NulA, RowA is H, if any?"
echo jasper
I know the matrix has a col/nul/row but not sure how H could be a col A, nul A or row A.
I know that the row A basis is practically the same as the given matrix, if that's what it's asking?
crystal raptor
What's your definition of nullA
echo jasper
The null space of the matrix A
crystal raptor
What is the null space
echo jasper
The only way I know how to explain it is that it has all the solutions for Ax=0
crystal raptor
Which is exactly H in the question
echo jasper
It would only be Nul A right? Could ColA and RowA also be the same in any situation? (not necessarily the matrix in the picture)
crystal raptor
If the matrix was square, colA and rowA could be the same
But here colA is a subspace of R³ and rowA is a subspace of R⁵
crisp flint
cedar kilnBOT
crisp flint
Wait
Let me re-render that problem
Im stuck probably
because newton's methd doesnt work
f(x) = ax² + 20x + c - 0
its what they told
Isnt it x_0 = \frac{\f({x)}}{\f'{(x)}}
Is it wrong way
spice pier
What are we trying to do here exactly?
crisp flint
Ordered pairs of natural numbers a, c
How many can be for a ,c pairs
And roots are integer
Isnt newtons method for finding roots
south tundra
Isnt newtons method for finding roots
It is totally unnecessary here
Just use the quadratic formula
spice pier
And roots are integer
If the roots are integers then discriminant of this quadratic must be a perfect square.
I am not sure about this bit but a=1 when roots are integers.
south tundra
And -b + sqrt(discriminant) must be divisible by 2a *
crisp flint
Not newtons method can find?
hidden osprey
hmmm
south tundra
Newton's method is for approximating 
hidden osprey
yes
newtons method isnt useful here because it just approximates the roots of the equation
hidden osprey
we need to use our knowledge of quadratics to solve this question
crisp flint
Not just equal as root?
hidden osprey
죄송하지만, 이해가 안 돼요
crisp flint
그러면 이차방정식의 근을 구할때 newton 의 방법의 사용할수 있나요?
hidden osprey
if i am not mistaken
the question doesnt want us to solve for x
we just need to find ordered pairs (a,c) so that x is an integer
hidden osprey
do you know what the solution to a quadratic equation is?
crisp flint
No
crisp flint
it cant be ax + bx form because it can only be ax - bx
hidden osprey
you can replace b in this formula with -b then
for example, b is -20
so you can replace b with -20
then -b = -(-20)
=20
-b=20
crisp flint
ax + (-bx) ≠ ax - bx
hidden osprey
ax+ (-bx) = ax-bx
south tundra
ax + (-bx) = ax - bx
crisp flint
How
hidden osprey
ax + (-bx) ≠ ax - bx
1+ (-1) = 1-1
hidden osprey
1+ (-1) = 1-1
맞나요?
hidden osprey
ok
hidden osprey
ax+ (-bx) = ax-bx
then it is the same for this
crisp flint
I cant understand how
hidden osprey
hmm
when you add -x to a number, you are subtracting x from that number
1 + (-x) =1-x
crisp flint
I dont see how
crisp flint
$1 + (-2 )\neq 1 - 2$
wraith daggerBOT
아리스킨충∪
crisp flint
I tried it myself
hidden osprey
if you believe that 1+(-2) ≠ 1-2
what do you think 1+(-2) is equal to?
crisp flint
I did it myself then it was 1
crisp flint
$-2 + 1 = -1$
wraith daggerBOT
아리스킨충∪
hidden osprey
ok
The commutative property of addition states that a+b=b+a
do you agree with this?
a+b=b+a
For ALL numbers a,b
crisp flint
How
hidden osprey
you can't say how
this is the commutative property of addition
this is an axiom
a+b=b+a is always true
crisp flint
then its like 3 - 1 = 1 - 3
hidden osprey
then its like 3 - 1 = 1 - 3
no
this is different as it is subtraction
i am talking about addition
a+b=b+a
this is always true
crisp flint
The commutative law applies only to multiplication
worn lichen
pfftt this problem is easy
hidden osprey
pfftt this problem is easy
yes but he is struggling with one concept of math so let's try to help him
hidden osprey
The commutative law applies only to multiplication
this is not true,
it applies for addition as well
worn lichen
whats the concept
hidden osprey
whats the concept
he is unable to understand why a+(-b) = a-b
i am trying to explain that to him
worn lichen
ok i will help both of u guys
hidden osprey
the more the merrier
crisp flint
The commutative law doesnt applies to subtraction but plus is changed to minis aswell
So its same as subtraction
worn lichen
When you add a negative number to another number, it is the same as subtracting the absolute value of that negative number from the original number. So, adding -b to a is the same as subtracting b from a, which gives you a-b. Therefore, a+(-b) is equal to a-b
dusk finch
a + (-b) = (-b) + a (by the commutative addition)
hidden osprey
a + (-b) = (-b) + a (by the commutative addition)
yes
worn lichen
who's the one having trouble here?
hidden osprey
who's the one having trouble here?
@crisp flint
worn lichen
he ain't even talking
hidden osprey
he is
worn lichen
bruh pacepalm
hidden osprey
because minus changed to plus
when?
dusk finch
When you add a negative number to another number, it is the same as subtracting ...
This doesnt even seem correct
crisp flint
But commutative law doesnt work on subtraction
hidden osprey
a+b=b+a
this is true for all numbers, even negative numbers @crisp flint
dusky plume
Think of it as a number line
$-3, -2, -1, 0, 1, 2, 3$
wraith daggerBOT
$NEO
worn lichen
@dusk finch how do u know if its wrong?
hidden osprey
But commutative law doesnt work on subtraction
a-b=b-a is not always true
but a+(-b) = (-b) + a is always true
worn lichen
@dusk finch explain why im wrong then
dusk finch
<@951190447185874994> how do u know if its wrong?
||It doesnt prove the general a+(-b) Instead it focuses on specific case where -b is negative||
||To me it's also less intuitive than original statement||
crisp flint
$3 + (-3) \neq (-3) + 3 because$
$3+ (-3) = 0$
$(-3) + 3 = 6$
wraith daggerBOT
아리스킨충∪
dusky plume
Think of it as number line easy
worn lichen
@dusk finch adding a negative number to a positive number is the same thing as subtracting the absolute value of that negative number from the positive number. So, for any numbers a and b, a+(-b) is the same as a-b, where -b can be any negative number.
dusk finch
but -b doesnt nesecarilly have to be negative
dusky plume
<@951190447185874994> adding a negative number to a positive number is the same ...
-4 + 8
Lol
crisp flint
Its just same as 4 ± 4
worn lichen
@dusk finch I apologize for the mistake. In general, adding any number with its opposite (or negative counterpart) will result in zero. So, for any numbers a and b, a+(-b) is the same as a-b or b-a, regardless of whether b is positive or negative.
hidden osprey
(-3)+3 =0
hidden osprey
<@951190447185874994> I apologize for the mistake. In general, adding any number...
only when a and b are equal
dusk finch
<@951190447185874994> I apologize for the mistake. In general, adding any number...
You now sound like chatGPT ngl
hidden osprey
@crisp flint 들어세요
a+b=b+a
this is true for all numbers a and b
this is a theorem
meaning it is never wrong
it is always true that a+b=b+a
crisp flint
음수여도 여전히 3±3
hidden osprey
음수여도 여전히 3±3
아니요
worn lichen
are you korean? bro i cant understand you
crisp flint
yes
dusky plume
Same i cant understand
worn lichen
what were you saying
dusk finch
A+B=B+A
Having A and B means the same as having B and A
Having apple and banana is same as having banana and aaple
Do you already understand that A+B=B+A?
crisp flint
-3 + 3 = 3 ± 3
dusk finch
-3 + 3 = 3 ± 3
Why do you think this should be right?
worn lichen
bruh even my 8th grade self would solve that problem
dusky plume
Relax we all were like that
dusk finch
bruh even my 8th grade self would solve that problem
Go solve riemann hypothesis then
I feel like that guy is chatGPT
hidden osprey
Go solve riemann hypothesis then
I feel like that guy is chatGPT
ignore him, he is likely a troll