The function range is from 1 to 4
#help-13
soft owl
$\int_a^b \pi ( f(x)² - g(x)² )dx$
wraith daggerBOT
Mehdi_Moulati
soft owl
Is it correct
yeah
limpid tree
Okay thanks
soft owl
anytime bro
wraith daggerBOT
soft owl
if b between a and c where $c > a$ then :
$$\int_a^c f(x) dx = \int_a^b f(x) dx + \int_b^c f(x) dx$$
wraith daggerBOT
Mehdi_Moulati
soft owl
yeah
soft owl
And from 2 to 6 we use second
yeah
limpid tree
2^-1
wraith daggerBOT
Mehdi_Moulati
limpid tree
i guess it will be 2^- instead of 2
This
Calculator can't function that
Syntax error
limpid tree
It will be 4
wraith daggerBOT
limpid tree
Yk both cases it will be 4 right
Try it
The 9 will give 1 to the next 9 making it 10 therefore it will be 2
soft owl
Yk both cases it will be 4 right
you mean the integral between 2 and 6 will give 4 also ?
soft owl
I meant if u integrate 0 to 2 same as 0 to 2^-
yeah
limpid tree
Okay so the answer is 20 total of integrals
soft owl
yes
soft owl
and since $(\frac{1}{tan(x)})' = \frac{-1}{sin²(x)}$
limpid tree
1/sin2x is csc2
wraith daggerBOT
Mehdi_Moulati
soft owl
We don't have a negative up
just multiply by -1
limpid tree
Okay
soft owl
$\int \frac{1}{1-cos²(x)} dx = \int \frac{1}{sin²(x)} dx= - 1 * \int \frac{-1}{sin²(x)} dx$
wraith daggerBOT
Mehdi_Moulati
soft owl
yeah
limpid tree
1/3 x³ - lnx int 2x-1/x?
bold vine
1/3 x³ - lnx int 2x-1/x?
You can check integrals by googling integral calculator and clicking the first result
An app called Maple can also do that for you
limpid tree
Okay
soft owl
1/3 x³ - lnx int 2x-1/x?
i don't think so
limpid tree
There is 1 part I'm mising
And don't understand
First part x³lnx/3
Then int
What do I write in the int
wraith daggerBOT
Mehdi_Moulati
soft owl
X³lnx/3 - x³/9
plus constant
limpid tree
Yep
soft owl
where is the last question 😆 ?
cedar kilnBOT
@limpid tree Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
soft owl
a)
since the slope is derivation of the function f at the point x
then f '(x) = xe^{-x}
so just integral an find the value of the constant
do the same thing to b)
cedar kilnBOT
limpid tree
a)
since the slope is derivation of the function f at the point x
then f '(x) ...
Oh okay
Thanks for help
soft owl
Thanks for help
anytime bro
cedar kilnBOT
Available help channel!
meager bay
Why is the derivative of k(sinx)^2=2ksinx*cosx
cedar kilnBOT
Why is the derivative of k(sinx)^2=2ksinx*cosx
inner glacier
d(sin x)^2/dx can be written as d(sin x)^2/d(sin x) * d(sin x)/dx
meager bay
chain rule right
inner glacier
yup
meager bay
ok, thx a lot
inner glacier
np
meager bay
k stays a constant so can you calcuate it as k * d(sin x)^2/d(sin x) * d(sin x)/dx
coral imp
Yep
meager bay
ok that answers my questions, thank you!
coral imp
K
meager bay
.close
glacial locust
what does it mean for a fucntion to be real valued?
cedar kilnBOT
what does it mean for a fucntion to be real valued?
crimson sedge
Assigns a real value to every member of its domain basically
solid juniper
usually means domain and codomain are both subsets of R
glacial locust
Assigns a real value to every member of its domain basically
ok so its domain is R basicaly?
glacial locust
but it has to be a subset of R?
flint plinth
but it has to be a subset of R?
not necessarily
glacial locust
codomain is a subset of R
what is the co domain again, it confuses me
flint plinth
what is the co domain again, it confuses me
the set to which the function is mapping (the set of possible outputs)
domain = set of possible inputs
glacial locust
the set to which the function is mapping (the set of possible outputs)
alright, so for a real valued function, co-domain is R?
flint plinth
yep
flint plinth
the outputs are real numbers
solid juniper
usually means domain and codomain are both subsets of R
ok i'd like to qualify that this is usually what it means in high school/calculus
cedar kilnBOT
cedar kilnBOT
Available help channel!
jade beacon
how do i keep sloving this equation ?
cedar kilnBOT
how do i keep sloving this equation ?
jade beacon
2x^2+3x-20=0
i mean
rain temple
And quadric formula
sly iris
(2x)^2+3(2x)-40=0
tropic oxide
is that really worth the trouble
coral imp
sly iris
Yes.
coral imp
Fr
sly iris
Let u = 2x, then:
u^2+3u-40=0
(u+8)(u-5) = 0
u = -8, x = -4
u = 5, x = 5/2
Simple
No point in using the formula when discriminant is rational
coral imp
can't you still factor
Fr
rain temple
2x^2+3x-20=0
crimson sedge
hm
coral imp
still does factor
rain temple
2x^2+3x-20=0
The right equation
sly iris
Yeah you can also split the linear term but thats more complicated to teach
crimson sedge
oop nvm
sly iris
Lol
coral imp
Lol
stiff heron
💀
rain temple
coral imp
This was the hardest formula for me to remember 3 years back
rain temple
For me it was inside the square root
crimson sedge
there are much more difficult ones 
coral imp
JESUS TF IS THIS?
rain temple
WTF
stiff heron
what you dont know that one?
rain temple
Oh its simplified
What happened to the a?
coral imp
Basically b/a = p in that
crimson sedge
What happened to the a?
divided out
coral imp
C/a=q out there?
stiff heron
2x^2 + 3x - 20 = 0
this you would have to divide by 2 first
coral imp
Damn new formula I'll save that shi
jade beacon
what the f
crimson sedge
not even a formula if you know how to use completing the square to solve a quad equation
rain temple
So now x^2 + 3/2 x -10 = 0 then use this
stiff heron
yeahh
crimson sedge
@jade beacon you know the quadratic formula or nah?
coral imp
u just need to find x
Then just yoink factorization Or quad eqn
crimson sedge
if you do, use it to solve
rain temple
Yea
jade beacon
<@603989665326039050> you know the quadratic formula or nah?
ye
crimson sedge
then use the formula to solve the quad equation
jade beacon
idk how
jade beacon
oh u want me to devide both sides by 2?
then just put it in -b+/-✓b^2-4ac/2a?
or without deviding?
rain temple
rain temple
or without deviding?
Without
jade beacon
Its just that i learnes it alone and didnt know when to use it
so can someone tell me when i need to use this formula?
rain temple
Now
jade beacon
ye but how woul i know to use it..m
i mean when do i need this?
when there is an ugly trinom?
coral imp
Amongus
cedar kilnBOT
@jade beacon Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
manic acorn
cedar kilnBOT
manic acorn
Why would 25C6.19C5.14C5 be wrong?
crimson sedge
Why would 25C6.19C5.14C5 be wrong?
What do you mean by that?
mighty drift
to me this is actually just reducing how many players are to be chosen and how many can be chosen
like you're just choosing 5 players among the 14 that can still be chosen
once you take the mandatory 6 and exclude the 5
manic acorn
What do you mean by that?
Theres 25 players, so if i want 6 to be always chosen, i do 25C6. Now there are 19 players and i want 5 to be excluded i do 19C5. When 6 players were included in team 5 spots left, and now 11 players included/excluded so 14 players left, so i did 14C5, thats how i got 25C6.19C5.14C5
manic acorn
like you're just choosing 5 players among the 14 that can still be chosen
That is the solution given as well however in a prev question something diff happened
mighty drift
words are flawed to convey rigorous mathematical meaning. That's the problem
manic acorn
crimson sedge
Theres 25 players, so if i want 6 to be always chosen, i do 25C6. Now there are ...
Oh ok, I wasn't familiar with that notation
mighty drift
so they are coherent
manic acorn
🗿
manic acorn
so they are coherent
Yes
So i just go with this is what this type of question means?
manic acorn
In class when we were doing this, the teacher would like give a specific name like 14 players, team of 9, number of ways so that chris isnt chosen
Then for some reason 13C9 made a lot more sense💀
mighty drift
words
that's why we always say to choose your words carefully
That's why in my first year of undergrad, my vocabulary was limited to "let, suppose, if, then/therefore, contradiction, set" and other words whose meaning is as unambiguous as possible
I always say "if you can't word it rigorously, you don't understand it enough"
for the math problems you deal with in undergrad
so it worked well
but these are more trying to be "applied math" but they just end up being poorly worded trivialities
applied math is best done in physics imo, or when working on a problem you came up with
cold briar
What's a good app for writing math equations? (Windows)
cedar kilnBOT
What's a good app for writing math equations? (Windows)
brisk dirge
New msword has good options to write math stuff
lusty grotto
geogebra?
lusty grotto
lol
lusty grotto
can u show an example
cold briar
not typing
crimson sedge
onenote? lol
lusty grotto
or even just paint lol
cold briar
or even just paint lol
no
im asking for one because i'm tired of drawing in paint
🙂
lusty grotto
oh lol
sacred grail
the newer one is more simplistic about the ui
lusty grotto
i guess in the newer version i cudnt find scrollbars
cold briar
for older ui
sacred grail
sacred grail
you mean onenote for windows 10?
lusty grotto
idk lol "whatever the hell the other one is"
crimson sedge
yeah thats what i meant
lusty grotto
yes
crimson sedge
if u r not using much then use that ig
crimson sedge
the ui looks uglier and lacks a lot of shit but thats my opinion soo
sacred grail
you can put so many colours
lusty grotto
idk why u cant pick like any color
cold briar
well this is mine
lusty grotto
wait
cold briar
using school account so i have to blur it
sacred grail
sacred grail
meh
latent bloom
Ooo you have Xournal++
sacred grail
cold briar
Ooo you have Xournal++
what's that?
sacred grail
ive got a bunch of colours
lusty grotto
still its just a few colors they let u pick from
latent bloom
what's that?
Xournal++ is free and has features for LaTeX and stuff from OneNote.
cold briar
true
latent bloom
And it's pretty easy to use
cold briar
Xournal++ is free and has features for LaTeX and stuff from OneNote.
so basically onenote?
latent bloom
Recently changed over to it
latent bloom
so basically onenote?
Yeah but lighter and uses LaTeX and other stuff
You can illustrate too
And you can have Plugins
lusty grotto
is it a windows app?
lusty grotto
no like i mean a microsoft thing
latent bloom
Nope
latent bloom
cold briar
thanks @latent bloom
lusty grotto
oh lol
latent bloom
lusty grotto
ig imma start using it too
latent bloom
Glad I helped :D
cold briar
tbh i just want the lines
https://xournalpp.github.io/installation/windows/ it's this one right?
marsh pond
cedar kilnBOT
marsh pond
Basic question but what’s the method for converting decimal to fraction again?
I’m looking at division as multiplying by the reciprocal of the second number but that doesn’t help
crimson sedge
i like to think of it this way:
[
0.1 \to \frac{0.1}{1} {\color{blue} \cdot \frac{10}{10}} = \frac{1}{10}
]
wraith daggerBOT
♡LexQa♡
cedar kilnBOT
long swan
S: X ->Y
T: Y -> X
T(S): X -> X
Try reading this again
@austere hearth
Somehow it got flipped around in your brain
Read this
Function composition starts from the inside
First apply S, then apply T
This should give you a mapping from X -> X
You don't technically need the middle
But its fine
Also your ordered pairs at the bottom are wrong
Even given that you did it the other way around. Remember that since its a function from X to X, your input and output should both be members of X
Yeah
Thats fine because its a relation
And not a function
Functions must have a unique output for each input
So for each element of the input set there is only one element of the output set that is mapped to through the function
Not one to one, but "vertical line test" if you will
cedar kilnBOT
cedar kilnBOT
Available help channel!
tardy basin
hi i cant really wrap my mind behind one of the solutions of the following problem:
tardy basin
the solutions are: ```
- p=-sqrt(7)
- p=sqrt(7)
- p=-4
now i understand how to reach the first 2
but i cannot understand why is -4 a solution
austere zealot
@tardy basin The equation (x-1)(x^2+2px+7) is a cubic equation and hence has up to three distinct roots.
What are the three roots in terms of p?
tardy basin
wdym in terms of p?
austere zealot
That is, what are the three roots of (x-1)(x^2+2px+7)?
tardy basin
well we know 1 is one of them
austere zealot
What are the other 2?
tardy basin
well they depend on p
austere zealot
well they depend on p
That's what "in terms of p" means by the way.
tardy basin
wait i dont understand where we're going
the other 2
could be reached if p= +/- sqrt(7) because
that's the only time
tardy basin
yeah ,right
but the problem does not care what the roots are
as long as they're exactly 2
austere zealot
We'll get there.
If you know what the three roots are, you can easily make two equal and now you have two distinct roots.
austere zealot
Find the three roots, and set any two to be equal to figure out what p is.
One root is 1. The other two are the roots of x^2+2px+7, which you can use the quadratic formula to find.
tardy basin
okay so for the roots as a function of p i find
(-2*p +/- sqrt(4p^2 - 28)) / 2
so what now?
austere zealot
Alright. (This can be simplified to -p +/- sqrt(p^2 - 7).)
We have three roots -1, -p + sqrt(p^2 - 7), and -p - sqrt(p^2 - 7).
We can pick any two and set them to be equal.
If -p + sqrt(p^2 - 7) = -p - sqrt(p^2 - 7), then what value(s) of p do you get?
tardy basin
sqrt(7), -sqrt(7)
tardy basin
undefined
austere zealot
Yes.
Setting -1 to be one of the roots gives -4 and no solution for the other.
This is how you would find the three solutions of p.
The general idea being to find all roots, and set some to be equal.
austere zealot
Granted, this method requires the roots to be found. There are other advanced techniques to tell if there are repeated roots. Though if you can state all the roots exactly, then the work is simpler.
Good luck!
wooden zephyr
need helppp
cedar kilnBOT
need helppp
versed kayak
See, in these kinds of questions , the logic lies with the guy who creates the question
crimson sedge
A doesnt have a closed curve either though?
I would say C as its the only one that definitely overlaps itself
versed kayak
Maybe c coz it has a straight line
wooden zephyr
thnxx guyss
cedar kilnBOT
Available help channel!
manic acorn
cedar kilnBOT
manic acorn
tried taking cases, is getting too lengthy and complicated
this was the solution given, dont understand it
solid juniper
that counts the number of ways to arrange the letters in eg CVNVMV
do you see why that number is the same as what it asks for?
manic acorn
that counts the number of ways to arrange the letters in eg CVNVMV
do you see wh...
What counts the number of ways to arrange letters?
solid juniper
6!/3!
wispy marten
The answer given does not seem right
wispy marten
What does "the order of vowels do not change" exactly mean?
manic acorn
The answer given does not seem right
I wont be surprised this pdf has been giving weird ans left and right
solid juniper
i think it means I comes before E which comes before A
solid juniper
No it doesnt?, That wpuld be 6!?
notice the 3 V’s?
wispy marten
Oh, ok, then it is right. 😄
manic acorn
What does "the order of vowels do not change" exactly mean?
Well as someone who also doesnt know but i am making an educated guess vowels in the original word are in the order I,E,A, so im guessing it wants the vowels to stay in this order and not be like E,I,A?
manic acorn
notice the 3 V’s?
Theres 3 Vs? Do you mean vowels?
wispy marten
Before starting a question, make sure you exactly understand what you have to do (here, what to count)
solid juniper
i chose V for vowel but it could have been smth else haha
manic acorn
Why would i be driving by 3!, Becuase of 3 vowels?💀
solid juniper
have you ever counted ways to rearrange letters in words when there are duplicate letters?
manic acorn
have you ever counted ways to rearrange letters in words when there are duplicat...
Yes
solid juniper
so you could count the ways to rearrange the letters in CVNVMV?
ignoring the original problem for right now lol
manic acorn
so you could count the ways to rearrange the letters in CVNVMV?
Well if V stands for letter V then 6!/3!
solid juniper
yep
solid juniper
so you could count the ways to rearrange the letters in CVNVMV?
do you see the connection between this and the original problem?
manic acorn
Nope
solid juniper
ok so
actually maybe this is easier
there are 6 choose 3 ways to fix the I, E, and A
manic acorn
Yes
solid juniper
then for each way to fix them, there are 3! ways to arrange the last 3 letters
manic acorn
The last 3?
solid juniper
the C, N, and M
manic acorn
You mean the other three?
solid juniper
manic acorn
I understand for every way to fix them theres 3! ways to shuffle C,N,M
but the 6c3 to fix i,e,a. Can also fix them like a,e,i?
solid juniper
no
solid juniper
i think it means I comes before E which comes before A
pretty sure it means this
based off the answer 💀
solid juniper
sure
solid juniper
yayyy ^-^
manic acorn
6c3 secures 3 place out of 6 place for i,e,a?
After securing the 3 places, the number of ways to achieve i before e before a is 1
solid juniper
yeppp
cedar kilnBOT
solid juniper
np ^w^
cedar kilnBOT
Available help channel!
kind patio
can someone help me show that 16^(12g-11) -3 is always divisible by 13
tropic oxide
is modular arithmetic allowed?
cedar kilnBOT
@kind patio Has your question been resolved?
kind patio
is modular arithmetic allowed?
ok
cedar kilnBOT
kind patio
.reopen
cedar kilnBOT
✅
kind patio
<@&286206848099549185>
crimson sedge
Is induction allowed?
kind patio
Ok?
crimson sedge
very cooperative
kind patio
it and modular arithmetic
Idk mod for exponents
kind patio
very cooperative
Everything is allowed for an answer
Maybe you can recommend somewhere from where I acn learn mod for exp
Eomeone
Noone
cedar kilnBOT
@kind patio Has your question been resolved?
wraith daggerBOT
Mehdi_Moulati
kind patio
**Mehdi\_Moulati**
Oh man thanks for the help I didn't really ask for the solution but am greatful
crimson sedge
guys i am doing matrix is [a b c ] 3x1 or 1x3
cedar kilnBOT
guys i am doing matrix is [a b c ] 3x1 or 1x3
crystal raptor
1x3
crimson sedge
thank you fam
crystal raptor
Yes
crimson sedge
thank you so much
crimson sedge
Trick (n x m)(m x p) = n x p
should i do it like this
crystal raptor
No those colours should be be going down a column
crystal raptor
Yes like the second
crimson sedge
alright
sacred grail
crimson sedge
👍 actual life saver
sacred grail
are you sure it's the second
crystal raptor
First entry should be a + 4b + 7c
You go down column of matrix but along row of your vector
Sorry your lines were confusing me
crimson sedge
15+0+0 the first one??
crystal raptor
Yep
crystal raptor
You got it
crimson sedge
sacred grail
there's that thing where you can write two matrices next to each other
crimson sedge
thats ^ when you lay out
sacred grail
and you can just follow the lines to calculate each entry of the product
lemme show
crimson sedge
yup
sacred grail
it also tells you the size of the result
crimson sedge
i appreciate it
sacred grail
because its whatever fits
and the top left blank has to be a square
for the product to be defined
in this case you can see its a 3x3 blank
digital shell
Hello, how can I solve this?
cedar kilnBOT
Hello, how can I solve this?
digital shell
I have no idea
lusty grotto
what did u learn about circles
digital shell
what do you mean
digital shell
I haven't learned about them really I just saw some videos on the standard form equation but couldn't understand them
so it didn't teach me anything
I was hoping I couldh get some help from here
to solve
lusty grotto
oh
lusty grotto
if u have the equation (x-a)^2 + (y-b)^2 = r^2
so is the "standard form equation" u saw this?
lusty grotto
and they explained nothing about what a, b, r are?
lusty grotto
yes
lusty grotto
change in x and y
what is the change in x and what is the change in y, in ur equation given
digital shell
how do you know that
digital shell
what is the change in x and what is the change in y, in ur equation given
I don't know
lusty grotto
okay then in the standard form equation
what is the change in x and what is the change in y
digital shell
I don't know how to calculate that
digital shell
I don't know what any of it stands for
lusty grotto
from distance formula
can u say what u learnt here
digital shell
I calculated midpoint by adding 2 coordinates then dividing by 2
lusty grotto
coordinates of what
digital shell
2 points
lusty grotto
yeah what 2 points
lusty grotto
graph of what
digital shell
hypotenuse
lusty grotto
can u send a picture of the diagram that these 2 poitns were on
digital shell
I don't have a picture I learnt that some time ago
it was just 2 points on a graph
then I constructed a triangle
lusty grotto
okay
digital shell
to get change in x and change in y
lusty grotto
so how can u do the same thing to find the radius of a circle
can u draw a triangle and using its hypotenuse find the length of its radius?
digital shell
yeah but I don't have a graph in this question
lusty grotto
okay u dont need one
but if u had a graph
how would u do it
how would u draw the triangle
digital shell
well you just draw a straight line from the points so you get the hypotenuse then contruct a right triangle from that
but now I don't know any points
lusty grotto
but if u had a circle what two points would u join
to find the radius
like u wudnt just pick 2 random points inside the circle
digital shell
any points on the circumference and the center
lusty grotto
yes
digital shell
but the problem is that I don't understand this standard form equation of the circle
lusty grotto
so this distance is the same whatever point u pick on the circle
and it is equal to the radius
?
digital shell
what distance
lusty grotto
any points on the circumference and the center
here
the distance between any point on the circumference and center
digital shell
yes that is the same
lusty grotto
yes
so pick any point on a circle and call it (x,y)
if the circle has center (a,b)
what is the radius now
digital shell
you can't know radius
digital shell
I don't understand
lusty grotto
okay lets say (5,6) was a point on the circumference of some circle
and this circle had center (1,2)
what is its radius?
digital shell
square root of 32
lusty grotto
how did u get that
digital shell
change in x^2 + change in y^2 = radius^2
digital shell
4
lusty grotto
how did u find it
.
digital shell
I just knew that 5 was 4 points from 1
lusty grotto
5-4
digital shell
I didn't do that
lusty grotto
okay then what if the two points i gave u were (522, 654) and (-554, 874)
how would u find the radius now
digital shell
okay then I would subtract x1 with x2 etc
lusty grotto
change in x = ?
yes
so now
in the same way
if (x,y) were the coordinates of a point on the circumference of a circle
and (a,b) was its center
what is its radius
digital shell
(a-x)^2 + (b-y)^2 = r^2
lusty grotto
yes
u can also write
(x-a)^2 + (y-b)^2 = r^2
right?
that is the standard form equation of a circle
do u get it?
so what we could do now is, pick some values for r, a, b. then just try putting in various values for x and y, until u find two values that satisfy the equation, and plot that point
when u do that, all the points u plot would end up being on a circle with center a, b and radius r
thats why we call that the equation of a circle
digital shell
do u get it?
no
lusty grotto
so what we could do now is, pick some values for r, a, b. then just try putting ...
u dont get this?
lusty grotto
(x-a)^2 + (y-b)^2 = r^2
u understand that this equation here is the same thing u wrote
?
digital shell
u understand that this equation here is the same thing u wrote
yes that I udnerstand
but I don't see how that relates to the standard form
lusty grotto
okay now lets say we pick a = 1, b = 2, r = 4
then that equation becomes (x-1)^2 + (y-2)^2 = 16
right
digital shell
yes
digital shell
0
lusty grotto
then that equation becomes (x-1)^2 + (y-2)^2 = 16
when u put x=1, and y=1, what do u get for (x-1)^2 + (y-2)^2
0?
digital shell
in that case you get 1
lusty grotto
yes
and 1 is not equal to 16
so the equation (x-1)^2 + (y-2)^2 = 16 is NOT satisfied when x=1 and y=1
do u get that?
digital shell
yes
lusty grotto
how abt when x=1, y=6? is the equation satisfied or not
digital shell
yes
lusty grotto
yes it is satisfied
so now if u were to draw a graph, u can plot the point (1,6)
like that u can keep putting different values for x and y
and plot the ones that satisfy the equation
do u understand what i mean?
digital shell
no
lusty grotto
i mean u can mark a point (1,6)
like make a dot
at that point
on a coordinate plane
coz (1,6) satisfies the equation
do u understand that
digital shell
I understand it satifies the equation but not the plot part
lusty grotto
well what u r now trying to do is, u r gonna try to show all the values of x and y which satisfy the equation
u know that when x=1 and y=6, the equation is satisfied, so to show this, u make a dot on a coordiante plane, the point where the x coord = 1 and the y coord = 6
do u get it
digital shell
no, why would you make a dot
lusty grotto
now if somebody looks at this coord plane, then they can see u made a dot at the point where x coord = 1 and y coord = 6, and theyll know that when x=1 and y=6, the equation is satisfied
so its like u r trying to tell someone what are all the values of x and y that satisfy the equation
rather than making a long list
this is easier
digital shell
but why would you put it on a coordinate plane
lusty grotto
okay this probably sounds weird but do u get it
digital shell
what meaning does the coordinate have
if 1, 6 satisfies it
is that the center? circumference?
lusty grotto
what meaning does the coordinate have
because we were talking about graphs in the first palce
digital shell
I'm confused what you mean by this
lusty grotto
okay so u understand a circle is a set of points that is the same distane away from some fixed point?
this distance being what we call the radius?
digital shell
from center yes
lusty grotto
yes "fixed point" there means the center
right so the "equation of a circle"
is just an equation that the x coords and y coords of these points satisfy
digital shell
what do you mean with these points
lusty grotto
okay so u understand a circle is a set of points that is the same distane away f...
the points in the set of points i mentioned here
digital shell
so the circumference?
lusty grotto
yes points on the circumfrence
so the "equation of a circle", is an equation that the x coords and y coords of the points on the circumference of the circle satisfy
digital shell
I don't understand, it's variables so there is no coordinates
lusty grotto
well yeah its not just one point that is on the circumference of a circle
there are many points
when u write something like (x-a)^2 + (y-b)^2 = r^2
lusty grotto
there are many points
u can pick any one of these points
lusty grotto
when u write something like (x-a)^2 + (y-b)^2 = r^2
and put its x coord in place of x here, and its y coord in place of y here
digital shell
I don't quite understnad how that relates to the standard equation of a circle
lusty grotto
what do u think "standard equation of a circle" should mean
do u know the equation of a straight line?
digital shell
y = 1
lusty grotto
Hello, how can I solve this?
i could just tell u how to answer this...but idk if thatll be helpful
digital shell
I just want to understand the standard equation of circle
digital shell
what is this
the equation of a straight line
lusty grotto
of a very particular straight line
thats the straight line that is horizontal and passes the point (0,0)
do u know about equations of like slanted straight lines
digital shell
what do you mean by slanted straight lines
digital shell
y = x
lusty grotto
right okay
y = 2x + 3
take this for example
what do u understand when u see this
why are u comfortable with calling something like this "equation of a straight line"
digital shell
what do you want me to do here exactly
lusty grotto
im trying to give u the same intuition u have about straight lines
to understand circles
but idk if im helping
lusty grotto
okay so if (x,y) is some point, and (a,b) is another fixed point, and r is some number, then (x-a)^2 + (y-b)^2 = r^2 is the equation of the circle that has center (a,b) and radius r
do u understand that
sorry if i wasted ur time
digital shell
no I don't
lusty grotto
what do u ntt understand
digital shell
okay so if (x,y) is some point, and (a,b) is another fixed point, and r is some ...
this
lusty grotto
yeah what part in it
if u r given some equation like (x-5)^2 + (y-3)^2 = 10^2, then this is the equation of the circle that has center (5, 3) and radius 10
digital shell
how can I know that
cinder arrow
General eq. of circle
(x-h)²+(y-k)²=r²
digital shell
General eq. of circle
(x-h)²+(y-k)²=r²
yeah
but I don't understand how to solve my prolbem
and find the radius and center
digital shell
cinder arrow
that's it
digital shell
ok so hk will always be center and xy is some point on circumference?
cinder arrow
Yes
cinder arrow
Center is -12,9 and radius is sqrt35
cinder arrow
so (12, 9) is center?
-12
cinder arrow
Yes
digital shell
they wrote +
cinder arrow
np
digital shell
.close
drifting latch
The probablity of X happening is 50%, then the probablity of x happening in 3 instances out of 5 is?
drifting latch
i get that it should be 3!/5!.2! but my question is w h y
cedar kilnBOT
@drifting latch Has your question been resolved?
short heart
Are you sure that's the correct answer??
This looks like a binomial distribution to me
drifting latch
yeah it should be done using the formula nCr right
short heart
Yeah
drifting latch
yeah so my question is why does it apply hear and whats the significance of the 50% probability?
would it be any different if the probability was different?
short heart
The probability would change but the idea remains the same
drifting latch
yeah so how would i go about if the probability was different?
as right now the probability of it happening and not happening is the same
short heart
If you see x favourable result out of n independent trials, it generally is Binomial distribution
short heart
yeah so how would i go about if the probability was different?
You would change the value of p variable in the formula accordingly
drifting latch
You would change the value of **p** variable in the formula accordingly
what is the p variable exactly?
short heart
Probability
drifting latch
im new to this concept since im learning it on my own so half of what you said bounced over my head
can you simplify?
short heart
Let's say you have n number of independent trials and you want an event to occur x number of times
Think of binomial distribution in such case
Event with probability p
cedar kilnBOT
cedar kilnBOT
Available help channel!
smoky whale
Hi guys, I am not sure how to solve for x here
cedar kilnBOT
Hi guys, I am not sure how to solve for x here
smoky whale
,rotate
wraith daggerBOT
bold lotus
what have you tried
smoky whale
,rotate
wraith daggerBOT
dull oxide
Try the other way
Instead of taking stuff out of logs
Put stuff into logs
More precisely, try to have just one log on each side of the equation
bold lotus
remember your log laws
wraith daggerBOT
smoky whale
remember your log laws
So which law do I use
bold lotus
So which law do I use
take a guess
smoky whale
2
bold lotus
good
dull oxide
I think you divided wrong
dull oxide
It's just x^2/(x+2)
smoky whale
So it’s x/2
dull oxide
As an example it doesn't work though, plug in x=1 and check if they are equal
dull oxide
,rccw
wraith daggerBOT
dull oxide
Yeah you can't cancel out fractions that way
You may want to review how fractions work in algebra
smoky whale
Hold up
smoky whale
No not yet
light pine
No not yet
Do u need some help
viscid mulch
No not yet
You seem to be forgetting about a very import log law
If an equation has log of the same base on both sides, it can be treated without the log.
Log(X+3) = Log(5-X)
X+3=5-X
2X=2
X=1
@smoky whale
Log X - Log Y is same as log X/Y
viscid mulch
Good job
viscid mulch
Yup looks good to me
smoky whale
This question really beats me
viscid mulch
What log to the base of e give us 1?
smoky whale
e
viscid mulch
Exactly
smoky whale
Yep
viscid mulch
Knowing that log e to the base e give us 1
smoky whale
Yep
viscid mulch
What's the equation here applying the knowledge of log of e to base e gives us 1
smoky whale
smoky whale
I’ll try
viscid mulch
Send me the equation you get once you're done
smoky whale
,rotate
wraith daggerBOT
