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#help-17
untold meteor
vocal sleetBOT
soft walrus
don't forget about your abs
untold meteor
Yeah what should happen to that?
Is it just a plus minus on the other end
@soft walrus
soft walrus
yea the function should have pm
untold meteor
Ty
untold meteor
.close
high hare
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of
1/5! (β−α) is _______
vocal sleetBOT
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. I...
high hare
!status
vocal sleetBOT
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
1
left crest
Ok, do you know what is an onto and and a one to one function
high hare
I was blank regarding this yesterday.
But I looked it up on web along with some people who helped me understand the concept in this server
The question's from Permutation and combination along with functions mixed
left crest
Just to recap,
A one-one function means that given one value in set A(Domain) there exists only one value in set B(Codomain)
An onto function means that if for every value in set B(Codomain) there will be at least value in Set A(Domain)
An onto function is called a surjection
high hare
So every house needs delivery in the colony for surjection
And
Every parcel has a unique house to be delivered to in injection
Houses are range
Codomain is the colony
Parcels are domain
left crest
Yeah, you could say that
Now coming to the permutation part, first for one - one function
Let say the first element in Set A is 'a' how many options does there exist for 'a' to choose from in Set B
left crest
yes
high hare
Injection can have some houses left without delivery right?
Meaning
Codomain != Range
Every parcel will get delivered though
left crest
now for the second element in Set A 'b', how many options does there exist for 'b' to choose from in Set B, given 'a' has chosen one, and 'b' cannot choose the same element as 'a' as this is a one-one function
left crest
6
Great similarly for the 3rd element there will be 5 options, for the 4th element there will be 4 options and for the 5th there will be 3 options. So how many options will be there
high hare
My hands are running wild.
I'm tapping random places.
Didn't mean to tap on emoji
high hare
Great similarly for the 3rd element there will be 5 options, for the 4th element...
5 options for 5 a
left crest
how?
left crest
ok, I think you got confused with my notation
a is the first element in Set A and b was the second element in Set A
left crest
Total possibilities are 7×6×5×4×3?
Yes, this is correct
high hare
I'll repost the question
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of
1/5! (β−α) is _______
Now onto function is left
spring cargo
Can someone help me?I need its Minimum, Q1, Q3, Maximum, and range, please help
high hare
But can we do it?
There's more houses needing delivery than available parcels
high hare
Can someone help me?I need its Minimum, Q1, Q3, Maximum, and range, please help
Go to #help-5
This one is occupied by me currently
🥶
So....
high hare
But can we do it?
There's more houses needing delivery than available parcels
?
Mr @left crest
The last thing made sense
left crest
But can we do it?
There's more houses needing delivery than available parcels
n < m, the number of onto functions = 0
high hare
When n is elements of A and m is elements of B?
left crest
yes
left crest
hence, number of onto functions is 0
left crest
So what comes out as the answer
left crest
No, number of surjection(onto) functions is 0
left crest
n means set A elements =5, and m is set B elements = 7
n < m, the number of onto functions = 0
left crest
But can we do it?
There's more houses needing delivery than available parcels
The logic you gave here is correct
high hare
n means set A elements =5, and m is set B elements = 7
n < m, the number of ont...
But they told us to take onto functions from Y -> X
7 parcels
5 houses, it can't be delivered?
left crest
Ok, I apologise, I think I made the mistake of taking it X->Y, I should have been more careful
we have to find the number of onto function from a set A with n number of elements to set B with m number of elements.
Thus,
Total number of functions from A to B = m^n
Total number of onto functions = Total number of functions – Number of functions which are not onto
high hare
I did it firsthand too
high hare
we have to find the number of onto function from a set A with n number of elemen...
The M^n is a Constant formula that we can apply everywhere?
Provided m is for A and n is for B?
left crest
n is set A and m is set B
high hare
Ok
First set goes on power
left crest
yes
high hare
So if we reverse the arrow, it'll be n^m?
left crest
yes
high hare
Also this will give ALL kinds of functions or Onto +injection?
left crest
Yes
For every element in set B there a n elements in Set A
and there are such m elements in Set B
high hare
I heard someone say functions can be of anything
Like a parcel can get delivered to more than 1 house or let's say all houses
It won't be sur/injection but it'll be a function
So the m^n won't give these kind of functions too?
left crest
I heard someone say functions can be of anything
Like a parcel can get delivere...
If parcels are the domain, then this is incorrect
high hare
If parcels are the domain, then this is incorrect
Yes, domain
Ok
left crest
A house can have 1 or more parcels
but a parcel can only go to one house
hence the parcel house anology
high hare
👍
left crest
Now, we have 7 houses and 5 parcels correct
left crest
Yes, 7 parcels and 5 houses
high hare
Okey
left crest
now total number of function implies, that 5^7
high hare
So the m^n won't give these kind of functions too?
Won't this also give us the functions where a single house gets all the parcels?
Though it won't be both sur/injective
left crest
Won't this also give us the functions where a single house gets all the parcels?...
yes, we are going to subtract those cases
left crest
Number of onto functions = No of Total functions - No of total functions which are not onto
So for No of total functions which are not onto
To avoid confusion, h=No. of Houses=No. of elements of Codomain=5, and p=No. of Parcels=No. of elements=7 in the domain
let us choose 1 house where no parcels are delivered then for the remaining h-1 houses the p parcels are delivered
or we could choose 2 houses where no parcels are delivered and the remaining h-2 house the p parcels are delivered
high hare
So
left crest
Just give me a minute, I will type it clearly on Latex and show you, I don't have paper with me right not
high hare
Sure, take your time.
Just ping me because I'm doing the next question
left crest
Number of functions which are not onto functions $\={{h}\choose{1}}(h-1)^{p}+{{h}\choose{2}}(h-2)^{p}+{{h}\choose{3}}(h-3)^{p}+\dots+{{h}\choose{h-1}}(1)^{p}$
twin meteorBOT
Encrpyt
left crest
@high hare
Number of functions which are not onto functions $\={{5}\choose{1}}(4)^{7}+{{5}\choose{2}}(3)^{7}+{{5}\choose{3}}(2)^{7}+{{5}\choose{4}}(1)^{7}$
twin meteorBOT
Encrpyt
left crest
Total number of onto functions will be:
$\5^7-({{5}\choose{1}}(4)^{7}+{{5}\choose{2}}(3)^{7}+{{5}\choose{3}}(2)^{7}+{{5}\choose{4}}(1)^{7})$
twin meteorBOT
Encrpyt
high hare
Makes sense
left crest
And for one to one the answer will be 7!/2!
high hare
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of
1/5! (β−α) is _______
One to one will be 7×6×5×4 ?
high hare
**Encrpyt**
Onto , this
left crest
Onto , this
Yes, this will be number of onto functions
The wording of the problem is very odd, and I got confused by that.
high hare
Agree with that
high hare
One to one will be 7×6×5×4 ?
?
left crest
One to one will be 7×6×5×4 ?
it will be 7x6x5x4x3
high hare
I used calculator
It comes in negative
I think we're doomed at some step
For onto
Sir @left crest
left crest
Yeah, I am checking my calc
high hare
left crest
the total number of functions
high hare
So m^n
for m in A and n in B?
left crest
Ok for the total number functions which are not onto, we have to inclusion exclusion principle
I just saw I made a mistake in the signs while so
the total number of functions is 5^7
Total number of onto functions will be:
$\5^7-({{5}\choose{1}}(4)^{7}-{{5}\choose{2}}(3)^{7}+{{5}\choose{3}}(2)^{7}-{{5}\choose{4}}(1)^{7})$
twin meteorBOT
Encrpyt
high hare
What?
high hare
I just saw I made a mistake in the signs while so
Didn't make sense
vocal sleetBOT
@high hare Has your question been resolved?
vocal sleetBOT
@high hare Has your question been resolved?
high hare
Bump
high hare
Bump
high hare
Bump
high hare
Bump
vocal sleetBOT
@high hare Has your question been resolved?
high hare
<@&286206848099549185>
patent nymph
I heard someone say functions can be of anything
Like a parcel can get delivere...
I meant that that would be a relation, not a function: for a function, you can’t tear the parcel in half
high hare
I meant that that would be a relation, not a function: for a function, you can’t...
I didn't have you in mind while saying it
Also since you came
Help
patent nymph
Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. I...
have you found the number of surjective functions yet
patent nymph
Can you summarize what you’ve done so far for that
high hare
We've drawn a rough diagram to figure out how the onto, one one works first
Then we found out the number of functions for one one
Now we're stuck at onto
high hare
To avoid confusion, h=No. of Houses=No. of elements of Codomain=5, and p=No. of ...
Here's what was the stuff we did in a nutshell for onto
vocal sleetBOT
@high hare Has your question been resolved?
sleek flame
hello, this method doesnt do anything for linear independent vectors right?
thin vale
pearl flower
log_x 3/10, rebase to 1. common log, 2. natural log.
vocal sleetBOT
log_x 3/10, rebase to 1. common log, 2. natural log.
pearl flower
at the moment im bit confused if i can make this to log (4) / log (10 + x)
or i'm only allowed to writedown as log (1/10) / log (x)
basically im not sure if im able to apply fraction rule for log
@reef grove anyone?
.cloe
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
can someone help me with equations a bit?
i keep doing these excercices to prepare for a test and keep getting them wrong.
idk what im doing wrong
vocal sleetBOT
can someone help me with equations a bit?
i keep doing these excercices to prepa...
timber orchid
lime hearth
sure, we can help
vast shale
yall want photos of the procedure i did so yall can check what i did wrong?
or do i type them down or smth
hasty pulsar
draw them
lime hearth
photo is probably faster
though, might also not be readable so idk do what you think would be the best option
vast shale
for example the answer for that is supposed to be x=1 yet i keep getting random shit
idk why the photo is upside down
lime hearth
i rotated it
vast shale
yes i know i write like shit
lime hearth
my writing is worse dw
worthy forge
is that first one 5-5(x+2)(x-3)
vast shale
387 is the number of the exercise dw abt it
worthy forge
so
why not just multiply the 2 binomials immediately
just curious
one thing youre doing wrong here
2nd step
youre basically pulling a 5 out
what you did was 5(x+2)(x-3) right?
and then you said ok 5x+ 10(x-3)
or maybe im a crazy insane psycho lunatic
vast shale
and then you said ok 5x+ 10(x-3)
5-5x+10(x-3) actually
vast shale
which is?
lime hearth
okay- step by step solution
5-5(x+2)(x-3) = -5(x+6)(x-2)
→ simplify: ÷(-5) on both sides
(x+2)(x-3) -1 = (x+6)(x-2)
→ multiplication of both binomials
x² -3x +2x -6 -1 = x² -2x +6x -12
→ simplify: -x² on both sides
-x -7 = 4x -12
→ simplify more: +x +12 on both sides
5x = 5
→ x = 1
vast shale
here it says the answer is supposed to be x=1
lime hearth
ah i see
worthy forge
other than that your answer works out
worthy forge
here it says the answer is supposed to be x=1
do you see what i mean when i said you dropped parenthesis?
lime hearth
okay- step by step solution
5-5(x+2)(x-3) = -5(x+6)(x-2)
→ simplify: ÷(-5) on bo...
(edited)™
vast shale
do you see what i mean when i said you dropped parenthesis?
yeah now i see
worthy forge
word
do you understand *why * thats an issue and why you shouldnt drop the parenthesis, mathematically?
vast shale
i dropped it since what i did was basically multiply the 5 by the (x+2)
worthy forge
and you get why thats wrong, right?
vast shale
i don't get why its wrong but now i do
vast shale
i remember my professor saying we can do that to simplify
worthy forge
not in this particular instance
i mean
yes you can distribute
but you cant now break it up into separate parts and then multiply the second thing
theyre 2 parts of 1 whole that is multiplying the second binomial (the x-3)
lime hearth
generally, these equations will often have a point where you need to make the equation a lot more complicated (here, it was the binomials)
so, my tip is: simplify, solve, simplify (just like i did in the solution)
worthy forge
you basically said "ok im just gonna take part of my initial thing and multiply with it"
which is not cool
vast shale
ty again for helping
worthy forge
yep
worthy forge
ty again for helping
be sure to close your post if you dont need help anymore
vast shale
if i get it wrong im probably still gonna need help
worthy forge
haha ok
vast shale
anddd i got it wrong again
2(x-6)-12=-4(x-6)
2x-12-12=-4x-24
2x-4x=12+12
-x=12
x=-12
answer is supposed to be 8
vast shale
yes
worthy forge
ok so far...2nd step is good, so good job
lime hearth
anddd i got it wrong again
2(x-6)-12=-4(x-6)
2x-12-12=-4x-24
2x-4x=12+12
-x=12
x...
the issue is with step 2 and 3
worthy forge
i agree
vast shale
what did i get wrong there
vast shale
the circled one
worthy forge
ok
eyah
you fucked up step 3
i see now
so its 2x - 12 -12 which is 2x -24
oh
AND step 2
you didnt distribute the negtive
its postive 24
so lets start there
2x- 24 = -4x + 24
lime hearth
lemme just do my step by step again
2(x-6) -12 = -4(x-6)
→ bracket removal multiplications
2x -12 -12 = -4x *+*24
→ simplify: +4x +24
6x = 48
→ simplify: ÷6
x = 8
vast shale
wait can you explain how you simplified +4x+24
worthy forge
is -4x + 25
24*
when you distribute that -4, the negative goes to both parts
oh i see what you mean
lime hearth
i added 4x and 24 on both sides
2x + 4x becomes 6x / -4x + 4x becomes 0
-12 -12 +24 becomes 0 / 24 + 24 becomes 48
vast shale
oh i see
lime hearth
the goal for these is to isolate x to be on one side of the equation
(for example: 6x = 48)
as from that point you're a single division away
lime hearth
you're welcome 
lime hearth
.close
vocal sleetBOT
lime hearth
its already closed
vast shale
it shows that i have it claimed
lime hearth
yeah thatll update in a bit
vast shale
aight
vocal sleetBOT
Available help channel!
glad python
The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-quarter of an inch has a resistance of 20 ohms. Find the electrical resistance in a 500 inch wire with the same diameter.
vocal sleetBOT
The electrical resistance of a wire varies directly as its length and inversely ...
glad python
How do I do this?
What I tried:
Let the electrical resistance be x. Since x varies directly with its length, x/l is constant. Additionally, x varies inversely with the square of the wires diameter, so xd^2 is constant. ]
after finding x/l an xd^2, i get two values of x and im confused
<@&286206848099549185>
vocal sleetBOT
@glad python Has your question been resolved?
vapid summit
there are two independent variables, so you have to consider them both
xd^2 / l will be a constant
you know since diameter stays the same in both situations you can treat it as a constant
so you could just consider x/l
mighty stone
help?
rose raft
what do you need help with
mighty stone
what do you need help with
what does the question mean?
rose raft
what values can be produced 2x^2 -2x-4
mighty stone
what values can be produced 2x^2 -2x-4
so we equal it to 0?
rose raft
no
rose raft
wdym
mighty stone
wdym
like i dont get what it means when it says "which interval represents the range of the function"
rose raft
do you know what a range is?
rose raft
no subtration
mighty stone
no subtration
substituion?
rose raft
NO subtraction for functions
mighty stone
NO subtraction for functions
so you subtract lowest to highest
vocal sleetBOT
@mighty stone Has your question been resolved?
rugged forge
how do you get the equation of this using a ti-84
vocal sleetBOT
how do you get the equation of this using a ti-84
devout ledge
so basically
devout ledge
click Stat > Calc > C:SinReg
rugged forge
error
rugged forge
i did allat still stays invalid dimension
vocal sleetBOT
@rugged forge Has your question been resolved?
vocal sleetBOT
@rugged forge Has your question been resolved?
lunar granite
How did I get these 2 questions wrong?
vocal sleetBOT
How did I get these 2 questions wrong?
lost bane
angle DBC is 60 degrees
lost bane
the 3 angles in the triangle need to be 60 degrees to be an equileteral triangle
lunar granite
I thought you were referencing that they gave me DBC is 60
Where did the 60 come from?
lunar granite
Yeah but if it were 60 then the sum of the triangle would be 190
lost bane
? how
lunar granite
70 + 60 + 60
lunar granite
I got the 70 from doing suplmentery angles to find angle BDC
By adding angles A and B then subtracting it by 180
lost bane
angle BDA is 120 degrees
lost bane
ok
lost bane
look at ur calculator when u key in numbers lol
the first one
angle 1 + angle 2 = 180 degrees
not equal
lunar granite
But it’s same side interior
isn’t same side interior congruent to each other?
Or is it the opposite
lunar granite
ohhh I even wrote that down in my note sheet but I’m guessing I looked at the wrong thing lol
lost bane
ok
lost bane
ok
vocal sleetBOT
@lunar granite Has your question been resolved?
indigo yarrow
In a 4x4 grid, some squares are painted black in such a way that: one row and one column have exactly one square painted black; a row and a column have exactly two squares painted black, a row and a column have exactly three squares painted black; and one row and one column have exactly the four squares painted black. In how many different ways can the grid be colored ?
vocal sleetBOT
In a 4x4 grid, some squares are painted black in such a way that: one row and on...
@indigo yarrow Has your question been resolved?
vocal sleetBOT
@indigo yarrow Has your question been resolved?
lyric fossil
In a 4x4 grid, some squares are painted black in such a way that: one row and on...
do you have the answer to this?
indigo yarrow
No
lyric fossil
i assume this is for a combinatorics class
do you know group theory?
actually we don't need group theory for this. i thought it'd be easier buy there should be a simpler way to frame the problem
@indigo yarrow i take it you know basic combinatorics
indigo yarrow
<@463779642936000533> i take it you know basic combinatorics
Well, yeah
lyric fossil
ok
think of the problems as follows:
you have the following 4 rows
o x x x
o o x x
o o o x
o o o o
and we're permuting their order
and after we permute their order, we permute the columns
for example, one permutation of the rows could be
o x x x
o o o x
o o o o
o o x x
and permuting the columns of that would look something like
x o x x
o o o o
o o o x
o o x x
there i swapped the first column with the second, and the third with the fourth
does this make sense so far?
indigo yarrow
Yes
lyric fossil
ok. now how many ways are there to permute 4 different rows?
indigo yarrow
4!?
lyric fossil
yes
and for each of those row orderings
how many ways do we have to permute the columns?
indigo yarrow
4!
lyric fossil
so the answer is at most 4! * 4!
indigo yarrow
24 *24
lyric fossil
now we just need to check if any two of the permutations give us the same configuration
this is a little trickier to see, and is where i was going to use group theory, but there's an easy way to get the answer
imagine our grid is the following:
- - - -
- - - -
- - - -
- - - -
then we must assign to each row and column a number 1 through 4
1 2 3 4
- - - - 1
- - - - 2
- - - - 3
- - - - 4
this number represents the number of black squares in each row/column
we're essentially permuting the numbers on the right
and then on the top
now, the question is, if we change the order of the numbers on the right, can that affect the order of the numbers on the top?
indigo yarrow
Yes?
lyric fossil
no
indigo yarrow
Oh
lyric fossil
we're only moving blocks up or down
so the number for each column would stay the same
and similarly, if we permute the numbers on the top, we are only moving blocks left and right
so the number for each row stays the same
then we sort of just proved that no two different permutations can give the same result, i.e. no repeats
so the number of configurations is exactly 24^2
lyric fossil
a big part of combinatorics is phrasing the question the right way
then the problems can become much easier
indigo yarrow
.close
weak halo
what happened here, why when the 2 was factored 7 becomes 7/2
vocal sleetBOT
what happened here, why when the 2 was factored 7 becomes 7/2
soft walrus
what happened here, why when the 2 was factored 7 becomes 7/2
$2\cdot\frac{7}{2}=7$
twin meteorBOT
XxMrFancyu2xX
boreal remnant
😮
weak halo
why was this done?
soft walrus
in order to complete the square it's required to have the coefficient in front of the x^2 to be 1
karmic imp
When you complete the square, it's preferred that a = 1
soft walrus
right preferred not required my wording was bad
weak halo
would I arrive at the same answer if I divided it also by 2?
soft walrus
no becuase then we get $\frac{1}{2}(4x^2-14x)$
twin meteorBOT
XxMrFancyu2xX
soft walrus
if that's what you mean
weak halo
let me write my answer and Ill show it to you, just a moment
heres my answer if I try to put it into the form that was asked
and heres the answer to the question:
lookin at this im very confused
but they're the same right?
vocal sleetBOT
@weak halo Has your question been resolved?
vocal sleetBOT
@weak halo Has your question been resolved?
crisp galleon
heres my answer if I try to put it into the form that was asked
do u need the root of it?
crisp galleon
heres my answer if I try to put it into the form that was asked
u forgot to multiply the numerator nd denominator by 2
I believe
vocal sleetBOT
@weak halo Has your question been resolved?
deft arch
vocal sleetBOT
deft arch
but here is 7pi divided by 6
tell me any1
hlooooooooooooooooooooooooooooo
help.exe
.help
vocal sleetBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
stoic drift
wont angle be 5pi didvided by 6
Then it would be positive.
You need it to be negative. Hence 7pi/6
Also don't spam.
stoic drift
I just added pi because then it would become negative. Refer the unit circle.
In quadrant 1: All are pos
2: sin is pos
3: tan is pos
4: c is pos
stoic drift
Trignometric? Yes. But it depends on the function. You can search periodic identities complementary and supplementary identities on google and read through them. I can exactly pin point the identity name but it's something. You can refer the unit circle till then.
sudden compass
What is the rationalizing factor of a^(1/m) - a^(1/n)?
vocal sleetBOT
What is the rationalizing factor of a^(1/m) - a^(1/n)?
sudden compass
.close
sterile silo
Could anyone help with this?
vocal sleetBOT
Could anyone help with this?
paper depot
have you done such optimization problems before?
sterile silo
have you done such optimization problems before?
No not really
I know the surface area but I just need to find out the equation
paper depot
ok well youre gonna need to know either some calculus or some stupid trickery to do this problem
the idea is you have two dimensions -- the radius (r) and the height (h)
write down expressions for the volume and surface area in terms of these
you will have:
maximize π r^2 h
subject to 2πr^2 + 2πrh = 75
and then you can express h in terms of r and turn this into a "find the maximum value of this function" problem
vocal sleetBOT
@sterile silo Has your question been resolved?
sterile silo
and then you can express h in terms of r and turn this into a "find the maximum ...
Then whats h if it's r now?
paper depot
i don't understand your question sorry
sterile silo
i don't understand your question sorry
How do I express h in terms of r?
sterile silo
solve this equation for h
6r^2+6h=75?
π is 3.14 and times by 2 is 6.228 which rounds to be 6
I'm really not good at this
Sorry if it's wrong
paper depot
yeah it's not even close to what i asked for
i didnt ask you to replace pi with 3.14 and i didnt ask you to round anything
i asked you only to solve this equation for h
to isolate h, to make h the subject, whatever you want to call it
paper depot
ok tell me
if i gave you the equation
2x + 8y = 10
and asked you to solve for x
would you be able to do that
sterile silo
I can only do 1 variable
paper depot
ok so then you need to relearn algebra for sure
but ok like. alright ok two variables intimidate you
what if instead it was
2x + 19 = 10
would you be able to solve for x then
paper depot
these are all unrelated to each other
im trying to give you progressively simpler equations to solve
sterile silo
ok?
paper depot
so that i can grab onto something youre able to do
and then extrapolate that onto more complicated scenarios
with you
sterile silo
So..like talking down?
paper depot
no?
sterile silo
Wait
paper depot
i mean ok
sterile silo
Could I try
paper depot
do you think im talking down to you
if at any point you want me to go away then just tell me to go away and i will
sterile silo
I think I might know
paper depot
and we will stop this abruptly
paper depot
go ahead and try
make it clear which equation you are starting with so that neither of us gets confused what you're doing
paper depot
ok great
so you are able to do things like add/subtract the same shit to both sides and divide by the same shit on both sides
thats all you need to do here
$2\pi r^2 + 2\pi r h = 75$
twin meteorBOT
Ann (glomed)
paper depot
i need you to solve this equation for h
sterile silo
Alright...
Question:do I move the entire 2πrh to the other side?
Since it's technically 1 variable?
paper depot
no
patent nymph
Since it's technically 1 variable?
yes it is one thing but I don’t know if you could call it “one variable”
paper depot
to both
you add __ to both sides
you subtract __ from both sides
you multiply by __ on both sides
you divide by __ on both sides
you do not "move".
paper depot
subtracting 2πrh from both sides is valid but is not super helpful
sterile silo
Then how do I rearrange it?
paper depot
well i could suggest subtracting 2πr^2 from both sides as a first step
sterile silo
So 2πrh=75-2πr^2?
paper depot
that is what happens when you do that yes
paper depot
write out in full what happens when you do that.
sterile silo
rh=75-r^2
sterile silo
Oh ok
paper depot
your next step is to divide both sides by 2pir
and be careful not to mess that up, especially on the right hand side
vocal sleetBOT
@sterile silo Has your question been resolved?
sly fog
hi! i just need help if the 2nd pic is the correct interpretation or wtv you cal it for problem on the 1st pic 😅
vocal sleetBOT
hi! i just need help if the 2nd pic is the correct interpretation or wtv you cal...
merry python
Yes
merry python
hi! i just need help if the 2nd pic is the correct interpretation or wtv you cal...
also it is given that initially base distance=6
floral seal
i would like to ask part b, the model answer is like this and i dont quite understand
vocal sleetBOT
i would like to ask part b, the model answer is like this and i dont quite under...
floral seal
strange crater
which part don't you understand
floral seal
idk why I-A=0 means it doesnt exist
strange crater
you can't invert the 0 matrix
strange crater
you use the fact that (I - A) is idempotent to show why A^{-1} doesn't exist if (I - A)^{-1} exists
vocal sleetBOT
vocal sleetBOT
Available help channel!
sullen girder
vocal sleetBOT
sullen girder
what does -1 <= y =< 1 mean when y is a vector?
light jay
you can't invert the 0 matrix
wait isnt I - A also equal to 0
so 0^-1 = 1/0 right?
which is indeterminate 💀
unless this is a different topc
strange crater
wait isnt I - A also equal to 0
so 0^-1 = 1/0 right?
which is indeterminate 💀
You have to open your own channel
vocal sleetBOT
@sullen girder Has your question been resolved?
sullen girder
.close
vast shale
sqrt(x-5) = 2- sqrt(x+3)
why both sides need to be positive before squaring?
I need to move - sqrt(x+3) on the left side:
sqrt(x-5) + sqrt(x+3) = 2
why?
worthy citrus
to avoid introducing "fake" solutions. e.g:
x = -1
x^2 = 1
x = 1 or -1
its not strictly necessary, you could square from the start, you would then need to check at the end that your solutions are valid
vast shale
to avoid introducing "fake" solutions. e.g:
x = -1
x^2 = 1
x = 1 or -1
I thought conditions would do that
x-5 >= 0
and
x+3 >= 0
worthy citrus
sure that would be a way to get rid of solutions you dont want
vast shale
but it seems I need both, conditions and making both sides positive..
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
it's still not perfectly clear
topaz depot
vocal sleetBOT
topaz depot
Any idea of how to find the unknowns ?
west raptor
First of all name the time which the velocity is zero, say a. Then compute the area in terms of a and equate the result to -7
vocal sleetBOT
@topaz depot Has your question been resolved?
topaz depot
First of all name the time which the velocity is zero, say a. Then compute the a...
But changing that will leave you with two unknowns? That method would be okay if it was only for the area above the axis but thats not total displacement so I can't equate the result to -7 ?
pale epoch
naive heron
paper depot
.close
rigid carbon
vocal sleetBOT
rigid carbon
how do i go about this
conditional probability with compliments only?
pr not cloudy given not windy
vocal sleetBOT
@rigid carbon Has your question been resolved?
vast shale
I know its physics, but its technically calculus
vocal sleetBOT
I know its physics, but its technically calculus
river minnow
You know product rule, right?
vast shale
yes
river minnow
Then the step they did shouldn't be something new to you
vast shale
product rule is differentiation
river minnow
How would you write d/dx(p * q)
vast shale
which variable are we differentiating wit hrespect to?
river minnow
There isn't any in particular
d/dx(p * q) = dp/dx * q + p * dq/dx
Consider that as "multiplying both sides by dx"
vast shale
i dont get it
and I passed calculus with a 8.5 out of 10
anyways
thanks for trying
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
elder coral
how to be smart at persent
vocal sleetBOT
how to be smart at persent
spiral arch
@river minnow dms
vocal sleetBOT
lime gorge
,w how to be smart at persent
twin meteorBOT
Requested by Stephen#4771
lime gorge
Not too sure pal
fiery egret
pls help
vast shale
.close
clear obsidian
vocal sleetBOT
clear obsidian
Is this correct?
river minnow
Yes
clear obsidian
.close
olive oasis
how did it go from one equation to the other in the screenshot
vocal sleetBOT
how did it go from one equation to the other in the screenshot
twin meteorBOT
kazzz
flat whale
serene parrot
@olive oasis ^
vocal sleetBOT
@olive oasis Has your question been resolved?
crimson sedge
vocal sleetBOT
crimson sedge
how come Q1 is 4th and 5th
could do it like this:
since 16 is even number you would have to do 16+1/4 = 4.25
4<4.25<5 so its in between 4th and 5th position?
vocal sleetBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185> anyone?
crimson sedge
yes?
light jay
lets start with a
crimson sedge
ok
light jay
determine the lower quartile
lower quartile means 25%
the data is already in order
16/4 = 4
we take the 4th number then
which is 58
crimson sedge
but the answer is 59?
light jay
"given the median is 68 , a does not equal to b, find out them values
light jay
but the answer is 59?
how so?
crimson sedge
this is the ansewr
light jay
is that the teachers answer?
oh right im dumb lmao
this is stem and leaf
not cumulative
so its n+1/4 16 + 1 / 4 --> 17/4 --> 4.25
4.25 lies between 4 and 5
so we take those 2 values and find the middle
4 is 58, 5 is 60
58+60/2 = 59
@crimson sedge
crimson sedge
so when do you not add 1 and when do you DO add 1?
light jay
but hold on
another source is saying something else hmmm
welp that is sus
guess we are both clueless xD
this one is saying round up
so 4,25 --> 5
5 is 60
light jay
uh so median is 50%
16+1/2 --> 8.5 --> 9th value?
crimson sedge
the guy that does the model answer have a phd in mathematics so im pretty sure hes righy
light jay
17/2 = 8.5 right?
crimson sedge
its something to do about discrete and kcontinous but i can't remember
crimson sedge
17/2 = 8.5 right?
yh
light jay
its something to do about discrete and kcontinous but i can't remember
yeah i get it now so stem and leaf is discrete
something like cumulative frequency graphs is continuous
light jay
something like cumulative frequency graphs is continuous
looks like this
that smooth curve
crimson sedge
yeahj
crimson sedge
no
light jay
what do you mean no tho
crimson sedge
its between 8 and 9th value
so you would have to find the midpoint of 8th and 9th value
ill show you the answers
crimson sedge
crimson sedge
professor google just lied to me then
what did you search?
crimson sedge
im pretty sure its different for when its an even or odd sample number
in my question it is even and in your video example it is an odd sample number
light jay
where did you get these answers from btw?
light jay
oh damn it
crimson sedge
y
light jay
xD
crimson sedge
wbu?
light jay
year 10
light jay
yeah rip sorry that i couldnt help, but uh
crimson sedge
what
light jay
find the function that goes through these points
2,2 3,5 4,17
crimson sedge
are you getting this from a paper?
show me the question
or are you just making it up
light jay
are you getting this from a paper?
its a question i got from one of the people in this server
the person themselves didnt have an image
light jay
idk if i can
the clue is that it is an exponential function
i believe in you, you can do it!
crimson sedge
cba
crimson sedge
what is it
light jay
what is it
i wont tell the answer straight up but ill do the starting working out
remember how i said its an exponential yeah?
how would you write an exponential graph?
whats the form?
vocal sleetBOT
@crimson sedge Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
velvet cove
How to factor $x^2+x\log_{3}{2}-\log_3{6}$
vocal sleetBOT
How to factor $x^2+x\log_{3}{2}-\log_3{6}$
twin meteorBOT
Jash
regal bane
log(6) can be broken down
velvet cove
log(6) can be broken down
log(6)=log(2)+log(3)
regal bane
And log3(3) = 1
So we could do
x² + xlog(2) - log(2) - 1
Not necessarily sure if that's helpful, lol. Just we can do that
velvet cove
so factor by grouping
regal bane
Oh yeah, smart
regal bane
Bingo, well said. What did you need me for
velvet cove
wait cant we just say $(x-1)(x+\log_3{6})$
twin meteorBOT
Jash
regal bane
Yes we can
velvet cove
Yes we can
how to simplify $\frac{-\log_3{2} + \sqrt{(\log_3{2})^2+4\log_3{6}}}{2}$
twin meteorBOT
Jash
regal bane
That looks like your quadratic plugged into the quadratic equation
velvet cove
it turns out to be 1 somehow
regal bane
So we should be able to simplify that to:
1/2 - 1/2 log(6) ± (1/2 log(6) + 1/2)
That way we can choose which factor by choosing the sign
velvet cove
wait is it possible to simplify $\frac{\pm a}{\pm b}$
twin meteorBOT
Jash
velvet cove
is that just $\pm \frac{a}{b}$
twin meteorBOT
Jash
regal bane
Are they the same sign? Then always just +a/b
velvet cove
for any a,b
regal bane
Otherwise if you're allowed to choose each sign freely, then yeah that's ±(a/b)
velvet cove
alr ty
regal bane
Anyway, I can't help but notice that
1/2 - 1/2 log(6)
= [ log(3) - log(6) ] / 2
= log(1/2) / 2
= -log(2)/2
So that's the part before the ± done
pliant coyote
I have to get the y' of this function, and I have no idea at all. I'm guessing that I have to derivate, but still don't know where I get the y'
vocal sleetBOT
I have to get the y' of this function, and I have no idea at all. I'm guessing t...
floral pike
I have to get the y' of this function, and I have no idea at all. I'm guessing t...
I don't think you understand the vocabulary yet
y' is "the derivative of y"
floral pike
You just defined what you wrote as y
pliant coyote
Wait
floral pike
Is that expression not equivalent to y?
pliant coyote
So I just need to derivate?
floral pike
So I just need to derivate?
"differentiate"
pliant coyote
On the problem it comes like this
floral pike
$\frac{df}{dx}$
twin meteorBOT
Disorganized
floral pike
Just take the derivative of the expression with respect to x
magic belfry
vocal sleetBOT
magic belfry
is it even possible for such a tree to exist?
the root node would contribute 1 vertex
and then go down a level, and you have 5 vertices
oh, I suppose it is possible
if you branch out a full 5 leaf nodes on every level
you'll go from the root node, to having 5 leaf nodes, and then for every one of those leaf nodes, branch out by 5 again... you have 25 leaves
and if you branch out again, you have 125 nodes
but, you could "trim" off some of the branches to end up with 100 internal nodes
vocal sleetBOT
@magic belfry Has your question been resolved?
bleak tundra
hello
empty frigate
,rccw
twin meteorBOT
bleak tundra
soo how should i start