Look up here
#help-10
warm shaleBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
plush vapor
im listening
fierce lagoon
Nvm I did a dumb
It's right
So
You get $y = k(x^2-2x-10)$. You have a point (4, -6) so you need to plug values in:
$$-6 = k(-2)$$
What would k be?
warm shaleBOT
Umbraleviathan
fierce lagoon
"k" is gonna be an amplifier btw
plush vapor
im writing stuff down rn but 3
warm shaleBOT
Umbraleviathan
wooden cipher
Do you know vietas foemulas
fierce lagoon
I gtg but DM me if you have questions about that one problem
wooden cipher
I can take over
plush vapor
**Umbraleviathan**
what you said ab this problem made sense ty
wooden cipher
Do you need any more help?
plush vapor
Do you need any more help?
not for the problem we just finished up but i have 2 more questions i posted
in case u know those
plush vapor
i tried to set them to eachother and then i put it into the quadratic formula but i got sum different than it said on the answer key
wooden cipher
Ok so you got
3x+5=3x^2-2x-4 right?
nocturne minnow
i tried to set them to eachother and then i put it into the quadratic formula bu...
Post your work
wooden cipher
Have you checked your x values in a calculator?
plush vapor
no
wooden cipher
Seen as the answer key has rounded numbers, check in a calculatir
nocturne minnow
Then you should check your answer by putting it in a calculator
wooden cipher
Also the first equation says 3x+5 and you did 2x+5
plush vapor
oh i messed up
wooden cipher
Think about how he simplified the fraction
He went from 6 to 3
He only multiplied by 2
nocturne minnow
Also that method you are doing, is not proper
The quadratic formula is used to find the roots and the roots occur when the equation equals 0
So you need to move everything to one side first before you can use the quadratic equation
plush vapor
alr
wooden cipher
He did move everything to one side
nocturne minnow
Then why is there a +5?
I don't understand what on earth you did after $$\frac{5 \pm \sqrt{133}}{6}$$
wooden cipher
To get the y coord he plugged it back in
warm shaleBOT
dldh06
plush vapor
To get the y coord he plugged it back in
^^
the x values are correct and the y values are wrong
nocturne minnow
Yes, because $$\frac{3}{6} \neq \frac{1}{3}$$
warm shaleBOT
dldh06
plush vapor
ok so how would i get accurate y values
plush vapor
oh its cuz my ass changed the denominator wdnkjwdn
ok i didnt understand what u said at first now i get it
obtuse pebbleBOT
@plush vapor Has your question been resolved?
plush vapor
can someone confirm the y values for me?
i dont know what it is still i know the denominator isnt 3
nocturne minnow
Simplify $3 \left(\frac{5 \pm \sqrt{133}}{6}\right)$
warm shaleBOT
dldh06
nocturne minnow
i dont know what it is still i know the denominator isnt 3
Knowing that $$\frac{3}{6} \neq \frac{1}{3}$$
warm shaleBOT
dldh06
plush vapor
my final question, if anyone can solve ping me with the solution
nocturne minnow
my final question, if anyone can solve ping me with the solution
We're not here to give you the answers. You know sine law, apply it
nocturne minnow
No, I'm not. It's part of the rules, if you read that
• When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.
plush vapor
in this question specifically there’s 2 triangles what would i do in that case
looking off the answer key it signifies there’s 2
high lily
consider the ambiguity of the sine law
obtuse pebbleBOT
@plush vapor Has your question been resolved?
warped kayak
Johnson plumbing charges $30 plus $50 per hour to make a house call, anderson plumbing solutions charges $60 per hour to make a house call. for what length of time is Anderson plumbing solutions more expensive?
obtuse pebbleBOT
Johnson plumbing charges $30 plus $50 per hour to make a house call, anderson pl...
@warped kayak Has your question been resolved?
warped kayak
<@&286206848099549185>
willow ravine
J = 30 + 50x
A = 60x
Solve for x.
Wait
Anderson's is always cheaper
Wait I’m going smooth brain
Disregard
warped kayak
Anderson's is always cheaper
No that's impossible, let's take 10 hrs of calling
Johnson = 30 +10(50)= 530
Anderson= 60(10)=600
I don't understand how to solve the question in terms of variables tho
Like making linear equations and stuff
willow ravine
Ahh I see
Yeah use my equations and go back to
30+50x < 60x
30<10x
3<x
So, every x greater than 3 Anderson’s will be more expensive
So [4, infinity) is the interval
Does that make sense?
So x = 0, 1, 2, 3 -> Johnsons is more expensive
x= 4, 5, 6, 7, 8, ... -> Anderson’s is more expensive
warped kayak
30+50x < 60x
I understand how u derived 30+50x<60x equation, but how did you come at the 30<10x, is it just simplifying the initial equation,if yes how did u do that?
willow ravine
You want to know when anderson’s is greater than Johnson’s
And Johnson’s = 60x
So let 60x > 30+ 50x
warped kayak
Yes i understand till here
willow ravine
You only flip the inequality when multiplying or dividing by a NEGATIVE number.
Addition and subtraction stays the same inequality.
timid silo
obtuse pebbleBOT
fierce lagoon
Complete the square
burnt blaze
lmao
fierce lagoon
Also is that homework
burnt blaze
that looks like a quiz
fierce lagoon
Wdym by instruction
timid silo
no ill show u
look
it goes warm up
then it teaches u how to do it
im on the instruction part
timid silo
which is teaching u
timid silo
im trying to get it
fierce lagoon
So you should complete the square
fierce lagoon
Well try competing the square
timid silo
So you should complete the square
ok so i add 8 to both sides correct
fierce lagoon
Yeah
timid silo
ok
fierce lagoon
Yeah
Wel actually
Before doing halving thing
Multiply everything by -1
So you get $x^2-10x = -8$
warm shaleBOT
Umbraleviathan
fierce lagoon
**Umbraleviathan**
(There's a negative 8)
fierce lagoon
Yeah
fierce lagoon
It is
Second one
(X-5)
Idk how you got (x+5)
When we literally had a -10x term
warm pivot
Omg
obtuse pebbleBOT
@warm pivot Has your question been resolved?
timid silo
well we know h and r right
spice basalt
What have you tried so far? The goal at hand is to calculate the surface area of the cylinder inside the box. For this you are given a formula which has two unknown quantities in general, you should know one and can calculate the other.
royal basin
@warm pivot do you still need help with this?
royal basin
ok
warm pivot
Yay
royal basin
do i understand correctly that you have made zero progress so far?
warm pivot
Yes
royal basin
ok
warm pivot
This ^3 is trippin me out
warm pivot
I do not know how to convert cubic centimetre to squared
royal basin
you don't
volume and area are fundamentally different quantities and are not interconvertible
warm pivot
Oh okay
royal basin
your first order of business is to find the value of the letter x in the diagram.
do you know how to do that?
warm pivot
X?
royal basin
lowercase x.
warm pivot
I don’t see x
royal basin
the base of the box is a square with side length 2x
look at the bottom of the diagram
royal basin
given that you know the volume of the box, do you know how to find the value of x?
brb
warm pivot
No could you please tell me how to do it?
royal basin
ok
warm pivot
Thank you so much
royal basin
do you know how to find the volume of a box given its length, width and height?
royal basin
ok, then tell me how you would go about doing so.
warm pivot
Times length, width and height
warm pivot
2x cm
royal basin
and the width?
warm pivot
2x cm
royal basin
and the height?
warm pivot
8cm
royal basin
great
now can you write down an equation that says "The volume of the box is 288 cm^3"?
warm pivot
Ok
royal basin
note however that i ONLY asked you to write down the equation, not solve it yet.
royal basin
you're using the same symbol for the letter x and for multiplication. this is not good.
warm pivot
Oh okay
royal basin
now solve the equation 2x * 2x * 8 = 288 for x.
warm pivot
Wait. I do not even have the x in (2x) solved
royal basin
idk what exponent laws you might want to apply here (other than maybe "multiplying something by itself is squaring") but like
maybe just do it and show me
warm pivot
like 2x^1 . 2x^1 = 2x^2
royal basin
2x * 2x is not 2x^2.
royal basin
4x^2
remember that the ^2 in 2x^2 only applies to the x, not to the 2 as well as it would in (2x)^2.
royal basin
your left hand side is 2 * x * 2 * x * 8
warm pivot
Do I add this together?
royal basin
add what together?
again i don't see what's stopping you from going back to your paper and just solving the damn thing. with algebra.
warm pivot
32^2?
royal basin
what does that mean? are you asking "does 2 * x * 2 * x * 8 simplify to 32^2?"
warm pivot
I think so. Let me go back and do it again
royal basin
what do you mean "i think so"??????
how can you be uncertain of what you yourself are saying?
royal basin
i asked you, "is this what you're asking or not?" the answer to that should be a definitive "YES that is what i'm asking" or a definitive "NO that is NOT what i'm asking" nothing else
warm pivot
Sorry Ive never done this
royal basin
you've never answered someone's question directly?
warm pivot
I have
royal basin
and NO, you are wrong. 2 * x * 2 * x * 8 does NOT simplify to 32^2.
warm pivot
I was unsure that my answer was correct
royal basin
ok then you should phrase yourself better
warm pivot
Ok
royal basin
instead of "32^2?" you should've said "i simplified the LHS to 32^2, is that correct?"
warm pivot
Yes
royal basin
anyway, it's not 32^2, it's 32x^2.
royal basin
you have the equation 32x^2 = 288.
the right-hand side is a number and needs no more simplification.
warm pivot
got it
royal basin
your goal is still to solve this equation for x.
royal basin
this is not yet the answer
also you were supposed to like
solve this equation as you would solve any other equation
instead of all this nonsense you appear to be going through
warm pivot
My bad
royal basin
,calc 288/32
warm shaleBOT
Result:
9
9
warm pivot
No. 9*9 is not 9
royal basin
then why are you saying x is 9?
warm pivot
Yes
royal basin
this one right here
and notice that the sides of the box are also diameters of the cylinder's circular base
warm pivot
Yes I see that
warm pivot
2x cm
royal basin
no
warm pivot
1x cm
royal basin
yes, the radius of the cylinder is x.
or, as we've so painstakingly solved for it now, 3.
now you know the radius and the height of the cylinder, and you've been supplied with the formula for the SA of a cylinder that'll give you exactly what is asked for in the problem
are you able to continue on your own or do i need to handhold you through plugging the numbers into it
warm pivot
No. I just want the answer checked by you once i'm done
royal basin
ok
spice basalt
Sounds good to me
royal basin
yes, this is correct.
warm pivot
ok
Also, Sorry for putting you through this tomfoolery. I think I have learned something from you
I have learned how to solve questions like this
And Hopefully your lesson will do we some good in my exam tomorrow. thank you so much and have a great rest of your day @royal basin
obtuse pebbleBOT
Available help channel!
celest zodiac
obtuse pebbleBOT
celest zodiac
can someone walk me through this or show me how to solve this step by step
obtuse pebbleBOT
@celest zodiac Has your question been resolved?
heady coral
I'm looking for pairs of functions f, g with this property:
g is symmetric to f across the (0, 1), (1, 0) diagonal for x in (0, 1)
obtuse pebbleBOT
I'm looking for pairs of functions `f, g` with this property:
`g` is symmetric t...
heady coral
I don't care at all about any x outside of (0, 1)
Here's an example of a function pair I found:
If a = b then f is symmetric across the diagonal to g
<@&286206848099549185>
obtuse pebbleBOT
@heady coral Has your question been resolved?
heady coral
I think I can achieve this for any function g that's 90° rotated of f.
spice basalt
After playing around for a second this should reflect the graph of any function you throw at it, obviously after reflection you won't always get the graph of another function like with what I left it with
spice basalt
np
heady coral
.close
lean pilot
hi could i have help with this question please
obtuse pebbleBOT
hi could i have help with this question please
lean pilot
so normally im used to 2x2 with a 2x2 basis
kind hawk
if $e_1(x)=1$ and $e_2(x)=x$ is the standard basis $E$, then $b_1=1+4x=e_1+4e_2 = \begin{pmatrix} 1 \ 4 \end{pmatrix}_E$
warm shaleBOT
Denascite
kind hawk
so using that you can convert from polynomials to vectors and back
to convert back, for example $\begin{pmatrix} 6 \ 12 \end{pmatrix}_B = 6b_1+12b_2 = 6(1+4x)+12(1+3x)$ and then simplify further
warm shaleBOT
Denascite
obtuse pebbleBOT
@lean pilot Has your question been resolved?
lean pilot
**Denascite**
so we would change the matrix T to basis B ? because i tried changing the basis B to E so it would be (1,4) and (1,3) but that didn't give me the solution
so i tried something like this
and i thought the answer would be (2,0) (0,3) but it wasnt
now i've got this but i'm confused on how to work on this
kind hawk
we want to know what T(e1) and T(e2) are with respect to the standard basis
we know what T(b1) and T(b2) are with respect to the basis B
from there it's more or less the same steps as the previous exercises
express e1 and e2 as linear combinations of b1 and b2
then calculate T(e1) and T(e2) using that and express those in terms of the standard basis
if you always keep track with respect to which basis each vector is written then this is a straightforward calculation
obtuse pebbleBOT
@lean pilot Has your question been resolved?
lean pilot
this is scrambling my brain
so i've got e1 and e2 as this
and also this wrt basis B
kind hawk
So we know e1=-3b1+4b2. Therefore T(e1)=-3T(b1)+4T(b2)=-3(6b1+12b2)+4(-b1-b2) =-22b1-40b2=-22(e1+4e2)-40(e1+3e2)=-62e1-208e2=(-62,-208)_E
Therefore the first column of T with respect to E is (-62,-208)
(check my math)
@lean pilot
We switch the basis around a lot
lean pilot
i'll get onto it in a second
kind hawk
We start in basis E, translate to basis B, use T with respect to basis B and then translate again to basis E
There is a 3b1b video about basis transformations, check that out for some intuition
lean pilot
ah okay i think i understood the steps you did now
thank u so muchj
lemme try it with e2 and see if it works
kind hawk
Maybe they have a life
pseudo swift
it's not like you need the helper role to help ppl
lean pilot
i'm still getting it wrong @kind hawk
would you mind checking my working for the e2
kind hawk
That is strange. What exactly did you put in?
lean pilot
ahh i'm an idiot i was putting it into the wrong question
hahaha that's my fault sorry
in my defence they're similar
so the only difference with this one is we wouldn't change it back to the standard basis?
kind hawk
Well in that one we need to change it "back" to basis B
We start in basis B, convert to E, apply T and then convert back to B
lean pilot
let me give that a go
i also wanted to ask if there's anything wrong with this solution
pardon the writing but my working was along these lines
which normally works for 2x2 matrix 2x2 basis but it didnt work this time
kind hawk
I don't see where you get (5,-4,-2) from
kind hawk
Ah
lean pilot
and then did solved the basis w/ that solution
kind hawk
That's wrong
The matrix is the representation with respect to basis B. So if you want to get T(b1) then you need to multiply that matrix with (1,0,0)_B
And that will give you T(b1)_B
We need to do the same stuff as before here, just with 3x3
Convert e1 to basis B, apply T, then convert back to basis E
Repeat for e2, e3
lean pilot
We start in basis B, convert to E, apply T and then convert back to B
could you go over how we do this? i'm confused on whether we'd put in the (4+2x) and (3+x) when going from basis e to b if we do that at all
so i think what i've done is like what we did before
so would we do 1+3x in terms of e1 and e2?
kind hawk
where do you get e1=4+2x from?
kind hawk
e1 is still equal to 1, e2 is still equal to x
kind hawk
b1=1+3x
lean pilot
b2=3+7x
kind hawk
T(e1)=(4,2)_E=4e1+2e2=4+2x
lean pilot
ah okay
kind hawk
b1=1+3x=e1+3e2=(1,3)_E
lean pilot
what would the process be? cause i put t(e) in terms of b1 and b2
and then i changed that to the standard basis
kind hawk
T is in terms of the standard basis
we know T(e1)=(4,2)_E and T(e2)=(3,1)_E
so T(b1)_E=T(e1+3e2)_E = T(e1)+3T(e2)=(4,2)_E+(3,1)_E=(7,3)_E=7+3x
kind hawk
then write 7+3x as a linear combination of b1,b2
lean pilot
so T(b1)_E=T(e1+3e2)_E = T(e1)+3T(e2)=(4,2)_E+(3,1)_E=(7,3)_E=7+3x
sorry is there a mistake here
does 3T(e2)=(3,1) ?
kind hawk
ah yes should be 3*(3,1)
lean pilot
then write 7+3x as a linear combination of b1,b2
would this be the solution?
so im guessing we write it as (.. , ..)
kind hawk
the coefficients of that are the first column of the matrix representation of T with respect to B
lean pilot
we wouldn't sub in the b1 b2 values?
yep
oh becuase this is with respect to the basis b?
kind hawk
yes this is with respect to basis B
so maybe more appropriately the first column is (-20, 9)_B
lean pilot
and i think if we wanted it to respect to e we would sub in those values for b1 and b2 and that would swap the basis back to E?
yep
kind hawk
we already have the representation with respect to E given
lean pilot
ahh okay
lean pilot
Convert e1 to basis B, apply T, then convert back to basis E
this is my last question, and this is the working i've done
do you think you could spot where i went wrong?
is that matrix on the bottom left in the wrong order? that was how i got those equations on the right
and then i went and did this
kind hawk
not sure what that matrix at the bottom left is supposed to achieve
lean pilot
not sure what that matrix at the bottom left is supposed to achieve
i used that augmented matrix to find e1 e2 e3 in terms of b
kind hawk
that seems correct. or it's at least the correct steps. don't really wanna check the math
lean pilot
then the math might be incorrect
kind hawk
i used that augmented matrix to find e1 e2 e3 in terms of b
I don't see how that matrix helps for that
lean pilot
how would you get it? because i just solved that system to find e1 in terms of b1 b2 b3
kind hawk
to find e1 in terms of B you need to solve the systems $\begin{pmatrix} 1 & 0 & 1 & 1 \ -2 & -1 & 0 & 0 \ 0 & 1 & 1 & 0 \end{pmatrix}$
lean pilot
and then repeated for e2 and e3
warm shaleBOT
Denascite
kind hawk
and then similarly for e2 and e3
lean pilot
oh that's probably where i went wrong then
you wouldnt solve it for the columns of this matrix?
kind hawk
no
lean pilot
oh because e1 is 1,0,0 and then the rest falls into place i guess?
kind hawk
those are already given in terms of B
lean pilot
righto
kind hawk
they are (5,1,0)_B etc
kind hawk
oh and I spotted that you forgot a minus
$\begin{pmatrix} 1 & 0 & 1 & 1 \ -2 & -1 & 0 & 0 \ 0 & 1 & -1 & 0 \end{pmatrix}$
bottom right
warm shaleBOT
Denascite
kind hawk
as a hint
do all the steps with the matrix $\begin{pmatrix} 1 & 0 & 1 & 1 & 0 & 0\ -2 & -1 & 0 & 0 & 1 & 0\ 0 & 1 & -1 & 0 & 0 & 1\end{pmatrix}$
warm shaleBOT
Denascite
kind hawk
then you are essentially solving all systems at the same time
lean pilot
i rref that big matrix?
kind hawk
yes
lean pilot
ok i haven't seen that before tysm
kind hawk
because otherwise you would essentialy rref the three left columns the same way three times
drowsy girder
If we arrange the numbers 1, 2,. . . , 8 into the vertices of the cube and then join each edge
the sum of the numbers in the vertices that that edge connects. Can we achieve so that all the numbers
the associated edges are different from each other?
I used google translate so question probably seems confusing
timid silo
ig it meant points along a circle?
pentagonal patterns?
the translation isn't making much sense 
proven zephyr
try deepl translate, it's usually better
drowsy girder
try deepl translate, it's usually better
Ill try that
drowsy girder
try deepl translate, it's usually better
Doesnt have the language i need 
kind hawk
so we want to assign numbers to the edges and vertices such that
- the vertices are numbered 1-8
- the number on each edge uv is the sum of the numbers at u and v
- the numbers for all edges are different
drowsy girder
Yes
Ig ( i dont know what vertices means) but i hope its what the question means
I tried it and i just got its false
My problem is making some valid proof
kind hawk
vertices = corners
drowsy girder
Oh yea thats it then
drowsy girder
do you know graph matchings?
Nope
This is how i drew the cube
In hope to make the problem easier
drowsy girder
so we want to assign numbers to the edges and vertices such that
1) the vertices...
I tried it enough times to get that i need to prove that you cannot do this
But idk how to prove it
drowsy girder
Its constant
kind hawk
maybe first what are the possible edge numbers
drowsy girder
Wait maybe it isnt
drifting wraith
it is constant
you can't put a number somewhere where it doesn't contribute three times
they all contribute the same
kind hawk
=108
drowsy girder
maybe first what are the possible edge numbers
3 to 15
drowsy girder
,w 15/2 * (15 + 1) - 3
warm shaleBOT
drowsy girder
117
warm shaleBOT
Result:
9
9
kind hawk
lul
yes ok
so we have every number 3 to 15 except 9
in particular we need to have the numbers 3,4,5 and 13,14,15
how can you write each of these?
drowsy girder
3 can be written as 2 + 1 , 4 as 3 + 1 , 5 as 4 + 1
13 is 6 + 7 , 14 is 6 + 8 , 15 is 7 + 8
kind hawk
can we have 6 and 7 next to each other if need to have 6 +8 and 7+8 ?
drowsy girder
No
kind hawk
good so 13 needs to be written as 8+5
same for 5 and not being able to write it as 2+3 btw
so we now know that the neighbors of 1 have to be 2,3,4 in some order and the neighbors of 8 have to be 5,6,7 in some order
drowsy girder
Well now we do
kind hawk
I'm not sure if there is a nice argument to finish the rest of the proof
but with a bit of casework we can see that those restrictions are impossible
essentially we can pick one corner to be 1 and then 2,3,4 the neighbor corners. with rotations/mirroring etc you only need to consider one case for that
then 8 needs to be opposite the 1 because that's the only corner left with three unfilled neighbors
and then we see that it's impossible to fill the remaining corners with 5,6,7 without creating a 9 sum
drowsy girder
Well this way is kinda nice because it shows what would need to happen in order to make this possible and prove its impossible.
My thought was just how to prove this is impossible
kind hawk
yes that is often the case with proofs
we show what would be necessary for it to be true
rose garnet
im sorry if my question sounds silly but what is 5=2^x
like do u need to use log to find x and if so how?
kind hawk
then we show that this necessary condition cannot be fulfilled
kind hawk
im sorry if my question sounds silly but what is 5=2^x
like do u need to use log...
get your own help channel #❓how-to-get-help
rose garnet
sorry
obtuse pebbleBOT
kind hawk
u2
obtuse pebbleBOT
Available help channel!
restive pilot
Greetings, I'm solving for y $$\int \frac{1}{y} dy = ln(|y|) = x + C $$
obtuse pebbleBOT
Greetings, I'm solving for y $$\int \frac{1}{y} dy = ln(|y|) = x + C $$
warm shaleBOT
Eichhorst
restive pilot
the x +C comes from my integral euqation, but how do I solve for y exactly now? if I take x+c to the power of e? is it e^(x+c) or e^x+e^C?
royal basin
e^(x+C)
summer spire
restive pilot
thanks for the help, but this is the wrong integral lol solution doesnt make sense
.close
supple basin
.help question
obtuse pebbleBOT
No command called "question" found.
supple basin
.help I
obtuse pebbleBOT
No command called "I" found.
supple basin
.help
obtuse pebbleBOT
Commands:
clopen: .close, .reopen
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
formal musk
obtuse pebbleBOT
timid silo
don't know logic, but isn't that just invalid because it's the converse?
formal musk
How is that converse.
The converse is flipping two statements.
He is not flipping two statements.
timid silo
it's the converse of the contrapositive
formal musk
How?
timid silo
what would the contrapositive be?
proven zephyr
is it not law of detachment btw 🙂
timid silo
it's not even true...?
proven zephyr
does law of detachment have to be true btw
cuz like...
if p is false
q is false
timid silo
but it's not provoked
proven zephyr
yeah exactly
formal musk
So then?
proven zephyr
it's not syllogism too
formal musk
So it is not syllogism and detachment?
proven zephyr
detachment idk
dusk mantle
the statement is false
proven zephyr
yeah exactly
dusk mantle
so just invalid, no?
proven zephyr
ig so
dusk mantle
detachment says nothing about q when p is false
formal musk
detachment says nothing about q when p is false
so for detachment to be an option both q and p have to be true?
dusk mantle
for detachment to be the answer, you need a statement of the type if p then q
and a statement p
proven zephyr
so for detachment to be an option both q and p have to be true?
ig so
formal musk
oh so it has to be conditional?
dusk mantle
here you have if not p then q, and a statement p
formal musk
oh so it has to be
dusk mantle
well the conditional here is implied
formal musk
true p and true q
dusk mantle
"if the dog is provoked, he will bark" is your statement saying if p then q
dusk mantle
"the dog is not provoked" is the statement not p
dusk mantle
yeah
formal musk
so it is invalid
dusk mantle
yes
formal musk
thank you.
dusk mantle
imagine here the dog barked no matter what
formal musk
yes
dusk mantle
then it is true that if the dog is provoked, he will bark
formal musk
that is a counterexample
dusk mantle
but it is also true that if he is not provoked, he will bark
dusk mantle
that is a counterexample
yeah
formal musk
formal musk
yeah
and wouldn't it be the same thing for this one
because john could be doing something else
dusk mantle
exactly
formal musk
no
dusk mantle
why not?
formal musk
he could be doing something else
dusk mantle
well imagine he is watching tv. can you say that he is eating lunch or playing soccer?
dusk mantle
right
dusk mantle
what is syllogism?
formal musk
a statement where a conclusion is drawn
formal musk
what is syllogism?
dusk mantle
I think a syllogism is of the form "if p then q" and "if r then p" so "if r then q", no?
dusk mantle
do you have implications here? (statements of the form if p then q)
dusk mantle
yes, but there are also no conditional statements
dusk mantle
contrapositive also uses an implication
it says that a statement "if p then q" is the same as a statement "if not q then not p"
formal musk
so it is converse and inverse at the same time
which is not being implied in here
so none of the options are right
then what?'
dusk mantle
I'm not sure exactly what the exercise defines the "or rule" to be, but I'm guessing it's something like "p or q and not q implies p"
but you know he's either eating lunch or playing soccer
so if he's not doing one of them
he has to be doing the other
static mason
obtuse pebbleBOT
static mason
what is the formula
proven zephyr
what?
static mason
radian is pi
static mason
idk
proven zephyr
ok so
if arc length = radius, what is the angle in radians?
@static mason can you answer this?
static mason
if arc length = radius, what is the angle in radians?
idk
proven zephyr
ok so
proven zephyr
this is called 1 radian
static mason
this is called 1 radian
1 radian is 180/pi?
proven zephyr
no
A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle.
static mason
so the circle is 3.14 radians?
proven zephyr
uhh i think no?
static mason
2
static mason
2r/r
proven zephyr
yes
static mason
thanks
static mason
tysm\
static mason
.close
obtuse pebbleBOT
proven zephyr
https://youtu.be/JmLN3QxshlE
watch this for better understanding @static mason
static mason
watch this for better understanding <@494907296145473557>
k
obtuse pebbleBOT
Available help channel!
formal musk
obtuse pebbleBOT
formal musk
How would you do this.
formal musk
How are chores in this problem
proven zephyr
yeah it isnt
formal musk
syllogism
proven zephyr
yes
formal musk
law og syllogism
proven zephyr
wait im not sure too
formal musk
could i get a helper in here
formal musk
wdym
cloud dove
Ive never done a math logic class, but ive done categorical logic in my eng class
like if A then B , if B then C, therefore A then C
er
hypothetical syllogism
thats what it was
proven zephyr
like if A then B , if B then C, therefore A then C
yeah syllogism
cloud dove
so Therefore, If I am at home, then the TV is not on
formal musk
ok thanks
proven zephyr
or not
formal musk
.close
obtuse pebbleBOT
obtuse pebbleBOT
✅
formal musk
@cloud dove
cloud dove
hello
proven zephyr
hola
formal musk
so many people could not understand this question
can you
We were talking about how there is no error
but then we weren't getting the exact idea.
proven zephyr
if p is true -> q is true
if q is true -> r is true
if p is true -> r is true
like this?
formal musk
i think
cloud dove
That is basically the same thing:
its in the form of
p->q
q->r
therefore p->r
rains is p
carrying is q
r is the state of being dry
cloud dove
so p->r is jsut
formal musk
thanks
proven zephyr
i never did that too
obtuse pebbleBOT
@formal musk Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wooden heron
obtuse pebbleBOT
wooden heron
This is my revision for a upcoming exam and whilst everything I understood I couldn't do this
drowsy girder
a or b?
main cedar
What is the largest possible time
main cedar
Since it asks for the range we have to subtract it by the smallest time
Which is given
wooden heron
Ahh so 20 minutes - 3 minutes 40 secs?
main cedar
Yes
devout rose
hi i just want to make sure is a = -1 for this
obtuse pebbleBOT
hi i just want to make sure is a = -1 for this
wooden cipher
Seems right to me
pseudo swift
+1 ^
wooden cipher
Np
devout rose
.close
wooden cipher
I need help understanding markov chains
obtuse pebbleBOT
I need help understanding markov chains
wooden cipher
I have something that looks like this
I dont know how to set up the expected value equation
brave bramble
Expected value equation is a bit later than you're at. You first want the probability of landing the second head in a row on flip n
brave bramble
It's a bit tough because we have to ensure there's no double-heads before flip n
wooden cipher
Wait no im thinking about a diff type of problem
brave bramble
I'd put that on your matrix, a column for "has flipped a double head and has stopped"
wooden cipher
We need matrices?
brave bramble
Yeah Markov chains use matricies for solving probability problems
wooden cipher
Ah shoot
I need to more research
https://artofproblemsolving.com/wiki/index.php/2021_AIME_I_Problems/Problem_12
Ive seen people do it without matrices so i was wondering
Ok so hold on, i would make a matrix like
Making it rq
Like this?
brave bramble
Oh okay, so your W is already set up for "has won"
brave bramble
Yeah you've got the right idea, the matrix represents probability of transitions
All columns should sum to 1, so that something happens
brave bramble
Excuse me, it's been a little while haha
brave bramble
Let's say something is W. What happens "next turn"?
brave bramble
Sorry I got distracted there. I'll call this matrix T.
wooden cipher
Ok
brave bramble
Multiplying this on the left by (0,1,0) (that is, if we pretend we start having already flipped a tail), will give us the probabilities of being in any given state after a flip
T² does the same except after two flips
wooden cipher
So we start with
0 .5 0
0 .5 0
0 0 0 right?
Then we just multiply by successive powers of the previous matrix?
brave bramble
With your matrix the way it is, the middle column gives the probabilities
wooden cipher
Ah cool!
brave bramble
,w matrix {{0,0.5,0.5},{0.5,0.5,0},{0,0,1}}^5
warm shaleBOT
brave bramble
Uh, no something is up. Give me a sec lol
Yeah nope, I mean the row, not the column
Sorry working transposed is getting me
At any point within 5 flips there's a 59.3% chance of flipping two heads in a row
,w diagonalizable matrix {{0,0.5,0.5},{0.5,0.5,0},{0,0,1}}
brave bramble
Nice. This matrix can be diagonalized as well, meaning we can use this to create a fast formula, rather than having to multiply matricies out
wooden cipher
Ok ive gotta go now, do you mind if i ping you again later?
brave bramble
Yeah! Feel free.
timid saddle
I don't really understand how theta = -sqrt(3)/2 is expressed as a straight line here or how it converts to (0, 1) rectangular
obtuse pebbleBOT
I don't really understand how theta = -sqrt(3)/2 is expressed as a straight line...
timid saddle
actually i get the graphing, not the conversion
wooden cipher
You have to graph the line, not just a coordinate
timid saddle
is the radius 1 in this case?
timid saddle
so how do u get (0,1) rectangular?
timid saddle
You have to graph the line, not just a coordinate
ya it's a line, that makes sense.
wooden cipher
It is not just (0,1) it could be (0,0.5) or (0,-69)
You need to find the equation for the line
Classic y=mx+b
timid saddle
well its a homework question , i got wrong & it shows the answer as (0,1)
timid saddle
ya u can see its grayed out
knotty crow
x/y = cot(-3pi/2) = 0 --> x = 0
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid saddle
How do I correctly convert the parametric equation (4 cos(t), 5 sin(t)), 0 <= t <= 2pi to rectangular form?
https://www.desmos.com/calculator/ifzpjxgmw6 when I convert, I only get a semi-circle in rectangular form