by sharing our ideas we will probably reach an answer
#help-26
balmy spruce
if you want i can send the professor's solution maybe it will be helpful? although i doubt that solution tbh
spare smelt
(A-B) + X + K = E, where K is everything in E, not in A or X, and these are all disjoint sets
let's rewrite:
X = E - K - (A-B) = E - K - A + B
now we just need to find a form for K:
K = (A + X)', where ' means complement
so we can write:
X = E - (A + X)' - A + B
but that depends on X
so nvm
if you want just send your prof's soln
somehow we have to use the fact that they're all in the powerset
spare smelt
yeah i'm lost lol. hopefully someone else can explain
topaz sinewBOT
@balmy spruce Has your question been resolved?
static juniper
can anyone help me with 9?
topaz sinewBOT
can anyone help me with 9?
static juniper
,rotate
thorny flameBOT
dense crescent
Is it like true or false?
neon iron
yo
static juniper
numerical
jade cape
Is it proof?
static juniper
need to find the radius
jade cape
Oh
dense crescent
need to find the radius
I c
static juniper
yeah
jade cape
Oh on a circle of radius ?
static juniper
Oh on a circle of radius ?
yes we need to find the radius of the locus of the centroid
dense crescent
Nop?
static juniper
sorry i dont follow
static juniper
but then we're assuming the centre to be 0 0 no?
dense crescent
Yea i mean
He didn't mention
So it's ur wish
Ull get same thing for every center
static juniper
what if they ask us to show our work lol.. in that case we need to take general coordinates for center
dense crescent
Well then
Consider a,b
And this is mains question right
Why would they ask to show work
static juniper
And this is mains question right
Why would they ask to show work
its my tuition they ask us how we did it sometimes
thorny flameBOT
static juniper
how
topaz sinewBOT
@static juniper Has your question been resolved?
topaz sinewBOT
@static juniper Has your question been resolved?
static juniper
.close
jagged tusk
can someone please explain to me why did they first moment at o using Rx and Ry only and not including the whole forces or by moment at o with all forces?
topaz sinewBOT
can someone please explain to me why did they first moment at o using Rx and Ry ...
jagged tusk
this is the problem
topaz sinewBOT
@jagged tusk Has your question been resolved?
topaz sinewBOT
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Available help channel!
icy dust
7y-1=2(y+3)-2
topaz sinewBOT
7y-1=2(y+3)-2
fair thorn
distribute the 2
icy dust
im confusd
fair thorn
then just move the constants to one side and the y-terms to the other
errant yoke
Anyone know how to calculate newton polynomials using table?
topaz sinewBOT
Anyone know how to calculate newton polynomials using table?
fair thorn
what
errant yoke
.close
hallow depot
what?
keen lance
How do I approach this question?
I believe ihave to use the conditional probability formula
long dawn
You certainly are afforded the opportunity to use the conditional probability formula
What have you tried so far?
keen lance
What have you tried so far?
well to start, I am unsure how to define the event A and B. Would the event A be the exactly 3 red cards and B be at least one queen?
since that will affect the rest of the problem if I can't define them correctly to begin
long dawn
I would agree
keen lance
Or perhaps they are flipped
long dawn
Assuming you're being dealt the three cards or picking them randomly
long dawn
Conditional probability is P(B|A) unless it's a bayes problem
So it would be P(You have at least one queen | you have three red cards)
keen lance
Conditional probability is P(B|A) unless it's a bayes problem
Okie got it, just watched a video that had it the other way so confused! But makes sense : )
long dawn
There's a version of it called Bayes' Theorem which handles cases where the order of events is backwards given context
Which uses P(A|B), with the implication being that event A typically happens before event B
keen lance
So it would be P(You have at least one queen | you have three red cards)
Yup! Okay so do I need to find B intersect A first?
thorny flameBOT
m. frost
keen lance
I think it is
$P(B|A) = \frac{P(B \cap A)}{P(B)}$
thorny flameBOT
sara 🧸
long dawn
$A \cap B$ is congruent to &B \cap A&
thorny flameBOT
m. frost
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
long dawn
That always threw me off in probability too but when I figured that out I stopped worrying about their order so much lol
Same is true of union afaik
keen lance
Okie got it : ) So that would be probability to have no queen with exactly 3 red cards?
long dawn
If event B is having at least one queen, and A is having three cards, their intersection would be having three cards, at least one of which is a queen
No queen with three cards would be A-(A cap B)
Draw your venn diagrams if it helps
neon iron
hello
keen lance
If event B is having at least one queen, and A is having three cards, their inte...
Okay this makes sense. Dk why I said no queen lol. Also the hand of cards is 5 cards. I forgot to mention that
long dawn
Oh that changes it a little
keen lance
So would it be their intersection is your hand of 5 cards, at least one of which is queen
Yeah
keen lance
At least one is a queen, and ...
At least one queen and exactly 3 red cards?
keen lance
So the other two cards can be anything, but are given to not be red
should I write out cases then see if I can derive a formula for that? so like
Case 1: 1 queen (spades or clubs), 3 reds (not including queen of hearts or diamonds), 2 black cards
Case 2: 2 queens (spades or clubs), 3 reds (not including queen or hearts or diamonds), 1 black card
etc...
Wait I think that would be way to long to write the cases actually.
Perhaps I need to generalize it more
long dawn
You could but it may take a while
Are you familiar with the choose and permute functions?
keen lance
yes, so like 52 choose 3 (for red cards)
Just becomes more complicated with the queens
long dawn
Are there 52 red cards?
keen lance
No sorry, I meant 26 choose 3
long dawn
And to get a probability there you want to divide by the total number of outcomes
$\frac{\binom{26}{3}}{\binom{\text{something}}{\text{something}}}$
Actually that's misinformation
It would be hypergeometric and need another term
Finding the probability of getting exactly three red cards, for example, would follow
$\frac{\binom{26}{3} \times \binom{\text{something}}{\text{something}}}{\binom{\text{something}}{\text{something}}}$
thorny flameBOT
m. frost
long dawn
$\frac{\text{P(get 3 red cards)}\times\text{P(get 2 black cards)}}{\text{P(get any 5 cards)}}$
thorny flameBOT
m. frost
long dawn
Sorry I don't wanna blab too much and throw you off lol
keen lance
Sorry I don't wanna blab too much and throw you off lol
Np!
long dawn
That'll be your probability of getting exactly 3 red cards
so P(A)
So to examine the problem at hand, you want to determine
$P(A \cap B) = \frac{\text{Number of hands with exactly 3 red cards and at least 1 queen}}{\text{Total number of possible 5-card hands}}$
thorny flameBOT
m. frost
keen lance
**m. frost**
I am not sure how to find the numerator. The at least 1 queen part is conflusing me
long dawn
One of the best approaches to some problems is to consider converse cases
Directly calculating the number of hands with exactly 3 red cards and at least 1 queen is more complicated than finding the number of hands with exactly 3 red cards and exactly 0 queens
And for any set, $P(A^{C}) = 1 - P(A)$
thorny flameBOT
m. frost
long dawn
Where $A^{C}$ is the complement space of A (everything not in A as opposed to everything that is in it)
thorny flameBOT
m. frost
long dawn
If that helps at all
I can be more specific if you want but I don't want to give you any clues that are too big lol
keen lance
I can be more specific if you want but I don't want to give you any clues that a...
Yup I am going to try it out myself : ) I was just writing the other stuff in a nicer way
long dawn
I've gotten an answer myself but it's been a while since I've done discrete probability so I'm sure I've made mistakes
Pay attention to details and context-check your work as you go, make sure it represents what you're trying to calculate in each step
(I messed up pretty badly finding P(A intersect B) and had to go back lol)
keen lance
(I messed up pretty badly finding P(A intersect B) and had to go back lol)
Would it be 24 choose 2 over 24 choose 3
for the intersection
long dawn
You have the right idea but the context is off
keen lance
**m. frost**
Yeah I don't think we are allowed to use this by my prof
or maybe we are but it didn't come up
keen lance
You have the right idea but the context is off
Okay
long dawn
$\binom{24}{2}\times\binom{24}{3}$ is the number of ways to have exactly three red cards and exactly zero queens
thorny flameBOT
m. frost
long dawn
Where $\binom{26}{3}\times\binom{26}{2}$ is that of having exactly 3 red cards
thorny flameBOT
m. frost
long dawn
So if $\binom{26}{3}\binom{26}{2}$ is the total number of ways to have 3 reds, and $\binom{24}{3}\binom{24}{2}$ is the number of ways to have exactly 3 red cards with exactly 0 queens, how would you use those to find the number of ways to have exactly 3 red cards and any number of queens
thorny flameBOT
m. frost
keen lance
**m. frost**
Subtract the no queens
long dawn
Mhm
$\binom{26}{3}\binom{26}{2} - \binom{24}{3}\binom{24}{2} = \text{Number of ways to have exactly 3 reds and any number of queens (in other words, at least one queen)}$
thorny flameBOT
m. frost
long dawn
This is using that converse property so if you're not allowed to use it we'd have to manually count the number of hands which would be pain
But if teach just hasn't mentioned it yet but you can use it then huzzah
keen lance
I think we are allowed to use it, just I don't think we have to mention the formula for it
Like the A^c
long dawn
It comes from the idea that everything in a sample space of probabilities adds up to 1, or 100%
So if event A has a 40% chance of occuring, it has a 100%-40% chance of not occuring
If the probabilities there were more complicated than 40% and 60%, and one is easier to calculate than the other, you can find the other using this property
keen lance
Okay got it thank you!!
long dawn
Counting the number of hands with 1, 2, 3, and 4 queens is a lot more work then counting the number of hands with no queens, and the number of all hands - the number of hands with no queens is by definition the number of hands with some queens
keen lance
yup
long dawn
So from here there's just a couple more steps; you want to find the ratio of the number of hands with at least 1 queen to the total number of hands, and divide that by P(B)
From when we had $P(A \cap B) = \frac{hands of 3 red and some queens}{all hands}$
thorny flameBOT
m. frost
keen lance
**m. frost**
Do I have to divide this by it's total outcomes to find P(A \cap B)
yes just what I was thinking
keen lance
Mhm
long dawn
So the bulk of this problem is just finding P(A cap B) lol
keen lance
yeah
long dawn
Gotta go but don't hesitate to ping helper role if you get lost
Here's my work you can compare later but it comes with the disclaimer that I may have messed up here and there. No peeking till you have your answer
keen lance
Here's my work you can compare later but it comes with the disclaimer that I may...
Okie yeah I want to try first : )
Thank you!
stuck hearth
the denominator should be P(A) not P(B)
keen lance
the denominator should be P(A) not P(B)
Yup!
I didn't look at the image, but yeah that's how I will be doing it
topaz sinewBOT
@keen lance Has your question been resolved?
topaz sinewBOT
@keen lance Has your question been resolved?
long dawn
the denominator should be P(A) not P(B)
As promised, I did a goof
keen lance
As promised, I did a goof
I completed it
I am confused because friends are saying they got 36%. I tried to change the rounding to see if that was my issue, but it should still give 34 so idk if I went wrong or they did
stuck hearth
I am confused because friends are saying they got 36%. I tried to change the rou...
your friends are wrong
and also you dont need to compute 52C5
its in both denom and numerator
keen lance
your friends are wrong
Yeah they weren't wrong my prof made an error on it and with the error it was 36% then once my prof fixed it it was 34%. So I just didn't look at the question as early as everyone else
Someone just told me that
keen lance
and also you dont need to compute 52C5
Okay thank you
stuck hearth
timid junco
Is this a competition probability problem?
keen lance
Is this a competition probability problem?
conditional probability problem
timid junco
Ah ok
polar drum
Let $ g:\mathbb{R}^4\rightarrow\mathbb{R}^2$ be linear mapping given by $g\left(\begin{pmatrix}
a\b\c\d
\end{pmatrix}\right)=\begin{pmatrix}
3c-a\
b
\end{pmatrix}$. To find $\text{Im}(g)$ can I just find image of $\begin{pmatrix}
-1&0&3&0\
0&1&0&0
\end{pmatrix}$, which is $\text{span}(\begin{pmatrix}
1\0
\end{pmatrix},\begin{pmatrix}
0\1
\end{pmatrix})$ and that span is eqal to Im($g$)?
topaz sinewBOT
Let $ g:\mathbb{R}^4\rightarrow\mathbb{R}^2$ be linear mapping given by $g\left(...
thorny flameBOT
Slowaq
topaz sinewBOT
@polar drum Has your question been resolved?
polar drum
<@&286206848099549185>
rigid ivy
Let $ g:\mathbb{R}^4\rightarrow\mathbb{R}^2$ be linear mapping given by $g\left(...
Yes. More-or-less by definition, the image of a linear transformation is the image of the transformation matrix. Proving that Im(g) is equal to the span of (1,0) and (0, 1) might require more wording though. I don't know which theorems you have at your disposal.
polar drum
Yes. More-or-less by definition, the image of a linear transformation is the ima...
can i just say that only columns 1 and 2 are pivotal (is that even a word) and thus only those two are linearly independent from the whole comuln space thus they form basis of image of g
split timber
yea, you might call them pivot columns
rigid ivy
can i just say that only columns 1 and 2 are pivotal (is that even a word) and t...
Yes. If you know dimension, those pivot columns show that the dimension of Im(g) is 2. And since Im(g) has dim 2 and is also a subspace of R², the final answer should be trivial.
topaz sinewBOT
@polar drum Has your question been resolved?
shy lava
i used highest degree, and this gives plus infinity right?
topaz sinewBOT
i used highest degree, and this gives plus infinity right?
shy lava
well i also factorized with x squared and it gave me the same thing so i think its right
ok thx guys i gota math exam tmrw bye
.close
topaz sinewBOT
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Available help channel!
novel solar
topaz sinewBOT
novel solar
Pls help me figure out how to find the probability of your hand having one pair and two pairs
This is the way I'm thinking about one pair, but I think I'm going to mess up somewhere
5 numbers (10s, Js, Qs, Ks, and As) choose 1 for the pair
5C1
4C2 for the numbers of the other two cards
but each has 2 options right
so 4C2 * 2?
or is it 4C2 * 4?
topaz sinewBOT
@novel solar Has your question been resolved?
topaz sinewBOT
@novel solar Has your question been resolved?
timid junco
lol
K so first 5C1 is five no duh
Wait a minute I’m doing probability :/
Well so total number of ways is 10x9x8x7=5040
Wait im still doing probability:/
Ah so 5C1=5
Then 5C2=10
timid junco
Ah so 5C1=5
This times 6x8 which will end up with 240
Or maybe it’s 4x3
Eh something like that
novel solar
huh
so like
I think with combinations
we'd get
5C1 * 4C2 * 2 * 2
divided by 10C4
novel solar
Or maybe it’s 4x3
confused how you got 6x8
timid junco
confused how you got 6x8
Well we have one pair right?
novel solar
yeah
timid junco
So we need to choose the other numbers to fill in the pair
novel solar
oh you're doing it with permutations
wait if you did it that way
wouldn't it be
10 for the first card of pair
and 1 for the second
timid junco
Oh yea
novel solar
and then 8 for one of the others
and 6 for final
10 x 1 x 8 x 6
and need to factor in rearrangements
novel solar
and you're dividing by 10 x 9 x 8 x 7 which is correct
novel solar
ok
timid junco
First is 1 pair
5 ways to choose the one pairs
Then we have 8 choices for the 2nd number and 6 (since cannot be other pair) for next
Then there are 3! ways we can rearrange
Leaves us 5x8x6x3!
Which is 1240
novel solar
yes, but you also have to factor in the ways you can rearrange the pair
like AB and BA
so *2 again
right?
timid junco
Oh fuck I calculated as pair
novel solar
yup
novel solar
but that's assuming the pair sticks together as one unit
the pair does not need to be drawn right after each other
like you can have A B C A
you don't need AA BC
novel solar
but are they not differnt suites
timid junco
What?
novel solar
so the two cards that are a pair would still be distinct
like they could be hearts or spades etc
timid junco
It doesn’t say we hafta do that so we can assume they are just A,K etc
They didn’t specify that
novel solar
ok
timid junco
If they don’t say it you don’t count
novel solar
ok
timid junco
Is this school work?
novel solar
no it's not
timid junco
Competition maths then
novel solar
yeah lol
novel solar
I made AIME last year luckily
timid junco
Really?
timid junco
Bruh this my first time doing amc 10
novel solar
bet
timid junco
So 2880
Yea then we get the 2 pairs
Which is 5C2
=10
But we get arrangements which is 4/(2!2!)
So 6
60 of those is total
That’s two decks so they are technically worth two pairs each so 120
120+2880=3000
(You know it’s right when it’s a perfect number like that
Then u divide by like 10(9)(8)(7)
Which is 3000/5040
U just gotta reduce now
timid junco
:/
Yea sorry I’m sorta not focused I’ve been prepping for the amc 10s and I’m pretty worn out
topaz sinewBOT
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Available help channel!
neon iron
guys
neon iron
and does it mean that when plugging in g(x) into f(x) where f(g(x)), does it mean g(x) is equal to x?
neon iron
than doing one function than the other then the other
what do oyu mean
you mean like is it just combining two functios?
finite storm
yes
finite storm
wait
neon iron
oki
finite storm
w is the composite function of g and f
using w is faster than doing f and then g
if i want to go from x to z
finite storm
wdym?
neon iron
like getting the c^2
actually nvm
but thank you
what other examples are there
to prove
that it is easier
finite storm
lets say i want u to find f(g(3)) where f(x) = x^2 and g(x) = \sqrt(x)
fog = x
is much faster than plugging in 3 in g(x)
and then use that result and squaring it
topaz sinewBOT
@neon iron Has your question been resolved?
frigid salmon
Anyone know convex optimization? I found a projection for a set S representing hollow sphere in n dimensions with radius 1, (norm squared of x = 1 for all x in the n dimension) which is x / norm x if norm squared x != 0 and any pt in x if x = 0, how can I show that if norm squared x != 0 then norm of projection of x minus x <= norm of y - x for all y in the set S?
topaz sinewBOT
Anyone know convex optimization? I found a projection for a set S representing h...
frigid salmon
quartz shoal
topaz sinewBOT
@frigid salmon Has your question been resolved?
topaz sinewBOT
@frigid salmon Has your question been resolved?
topaz sinewBOT
@frigid salmon Has your question been resolved?
snow flicker
willow void
topaz sinewBOT
smoky sparrow
split into two integrals
if the x-coordinate of the intersection between red and green is A
and the x-coordinate of the intersection between green and blue is B
then you have $\int_A^0 (4 - x^2) - (-3x) \ dx + \int_0^B (4 - x^2) - (3x^2) \ dx$
thorny flameBOT
south's secret twin brother
willow void
Okay
rustic oracle
@smoky sparrow very off-topic question but how do you use this TeXit bot like that?
smoky sparrow
<@1151031274413228043> very off-topic question but how do you use this TeXit bot...
here's a guide
rustic oracle
here's a guide
i'll read it, tysm mate
smoky sparrow
ah so look at your grpah
you want x = -1
cause from your graph, the intersection between green and red has a negative x-coordinate
similarly for the other intersection, use x = 1
x = -1 doesn't even exist due to the domain of x = sqrt(y/3)
but yes your work is correct
topaz sinewBOT
@willow void Has your question been resolved?
smoky sparrow
.close
uneven ginkgo
topaz sinewBOT
rustic oracle
you have 2 eqn in x and y
you will get more than 1 solution
since 1 eqn represents a circle and other eqn a line
uneven ginkgo
since 1 eqn represents a circle and other eqn a line
oh
the other soluition is
-105 -100
btw i forgot to put the sqrt there
topaz sinewBOT
@uneven ginkgo Has your question been resolved?
uneven ginkgo
<@&286206848099549185>
tight hawk
what?
topaz sinewBOT
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crude crystal
Is there any way to solve this integral
topaz sinewBOT
Is there any way to solve this integral
steady escarp
,rccw
thorny flameBOT
crude crystal
r is constant
steady escarp
probably if u let x = r*tantheta
crude crystal
How will I understand that’s how I need to solve this
steady escarp
because u have r^2 + x^2
crude crystal
probably if u let x = r*tantheta
Won’t I have theta then
Then I have change dx to d theta?
crude crystal
Ok thanks
topaz sinewBOT
@crude crystal Has your question been resolved?
topaz sinewBOT
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ivory sorrel
Trying to write this as a sum
topaz sinewBOT
Trying to write this as a sum
ivory sorrel
$\lim_{n\to \infty} \frac{10^6-2^6}{n} \sum_{i=1}^{8n} \left(2+\frac{i}{n}\right)^6$
would this be it
This feels very sus
thorny flameBOT
A dense set
placid token
gl with that
ionic oar
why the 10^6 - 2^6?
ivory sorrel
to find the "base" of the reactangle
ionic oar
uh
thorny flameBOT
neon
ionic oar
I'm not sure what exactly you've done but it doesn't seem to be lining up
ivory sorrel
I'm confusedd
ionic oar
I'm trying to maintain this structure here
ionic oar
what I'm saying is that besides to 10^6 - 2^6 everything else seems fine
topaz sinewBOT
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Available help channel!
rain rock
topaz sinewBOT
rain rock
credits: 25th Philippine Mathematical Olympiad
how do you solve this? I'm trying to find a solution
ionic oar
(3 - x)/(3 + x) needs to lie between -1 and 1
rain rock
I first tried to find the values that do not satisfy the equation
ionic oar
and x cannot be -3
rain rock
but then again, my thought was far from the answer
rain rock
(3 - x)/(3 + x) needs to lie between -1 and 1
wait let me try
rain rock
(3 - x)/(3 + x) needs to lie between -1 and 1
so i tried that inequality
it showed me something contradictory
oh wait no
oh
what
vernal ledge
(3 - x)/(3 + x) needs to lie between -1 and 1
why so?
vernal ledge
Hint 1: Try converting the numerator into an integer instead of an expression with x.
vernal ledge
oh mb
topaz sinewBOT
@rain rock Has your question been resolved?
velvet spear
I'm struggling to understand the following statement from my book: "if $\emptyset |= A$, then A is a tauntology.$"
topaz sinewBOT
I'm struggling to understand the following statement from my book: "if $\emptyse...
thorny flameBOT
Pen
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
velvet spear
My confusion stems from this: when is it that when is any formula, A, not a logical consequence of the empty set of formulaes?
velvet spear
I'm struggling to understand the following statement from my book: "if $\emptyse...
Wouldn't this mean that every formulae A is a tautology?
topaz sinewBOT
@velvet spear Has your question been resolved?
brisk ice
Any idea how to do this?
topaz sinewBOT
Any idea how to do this?
median pivot
well u can try substituting u = x² + 1
brisk ice
Use trigonometric subtitution
how do i do that exactly, i don’t think we’ve learned it
torpid sparrow
x = tan(u)
median pivot
Use trigonometric subtitution
ig this could work too
brisk ice
i’ll close it for now because i gtg thanks for the idea
brisk ice
well u can try substituting u = x² + 1
i’ll try this too but i’ve tried just substituting a lot of things and it didn’t work
i don’t think i tried that tho
median pivot
thats the obvious one to substitute
in 70% of cases, use u substitution for whatever is under the roots
slate pebble
in 70% of cases, use u substitution for whatever is under the roots
have you tried that in this case ? :)
brisk ice
thanks!
median pivot
have you tried that in this case ? :)
is it false?
brisk ice
i tried substituting the sqrt itself and it didn’t work
torpid sparrow
Do as I said and tell me how it goes
topaz sinewBOT
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indigo wren
If Jói gets 392.235 kr netto, what does he get brutto if the tax is 34,29%?
south talon
If Jói gets 392.235 kr netto, what does he get brutto if the tax is 34,29%?
sorry i dont understand the question
please can you re write it?
topaz sinewBOT
@indigo wren Has your question been resolved?
brisk ice
sorry i dont understand the question
if joi’s salary received after taxes is 392.235 kr, what is his salary before taxes if the tax is 34.29%
topaz sinewBOT
south talon
.reopen
south talon
@brisk ice
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indigo wren
in the market, salaries rised by 4,5% then 3% then 2,5% by how much did the salaries rise this year?
topaz sinewBOT
in the market, salaries rised by 4,5% then 3% then 2,5% by how much did the sala...
indigo wren
i did 0,955 * 0,97 * 0,975 = 0,903
rocky salmon
It is rise
rocky salmon
1.045…
rocky salmon
1 - 0,903 =
🙂↔️
topaz sinewBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
snow gull
Hello. I am no longer a student and my math skills are rusty.
I am learning about inverse functions and as far as I understand it, this question does not make sense to me. Isn't f(x)=8 a constant function so I can't solve for an inverse? I have no clue why it's there. I would appreciate your insight on whether this can be solved.
Thank you.
jade cape
wait thats weird
agile harness
f(x) = 8 doesn’t have an inverse
thorny flameBOT
reaver
agile harness
it looks like 8-
snow gull
Thank you for opening my thread. I am wracking my brain at this.
agile harness
**reaver**
no
f is the inverse of f^-1 so what you’re proposing doesn’t make sense
that’s still assuming f(x) = 8 has an inverse
agile harness
is there something after the 8
^
snow gull
This image was supplied as-is and appears to be scanned from a physical paper.
So, my question is, as it stands, is this question missing data which would make it solvable?
wide juniper
it looks like you are supposed to find what f(x) is
agile harness
yea ignore the f(x) = 8
it appears that you’re supposed to give the pairs of f(x) given the pairs of f^-1
agile harness
yea ignore the f(x) = 8
it probably has something after it which we can’t see
if f^-1 contains the pair (1, 1.4) what does f have
snow gull
Would ignoring the f(x)=8 part allow the rest of it to be solved?
agile harness
this is a horrible question
they said given the description of f^-1 then it says f(x) = 8
🤔🤔🤔
snow gull
My mind automatically drew up the straight line of a constant function.
wide juniper
ooh I think it want you to find what x value makes f(x) = 8
agile harness
well i mean it’s not linear
agile harness
ooh I think it want you to find what x value makes f(x) = 8
maybe
jade cape
ooh I think it want you to find what x value makes f(x) = 8
that makes sense
snow gull
That is as close as I was to understanding it, but how can I connect this to the ordered pairs and the inverse function to find x?
snow gull
I got that...
agile harness
I got that...
so if the y value of f is 8
wide juniper
if f(10) = 100 (10, 100)
then f^-1(100) = 10 (100, 10)
agile harness
look for the pair with the x value of f^-1 being 8
and give its corresponding y value
if f(x) = 8 then f^-1(8) = x
snow gull
i'm thick as a brick wall rn, does this question need me to provide an answer for all the given sets or to look for the right one?
agile harness
no you’re just looking for the x value that makes it true
it’s like solving for the roots of a quadratic
when we have f(x) = 0 you solve for the x values that make it true
agile harness
if f(x) = 8 then f^-1(8) = x
^^
agile harness
look for the pair with the x value of f^-1 being 8
i cant be any clearer than this
agile harness
and give its corresponding y value
^
snow gull
Thank you. Bear with me as I solve it at my end.
Pardon me, I am still at a loss.
Just to clarify, are the ordered pairs provided supposed to be plugged in or anything?
agile harness
Just to clarify, are the ordered pairs provided supposed to be plugged in or any...
well look for the ordered pair that has 8 as the x value
the corresponding y value will be the x value that satisfies f(x) = 8
snow gull
That would be (8, 8.6), I suppose
snow gull
...8.6?
Does the whole equation actually boil down to just this? Finding the ordered pair from the set that fulfills the given f(x)=8?
hollow plaza
Hey knief 👋
snow gull
I was blue screening because there isn't another variable like what I'm used to; as f(x)=y
Just to try and summarize... For showing the work for this question, would a table of the ordered pairs and their inverse be sufficient?
.close
topaz sinewBOT
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tropic zephyr
Can someone check if this is right or if i did something wrong where did I mess up. Not a homework question
topaz sinewBOT
Can someone check if this is right or if i did something wrong where did I mess ...
loud oasis
(-1)!! = 1 by definition (this is to keep consistency with formulas relating it to the factorial and that 0! = 1)
tropic zephyr
To me it feels like I didn't break any math laws but does equality hold here
It looks different than the legendre duplication formula
topaz sinewBOT
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@humble kraken Has your question been resolved?
Available help channel!
swift slate
hiya, i was wondering why the end results for each branch has a denominator of 30? why are the fractions multiplied?
topaz sinewBOT
hiya, i was wondering why the end results for each branch has a denominator of 3...
@swift slate Has your question been resolved?
lean pebble
well basically we are using the fact that P(A, B) = P(A|B) * P(B)
swift slate
ah okay
lean pebble
so for example the probability of first getting a a red marble then a white marble, is the probability of getting a red marble times the probability of getting a white marble given that you got a red marble at first
swift slate
so (r,w) would be ((4/6) / (2/5)) * (2/5)?
swift slate
so for example the probability of first getting a a red marble then a white marb...
is that right?
lean pebble
wait im a bit confused how you got that
swift slate
no it couldnt be
lean pebble
first the probability of getting a red marble is 4/6
and then getting a white marble after getting a red marble is 2/5
so it's just 4/6 * 2/5
topaz sinewBOT
swift slate
thank you!!
swift slate
.reopen
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swift slate
why is the 12 squared?
swift slate
sqrt(12²12) = sqrt(12³)
isnt it sqrt(12^1)?
swift slate
yes
golden blade
and 144 = 12²
12 * sqrt(12) = sqrt(12²) * sqrt(12) you get
which is sqrt(12² * 12)
sqrt(12³) = 12^(3/2)
swift slate
so you make the 12 into sqrt(144) which you simplify to be sqrt(12) * sqrt(12)?
golden blade
ya
swift slate
12 * sqrt(12) = sqrt(12²) * sqrt(12) you get
but then how do you only have just 12 and not sqrt 12 in this?
golden blade
huh
golden blade
,, 12\sqrt{12} = \sqrt{144}\sqrt{12} = \sqrt{12^2}\sqrt{12} = \sqrt{12^2 \cdot 12} = ...
thorny flameBOT
bacc (unhelpful)
golden blade
,, \sqrt{12^3} = (12^3)^{\frac{1}{2}} = 12^{\frac{3}{2}}
thorny flameBOT
bacc (unhelpful)
golden blade
then i simplified with my laws
swift slate
thank you bro... you're a lifesaver
golden blade
no problem lusilly
topaz sinewBOT
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dusky crow
How do you find the angle between two 3d vectors? (this counts as math right?)
The problem is:
topaz sinewBOT
How do you find the angle between two 3d vectors? (this counts as math right?)
T...
cinder hawk
try w/ dot product instead of cross product
dusky crow
oh yeah
cinder hawk
easier computationally
cinder hawk
my bad
technically your answers should be the same, but there's more of a chance to mess up when calculating the cross product at least for me
dusky crow
hmm ok
topaz sinewBOT
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jaunty reef
Hey guys I need help with my ap pre calc hw. I’m stuck on 2c. I rlly appreciate the help since I don’t rlly know where to start.
topaz sinewBOT
Hey guys I need help with my ap pre calc hw. I’m stuck on 2c. I rlly appreciate ...
@jaunty reef Has your question been resolved?
hazy pumice
Hey guys I need help with my ap pre calc hw. I’m stuck on 2c. I rlly appreciate ...
I don't remember the particulars, but a property of regression (or at least linear regression, polynomial, and exponential regression models) is that scaling the explanatory variable (x input) is not going to change r or r^2. only the b regression variable will change. a will stay the same
b works out to 0.4089, accurate to 4 decimal places
You would do all this exactly the same way as you did it for part a. If you did it by hand ("god bless ya"), it's the same process. I punched it into an online calculator but scaled the input values by 1/12.
jaunty reef
Mmmmok
I think I get it.
I figured out how to get the answer
I don’t quite understand the logic. But it’s ok thx sm
hazy pumice
I figured out how to get the answer
what, lol
jaunty reef
I just got the b value and rooted it by 12
hazy pumice
scaling by 1/12? you don't get that?
hazy pumice
I just got the b value and rooted it by 12
rooted it?
hazy pumice
oh, that is interesting
well it would fall directly out of the formula for getting b in the first place
scaling the x-input by 1/12 works out to literally taking the 12th root ("12 factors of what number gives you the number you started with?") of b
@jaunty reef
oh that is exactly the inverse though
riiiight...
because this is showing up for the NEW b value
jaunty reef
Sorry I suck at math I don’t understand what I’m being asked 😅
I appreciate the help but I think I can figure out the rest from here thx sm
hazy pumice
I appreciate the help but I think I can figure out the rest from here thx sm
ok. I taught AP stats about a year ago
jaunty reef
Oh cool
hazy pumice
the direct calculation for the regression variables is based parially on the linear model
(a and b)
if using a rule to transform the data is good enough for you right now, that's fine. I don't want to jumble your brains
(or root through the internet looking for a decent source for the direct calculation)
we used an open-source curriculum though and it was EXCELENT
jaunty reef
I see ok
Cuz my teacher uploaded the work but it kinda sucks. But thx again
.close
topaz sinewBOT
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hushed cloud
wait how do u find if triangles are congruent or not
topaz sinewBOT
wait how do u find if triangles are congruent or not
hushed cloud
Can anyone pls explain
topaz sinewBOT
@hushed cloud Has your question been resolved?
fading owl
wait how do u find if triangles are congruent or not
So there are several methods
This might help
hushed cloud
thx
fading owl
Np
topaz sinewBOT
mortal steeple
draw a diagram for it
do you know about sine law?
not sine = perpendicular / hypo
sine law
oh
if this is a school problem,
then try using the concepts learnt in class
rare sage
There are at 2 such triangles and 2 variants for the area accordingly
you can use the law of cosines to find the third side (you will get two values from quadratic equations). And the height is 12*sin(30)=6.
swift slate
hiya, i was wondering what the most appropriate way to graph this data would be :)
topaz sinewBOT
hiya, i was wondering what the most appropriate way to graph this data would be ...
swift slate
yes
the first would organise the number by the hundred
e.g. 0 is numbers not in hundreds, 1 is numbers in the 1 hundred range
mortal steeple
oh got it
swift slate
the 2nd one, which ive seen most commonly, uses individual beginning numbers to categorise
mortal steeple
the first would organise the number by the hundred
yes this method is good for the second table
topaz sinewBOT
mortal steeple
wlcm 
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slate spade
can someone help me 
topaz sinewBOT
can someone help me <:emoji_Pray:1152172006628933692>
arctic prairie
drop your question
arctic prairie
the derivative of f/g
is (f' g - g' f)/g²
in your exemple you have f is 3x² - 6
f' is 6x
slate spade
yea
slate spade
yep
craggy haven
can i recommend a different strategy
slate spade
can i recommend a different strategy
yea
arctic prairie
can i recommend a different strategy
yes
slate spade
hopefully its the same one i use 😭
craggy haven
write it as $f(x) = (3x^2-6)(x^{-\sfrac23})$ and distribute
thorny flameBOT
hayley is stateside!!
craggy haven
and then just use power rule
arctic prairie
so it is over
slate spade
no
slate spade
when i expand the brackets
im getting 4/3 as my power
but
the website im using says its something else
arctic prairie
give me the result you have got and what the website says
arctic prairie
and what did you get ?
slate spade
the website doesnt even explain how he got to that
it gives me this as the function before we find the derivative
if that helps
craggy haven
that can't be the same problem
arctic prairie
i got -4x^-7/3 + 4x^-5/3
wait
why -7/3 ?
slate spade
wait
why -7/3 ?
oh wait
i found why its not -7/3
its -4/3
so the answer i got was
i got -4x^-4/3 + 4x^-5/3
craggy haven
that doesn't make sense either
when you distributed that x^-2/3 what did you get for f(x)?
craggy haven
please write your answer in one line, in the form of f(x) = .......
slate spade
f(x) = 3x^-4/3 - 6x^-2/3
craggy haven
ok well that's not right
thorny flameBOT
hayley is stateside!!
craggy haven
in particular look at the product rule
slate spade
yes
smoky sparrow
no because -6 * -2/3 is not 12
smoky sparrow
yeah there's a mistake on the website
slate spade
yeah there's a mistake on the website
tyty
slate spade
no because -6 * -2/3 is not 12
yeaa
craggy haven
$f(x) = 3x^{\sfrac13} - 6x^{\sfrac{-2}3}$
thorny flameBOT
hayley is stateside!!
slate spade
so is this right
slate spade
to make sure, this is correct?
craggy haven
yeah it is, i messed up my f(x) though
$f(x) = 3x^{\sfrac{\red4}3} - 6x^{\sfrac{-2}3}$
thorny flameBOT
hayley is stateside!!
craggy haven
if this doesn't make sense to you, review exponent laws
topaz sinewBOT
@slate spade Has your question been resolved?
trim chasm
I was able to find the radius of the second smallest circle to be $3-\sqrt2$, but I am stuck on the smallest circle.
topaz sinewBOT
I was able to find the radius of the second smallest circle to be $3-\sqrt2$, bu...
thorny flameBOT
Cube
topaz sinewBOT
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tiny pawn
topaz sinewBOT
tiny pawn
Ja aber warum sind sie getrennt geschrieben?
golden blade
Ja aber warum sind sie getrennt geschrieben?
was meinst du
tiny pawn
Hier ist eine Matrix als 3 Vektoren geschrieben.
golden blade
Hier ist eine Matrix als 3 Vektoren geschrieben.
Hast du vergessen, dass [\operatorname{rang}(A) = \operatorname{rang}(\mathbf{a}_1, : ... : , \mathbf{a}_n ) ]
thorny flameBOT
𝔸dωn𝓲²s
tiny pawn
Aber was ist der Unterschied.
Wie rechne ich wenn ich so schreibe?
Könntest du mir ein Beispiel geben?
golden blade
Könntest du mir ein Beispiel geben?
Es ist so ziemlich das gleiche Getue. Du zählst die Anzahl linear unabhängiger Vektoren a_i. Diese Anzahl ist der Rang.
Ob du jetzt die Vektoren in eine Matrix A packst und die Matrix dann auf Zeilenstufenform bringst, oder ob du die Vektoren nimmst und das homogene LGS löst, um zu schauen, welche linear unabhängig sind, läuft aufs gleiche hinaus.
topaz sinewBOT
tiny pawn
.reopen
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tiny pawn
@golden blade darf ich mich behaupten, dass die Abbildung nicht injektiv ist, wenn rang(kern(A))>0 ist?
golden blade
<@587715738484211754> darf ich mich behaupten, dass die Abbildung nicht injektiv...
Ja
Weil dann gibts ja mindestens eine nicht triviale Lösung
topaz sinewBOT
topaz sinewBOT
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fossil moss
Just wanna check my answers and not sure about OC
AB= b-a
AC= a+⅘(b-a)
CB= b-½(b-a)
OC=?
fossil moss
twin linden
how can i help you
fossil moss
I'm just being dumb rn
fossil moss
Just wanna check my answers and not sure about OC
AB= b-a
AC= a+⅘(b-a)
CB= b-½(...
Gotta answer this
I had a rough night out yesterday lol
twin linden
ok
fossil moss
This should take me maybe 30 seconds to do in my head tho so it's stressful that I can't do it rn
twin linden
OC = OA + AC