it’s measure theory
#help-17
crisp ermine
oh then im even worse off
half imp
What else does the "non-inclusion" tell you
carmine prairie
It don’t know
I just know there exists x in T1 but not in T2
And y in T2 but not in T1
Can you really help me ?
@here
@everyone
vocal sleetBOT
@carmine prairie Has your question been resolved?
buoyant echo
Hello, I have been rlly struggling with finding the average rate of change of this function f(x) =x^2 *(2x^5)^8÷x^7 Between x = 3 and x = 5. I would appreciate if someone help me with this, because the results I got doesn't make sense
vocal sleetBOT
Hello, I have been rlly struggling with finding the average rate of change of th...
mild flower
average rate of change is just the end - start, divided by the difference in x
it's the slope from (3, f(3)) to (5, f(5))
so, what did you try?
buoyant echo
I was trying to first trying to get the result of f(3)=3^2 (2(3)^5)^8÷3^7 and my problem was that I was getting a big number by this, so I was looking another way to do it
outer warren
the function can be simplified a bit from exponent laws
was this a multiple choice question?
buoyant echo
no it isnt
outer warren
it's also a bit strange for the function to be presented like that for this type of question
buoyant echo
I have to simplify the exponents first right?
outer warren
you don't have to, but it makes stuff less tedious
applying the definition of average rate if change, there isn't much else you can do
if the work is valid that'll be the answer
buoyant echo
For finding it, it is always neccesary to use this formula?
vast shale
A clinic has 10 doctors specialized in many areas: 3 cardiologists, 4 orthopedist and 3 ophthalmologist. Each of six patients made one appointment with one doctor (they chose whoever they wanted). What's the probability that exactly 3 of 6 patients choose to do a query with a cardiologist?
vocal sleetBOT
A clinic has 10 doctors specialized in many areas: 3 cardiologists, 4 orthopedis...
golden yew
A clinic has 10 doctors specialized in many areas: 3 cardiologists, 4 orthopedis...
Well, how many ways can we arrange the people such that 3 of them are with a cardiologist
vast shale
Well, how many ways can we arrange the people such that 3 of them are with a car...
I don't know if it can be simple to calculate that
I found 1/6 but not exactly sure
golden yew
A clinic has 10 doctors specialized in many areas: 3 cardiologists, 4 orthopedis...
This seems underspecified, actually
Are we assuming that multiple people can't pick the same doctor?
vast shale
Yeah
One doctor for one person
I assumed that the 3 cardiologists are the same, since what matters is that we choose the cardiologists
same thing for the other 2 types
golden yew
I assumed that the 3 cardiologists are the same, since what matters is that we c...
Oh, I was assuming we were considering cardiologists (and doctors in general) to be distinct
vast shale
Yeah, I don't think you should
Since the problem just wants you to choose the category cardiologist
golden yew
Are we assuming patients are distinct?
vast shale
At least I am haha
Now you got me wondering if I should consider the doctors all different but I don't think so
probably just
3C - cardiologists
4O - orthopedist
3F - opthalmologist
what I did was
we have 6!/3!3! = 20 ways to choose 3 patients. The probability that the 3 cardiologist are choosen is 3/10 * 2/9 * 1/8 = 1/120.
20 * 1/120 = 1/6
but yeahhhhhhh don't know if I can do that]
most definitely not
golden yew
we have 6!/3!3! = 20 ways to choose 3 patients. The probability that the 3 cardi...
I'm not sure this works, order shouldn't matter
You found the number of way to choose 3 patients to assign to 3 cardiologists, and we can't assign any more to cardiologists
So now we just need to find the number of ways to assign the last 3
vast shale
I also thought of another way to do it
fallen hawk
Wouldn't it be a bit easier to find the probability the 3 chose to go to the other doctors
Then just subtract that from 1
golden yew
Wouldn't it be a bit easier to find the probability the 3 chose to go to the oth...
Would it?
It seems harder to find the probability that 0, 1, or 2 people choose cardiologists than to just find the probability that 3 do
golden yew
I also thought of another way to do it
What was your way
vast shale
What was your way
1 sec, just writing it
vast shale
I also thought of another way to do it
since we want 3 cardiologist, lets choose which patient each one will have.
6.5.4/3.2.1 = 20
now, we just have to choose the other 3. There are 4 cases:
ortho | opthal
case 1: 0 and 3
case 2: 1 and 2
case 3: 2 and 1
case 4: 3 and 0
3!/3! + 3!/2! + 3!/2! + 4!/4! = 1 + 3 + 3 + 1 = 8
20 * 8 = 160 probable cases
yeah now it becomes even more difficult trying to find the total cases
vast shale
It seems harder to find the probability that 0, 1, or 2 people choose cardiologi...
Maybe it is tbh. We will just have to deal with 2 types of doctors
and 7 in total
golden yew
since we want 3 cardiologist, lets choose which patient each one will have.
6.5...
Yeah, it seems pretty annoying to find the number of total cases if we assume doctors are indistinct
This makes it seem to me like it's possible they were assuming you'd treat them as distinct
Also, consider that people are usually different from each other
vast shale
but then don't you think the doctor's category would be irrelevant to the problem?
Feels sad that I won't know the answer to it for some time
golden yew
but then don't you think the doctor's category would be irrelevant to the proble...
No?
golden yew
Yeah it happens
golden yew
Ok so if we assume distinct doctors and patients this gets easier, right?
It's now much faster to find the number of ways to assign the non-cardiologist patients and to find the number of ways to assign all 6
vast shale
wouldn't it just be 6.5.4.7.6.5/10.9.8.7.6.5 = 1/6
we first assign the patients for the 3 cardiologists and then choose 3 of 7 remaining doctors for the 3 last patients
golden yew
wouldn't it just be 6.5.4.7.6.5/10.9.8.7.6.5 = 1/6
I'm not sure that denominator is right
golden yew
wouldn't it just be 6.5.4.7.6.5/10.9.8.7.6.5 = 1/6
Seems like it should be [assign cardiologist patients]*[assign others]
[assign cardiologist patients] should be 6P3, no?
golden yew
wouldn't it just be 6.5.4.7.6.5/10.9.8.7.6.5 = 1/6
Oh I see what you've done here
Ok so
vast shale
We first choose the patients for the 3 cardiologists. Since everyone is different, then we have patient 1, 2, ..., 6 as well as cardiologist 1, 2, ..., 6. Then, we have: 6.5.4
Now we just gotta the other 7 type of doctors remaning 7.6.5
golden yew
The denominator shouldn't be 10P6 because the numerator wasn't only picking doctors
In the numerator, we picked patients and then doctors
vast shale
The denominator shouldn't be 10P6 because the numerator wasn't only picking doct...
but didn't we just calculate the probable cases?
6.5.4.7.6.5 is just the cases that we want
golden yew
6.5.4.7.6.5 is just the cases that we want
Not quite
vast shale
10.9.8.7.6.5 is the total
golden yew
Order shouldn't matter
vast shale
Order shouldn't matter
it does, no? Every doctor is different
golden yew
Sorry, that was ambiguous
Order we assign the people in shouldn't matter
ie, if we assign person 1 to cardiologist 1 first, that shouldn't be distinct from assigning them to doctor 1 second
vast shale
ohh
yeah that's true
but that would still give the same result no?
oh, i dont think this is right
ok, I'll start from the beginning. Let's consider the order P1, P2, P3, P4, P5 and P6 (P is patient). So, in total, we have 10.9.8.7.6.5 cases. We wanna choose 3 patients for the 3 cardiologists. There are 6.5.4/3.2.1 = 20 ways. Now, we have 5.4.6. Why? Because we have 20 ways to choose 3 random patients (let's say P1, P2 and P3) and we have three different cardiologists (C1, C2, C3)
The last 3 patients are already chosen (let's say P4, P5 and P6). We just have to choose the 7 remaining doctors of any type for them. That would give us 7.6.5
So: 6.5.4.7.6.5/10.9.8.7.6.5 = 1/6
yeah, I don't see what's wrong with this
golden yew
ok, I'll start from the beginning. Let's consider the order P1, P2, P3, P4, P5 a...
I don't follow the reasoning for getting rid of the /3*2*1, but regardless you shouldn't be doing that
vast shale
I don't follow the reasoning for getting rid of the /3\*2*1, but regardless you ...
because choosing P1, P2 and P3 is not different from P1, P3, P2 or P2, P1, P3 or P2, P3, P1 etc
we chose the 3 patients, okay
P1, P2, P3 (lets say) for C1, C2 and C3
golden yew
because choosing P1, P2 and P3 is not different from P1, P3, P2 or P2, P1, P3 or...
Wait sorry, I made an arithmetic error 
Yeah, we're getting the same thing
Ok, really sorry for dragging this on longer than it had to go, you've got the answer (assuming we're interpreting the question right, which I think we are)
vast shale
You're good, this question does give an open space for ambiguity though
But yeah, I assume your interpretation is right. Otherwise, this problem would be a real pain 
vocal sleetBOT
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finite trout
I fingured out how to solve (b) and (c) but i cant find out how to sove (a)
finite trout
can someone help me
boreal remnant
let's look at the right side of the equation
you have something, then a line, then something beneath the line
what does the line mean
@finite trout
finite trout
you have something, then a line, then something beneath the line
we are dividing the numerator by the denominator
finite trout
0
finite trout
yes
boreal remnant
so the condition is that 3a+5b /=/ 0
finite trout
yes
boreal remnant
understood?
boreal remnant
that's the same thing
finite trout
wait are we allowed to shift things to the other side when there is /=
boreal remnant
3a + 5b = 0
3a = -5b
a = -5b/3
actually their solution is wrong
missing a negative sign
vocal sleetBOT
boreal remnant
nice work!
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undone pecan
need some help with trig, my solution is - sin(y+a) even though the solution given is sin(y+a) dunno where i went wrong with the signs
vocal sleetBOT
need some help with trig, my solution is - sin(y+a) even though the solution giv...
brazen eagle
where did i go wrong?
At the second line, you forgot a minus in front of the 2 at the numerator
undone pecan
At the second line, you forgot a minus in front of the 2 at the numerator
yeah i figured it out
my a and b were flipped
so i had b+a and b-a
instead of a+b and a-b
brazen eagle
That's it
vocal sleetBOT
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pallid talon
just a desmos thing, how would i flip this graph? im trying to draw something
pallid talon
y=\log\left(x-3\right)1.5^{x}\ +20\left{18\le y\le25\right}
kind light
$y=\log\left(x-3\right)1.5^{x}\ +20\left{18\le y\le25\right}$
twin meteorBOT
Skill_Issue
kind light
uh can you try changing x to -x?
pallid talon
what it turns out being
im dumb sorry
i turned both x's negative and it works
LOL THANK YOU
dense flume
How do you solve $n^2+n=2n+12$
vocal sleetBOT
How do you solve $n^2+n=2n+12$
twin meteorBOT
leyi
outer warren
rearrange to general form
scenic ravine
quadratic formula
outer warren
then factorise or QF or vietas
dense flume
I'm not sure
dense flume
I think so?
kind light
have you seen this type of questions?
dense flume
I think so
kind light
ok
dense flume
have you seen this type of questions?
for like perfect square trinomials and stuff
kind light
where everything is on one side and it equals 0
kind light
for like perfect square trinomials and stuff
uh you can do that yea
dense flume
can you change the question into that format?
kind light
send them all to one side
twin meteorBOT
leyi
dense flume
then simplify?
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vocal sleetBOT
@sweet notch Has your question been resolved?
thorn coral
it is option c -17/3
thorn coral
it is a basic graph question, just count the grid and find out the maximum and minimum points
round belfry
quick question! is this true?
vocal sleetBOT
quick question! is this true?
brazen eagle
Of course
round belfry
nice! thank you!!!
sullen shoal
quick question! is this true?
yes
round belfry
.close
vocal sleetBOT
viral copper
@round belfry only if both limits exist
round belfry
<@793815061852454913> only if both limits exist
yeye 👍
coarse stirrup
billy butcher
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umbral wigeon
vocal sleetBOT
umbral wigeon
can you help me
umbral wigeon
one sec
sullen shoal
mhm
umbral wigeon
sullen shoal
yes
sullen shoal
sry i was busy
sullen shoal
put z=3x and y = 2x-8 in 1st eqn?
oh nvm
this has many solutions
u should be getting
(x, 2x-8, 3x) for any x
that will be the force
@umbral wigeon
umbral wigeon
thx bro
sullen shoal
np
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sudden cloud
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sudden cloud
Can someone help me for q 10
vocal sleetBOT
@sudden cloud Has your question been resolved?
vocal sleetBOT
@sudden cloud Has your question been resolved?
spiral turtle
!status @sudden cloud
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
!showwork
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
languid spruce
n people want to sit on 2 tables which can contain up to 6 chairs each. how many options are there?
vocal sleetBOT
n people want to sit on 2 tables which can contain up to 6 chairs each. how many...
languid spruce
assume n <= 12
uncut pumice
languid spruce
yeah
i can do it with a summation based on how many will sit on the first table, but im wondering if theres a more elegant solution
languid spruce
so if we first split the group into how many will sit on table 1 and how many on table 2 we get these options:
0 at table 1, 4 at table 2
1 at table 1, 3 at table 2
2 at table 1, 2 at table 2
(the tables are unlabelled)
and we want the number of ways to order the people at teach table, for each number of people at every table
so that would be 3! + 1!*2! + 1!*1!
so a total of 9 ways for n=4
dark kiln
that makes no sense
languid spruce
what part?
languid spruce
its the number of ways to order 4 people on a round table
languid spruce
so if we first split the group into how many will sit on table 1 and how many on...
we also have to take the number of ways to split the 4 people
because the people are labelled
alright ill take an answer with a summation too
lol
languid spruce
we also have to take the number of ways to split the 4 people
so for n=4 it would be 3! + 2*4 + 1*6
languid spruce
1 and 3 = 4×2! = 8
0 and 4 = 3!
2 and 2 = 3
yup
wait no
2 and 2 would be (4 choose 2) * 1
no?
dark kiln
no
languid spruce
why?
languid spruce
oh right yeah
dark kiln
no idea sorry
dark kiln
it's like you permute n−1 people, everyone except p1
then you insert the 4th one anywhere
p1 sits with 1 other = 3! / 2
total = 3!/1 + 3!/2 + 3!/3 + 3!
it only breaks because tables are capped at 6
languid spruce
alright im going to assume i people sat at table 1
languid spruce
it only breaks because tables are capped at 6
yeah thats the issue
languid spruce
alright im going to assume i people sat at table 1
n!/[2*(i-1)!*(n-i-1)!]
that would be the number of ways to order n people around 2 round tables where i people sit at table 1 and n-i sit at table 2
right?
languid spruce
alrigith im also going to assume i doesnt equal 0
actually i cant equal 0
this is part of a bigger question that i didnt write here
the range of n is 10-12
wintry vine
i can do it with a summation based on how many will sit on the first table, but ...
I don't think so, it is just the partitioning of n into a, b where a, b <=6, and then consider the ways for each pair (a, b)
wintry vine
no its a good question
languid spruce
i meant when i said i can do it with a summation
wintry vine
yeah just wondering if bionomial coefficients identities may be useful
in the summation
probably not
echo verge
did you solve it?
languid spruce
the old question? nope
echo verge
this one?
echo verge
what about: x_1 + x_2 = 12 where 0<=x_1,x_2 <=6
languid spruce
what do you mean
wintry vine
what about: $$x_1 + x_2 = 12$$ where $$0<=x_1,x_2 <=6$$
twin meteorBOT
violet
echo verge
like the possibilities to write 12 as the sum of two numbers
languid spruce
what about it?
wintry vine
what about: x_1 + x_2 = 12 where 0<=x_1,x_2 <=6
there is only one solution, namely x_1 = x_2 = 6?
languid spruce
the people are labelled
so its the number of options to split 12 people into 2 groups of 6
languid spruce
yeah
echo verge
there is only one solution, namely x_1 = x_2 = 6?
yeah thats wrong
wintry vine
x_1 <= 6 implies x_1 + x_2 = 12 <= 6 + x_2 which implies 6 <= x_2, but x_2 <= 6
we have 6 <= x_2 <= 6, therefore x_2 = 6, consequently x_1 = 12 - 6 = 6
i am not sure who it is wrong
how*
echo verge
no i mean the solution is not that
wintry vine
alright
wintry vine
if youre doing probabliity or counting try this exercise
it is less mathematical/ more intuitive
languid spruce
i dont see how its related to this one
wintry vine
it is also the number of ways
languid spruce
its a combinatorics question yeah
echo verge
You could do it by force
languid spruce
yeah thats what i just did
languid spruce
the range of n is 10-12
languid spruce
look for patterns
the issue is that the tables have a max number of people
languid spruce
so given a number n id need to know the number of ways to split them into 2 groups of max 6 people
echo verge
2+6
languid spruce
and thats an entire different question on its own
languid spruce
why couldnt it also be 8
because this problem is a part of a bigger question
this is the only piece left
and n is 10-12
so ill brute force it
echo verge
so given a number n id need to know the number of ways to split them into 2 grou...
x_1 + x_2 = n
where x_1,x_2 <= 6
languid spruce
well not just the number of ways
i need to know what the options actually are
id need a function that returns them
somehow
so anyway bruteforcing
i defined f(n, i) which returns the number of options to order i labelled people around an table, and n-i labelled people around another table
f(n, i) = (n choose i) * (i-1)! * (n-i-1)!
echo verge
ok wait a minute the table is round?
languid spruce
and i just summed up all the options
languid spruce
ok wait a minute the table is round?
lol yeah
languid spruce
and i just summed up all the options
f(10, 6) + f(10, 5) + f(11, 6) + f(12, 6)
echo verge
ohh okay
vocal sleetBOT
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loud narwhal
vocal sleetBOT
vocal sleetBOT
@loud narwhal Has your question been resolved?
nocturne mantle
clear obsidian
3/x^4
clear obsidian
how do I integrate this?
vagrant solar
If something is to the power of -1 it means it goes to the denominator
so x^4 as the denominator would be x^-4 as the numerator
and then do you know know to integrate a normal equation
clear obsidian
so 3*x^-4?
vagrant solar
yeah
vagrant solar
You add one to the power
so -4 + 1 = -3
then it is 3 divided by -3
which is -1
vagrant solar
the answer is -x^-3
The indicted starts with -4, you add one to get -3 then you divide 3 by -3
and then you add a +C on the end depending on the context
vagrant solar
np
vocal sleetBOT
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proven nebula
proven nebula
my question
frozen bobcat
since $\sqrt{ab} = \sqrt{cd}$ you can subtract $2\sqrt{ab}$ from the left of $a+b=c+d$, and $2\sqrt{cd}$ from the right.
Then $a - 2\sqrt{ab} +b = (\sqrt a - \sqrt b)^2$, and similar for the other side.
twin meteorBOT
Zybikron
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terse fiber
Could we basically remove the 6* and /6 since it cancels it out?
wary dagger
Yee
terse fiber
if we would 6x everything and then / everything
i see yeah, just wanted to double check that, thank you
.close
vocal sleetBOT
wary dagger
You could also just say 6/6=1
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magic lantern
Help how to do this, I attempted and failed
vocal sleetBOT
Help how to do this, I attempted and failed
atomic pine
Help how to do this, I attempted and failed
from second line to third line, you 3x and 4x turned into 12x but it should be 12x^2
magic lantern
from second line to third line, you 3x and 4x turned into 12x but it should be 1...
Oh thank you
atomic pine
Help how to do this, I attempted and failed
as well 2x^2+1 evaluated at 2 is 9 so you should get 3\sqrt 9 on the right which is 9
magic lantern
Omg what is wrong with me 😭
atomic pine
you did it correctly for the fractional part tho
magic lantern
thanks a lot
atomic pine
lastly 6*2 is 12 but you put 16
atomic pine
I think I’m drunk
just use a calculator, calculation by hand is brain rot
@magic lantern you got the answer?
obtuse umbra
Help how to do this, I attempted and failed
just do the derivative simply
atomic pine
just do the derivative simply
isnt that what they did
obtuse umbra
the outcome becomes f'(x) = 3root(2x^2+1) + 6x^2/root(2x^2+1)
urban edge
the outcome becomes `f'(x) = 3root(2x^2+1) + 6x^2/root(2x^2+1)`
second term is wrong
oh nvm
obtuse umbra
???
magic lantern
<@1184409530789023764> you got the answer?<:fishthonk:477821628382969866>
Yesss thank you so much
urban edge
chain rule moment
obtuse umbra
the outcome becomes `f'(x) = 3root(2x^2+1) + 6x^2/root(2x^2+1)`
then put 2 in there
ok done
atomic pine
then put 2 in there
yeah they did the same its just a couple mistake they wanted to be pointed out
vocal sleetBOT
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blazing shard
Hi
blazing shard
Can you show your work
crap
is it
radical 8?
but yes give me a sec
just 8 actually
or 6
idk
golden yew
just 8 actually
Can you show your work
blazing shard
i think i may be stupid
yeah
ill right it out
6/pr equals st/8
6/pr equals ps -2 /8
6/6+x = x-2/8
6 x 8 = (x -2)(6+x)
x^2 +4x - 60 = 0
(x+2)^2 = 64
x+2 = 8
x=8 -2 = 6
@golden yew
u see
golden yew
Yes, 6 is correct
blazing shard
ok thank u
i got 26
is this right?
a=12 b=23 c = ^(12^2+23^2)=26
@golden yew
sry for pinging u but i just want a good grade and its very nice to get someone who acn tel me if im right or noyt
proper dock
i got 6
vast shale
12 foot pole but 6 foot wire?
proper dock
yeah i fked up prob
blazing shard
Ok thank you
proper dock
wait
golden yew
dont think its the only step
It's not, but let's not spoonfeed
proper dock
why did i get 73 now
vast shale
😭😭😭
golden yew
why did i get 73 now
!nosols
proper dock
yeah i got 72.8
blazing shard
that part is 12
vocal sleetBOT
why did i get 73 now
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.
vast shale
idk i haven’t worked it out
blazing shard
i can sho wmy work
vast shale
yes 13 feet
blazing shard
hes not giving me the answer but i think 73 is right if i also got it
ill show my work
golden yew
hes not giving me the answer but i think 73 is right if i also got it
It is 73, yes
vast shale
😭
proper dock
bro i used similarity to find the height of the tower and di some massive pythagorean theorem
blazing shard
ed = square root of 5^2 +12^2 = sqaure root of 169 that equals 13 ft
5/23+5 = 13/AD
AD= 13x28/5 = 73
golden yew
AD= 13x28/5 = 73
Well the exact value is 72.8 but yes it rounds to 73
vast shale
bro i used similarity to find the height of the tower and di some massive pythag...
u only had to find hypotenuse of small triangle then apply similarity (multiply by 28/5)
vast shale
😭 whatever way works best for u
blazing shard
mb
vast shale
1.45m is nuts 😭😭😭
golden yew
1.45/26.7 = h/31.55
This isn't how we should set it up
blazing shard
crap
golden yew
Try to draw a picture
vast shale
draw a diagram w ur similar triangles again
vast shale
for the height of the tree??
golden yew
2.68 right
Can you show your work
vast shale
i aint so sure chief
low flare
who here is competing in the interswitch spak competition
blazing shard
idk what that is
golden yew
who here is competing in the interswitch spak competition
Uh
Not the appropriate channel
Try #competition-math I guess?
low flare
ok thanks nd sorry
vast shale
who here is competing in the interswitch spak competition
not me, not a student under 18
😭
vast shale
show the working!!
blazing shard
sure
vast shale
ion wanna work it out
low flare
can u show the ques?
golden yew
Yes, they are
golden yew
Yes
proper dock
yes
proper dock
yes
blazing shard
ohhh
55.6
thank u
we r light n L
the circles one cannot represent right>
3
vocal sleetBOT
@blazing shard Has your question been resolved?
proper dock
yes
vocal sleetBOT
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junior briar
hi
junior briar
i need help with this question
i dont get how calculating range works with fucntion opps
fervent wasp
Do you know the function of f and g?
junior briar
no thats all they give, but i guess you could find the function by looking at it
fervent wasp
Alr, write them down
junior briar
f(x) = -|x| + 2 and g(x) = -|x| + 4
would you do two cases when u multiply the fucntions together
fervent wasp
would you do two cases when u multiply the fucntions together
It’s not a multiplication
junior briar
isnt closed circle mutliplication
junior briar
no worries
would i make multple cases though since its using absolute value fucntion
vocal sleetBOT
@junior briar Has your question been resolved?
junior briar
.close
rough notch
Any determinant properties that can help me simplify this?
vocal sleetBOT
Any determinant properties that can help me simplify this?
rough notch
I do know for a fact that:
vocal sleetBOT
@rough notch Has your question been resolved?
vocal sleetBOT
@rough notch Has your question been resolved?
vocal sleetBOT
@rough notch Has your question been resolved?
rough notch
.close
vocal sleetBOT
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Available help channel!
atomic mica
vocal sleetBOT
atomic mica
i’m confused because if you plug in -10 equation equals to zero so how is it continuous? Have I gotten the definition wrong?
scenic ravine
!original
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
scenic ravine
is this a test
atomic mica
is this a test
no it’s pearson practice 😭😭
atomic mica
find extremum values and increasing or decreasing tendency
i just asked i’m confused because if you plug in -10 equation equals to zero so how is it continuous? Have I gotten the definition wrong?
like
lean flume
i just asked i’m confused because if you plug in -10 equation equals to zero so ...
0 doesnt mean discontinuity lol
atomic mica
I don’t understand how I can tell if a function is continuous or discontinuous within its domain
scenic ravine
define continuous
lean flume
the function has a value of 0
atomic mica
man i getting it confused
lean flume
exactly
scenic ravine
yes
vocal sleetBOT
vocal sleetBOT
Available help channel!
junior briar
I had a permuation and combination question
How would you go about solving this?
"The number of arrangements formed from the word NUTCRACKER if the vowels are in alphabetical order is..."
vocal sleetBOT
I had a permuation and combination question
How would you go about solving this?...
@junior briar Has your question been resolved?
solar barn
I myself would first find the arrangements of the consonants (imagine stripping the word from all vowels).
After that I would arrange the vowels by 'placing' each of them in order A, E, U in some place before, after or in-between the consonants in the arrangement.
It could be argued that both parts are independent, so the result would be multiplying the amount of combinations for both arrangements.
Note that there may be better/more appropriate ways for you of doing this (which I don't know of).
junior briar
So I would have to manually place each of the vowels in different places while keeping them in order? Wouldn't that take a long time?
solar barn
more like contemplate a specific arrangement of the consonants, each arrangement would have the same amount of consonants, and therefore the same amount of slots where you can place the vowels.
junior briar
Okay let me try it your way
I understand the constonant part, but idk how to arrnage the vowels in the specific places
Im tryint to do it using the fundamental counting priciple
So far i have 7!/2! which accounts for the consonants and the repitition
just dont know how to add the vowel part
solar barn
Imagine you have the following arrangement of consonants:
NTCRCKR
There are 'slots' (marked with _) as follows:
_N_T_C_R_C_K_R_
This would look similar for any arrangement of consonants. In this case you have 8 slots in which you can place vowels.
Notice that there can be several vowels in a single slot.
junior briar
umm i get that but now do u individually count the ways AEU can be arranged in the spots?
solar barn
Imagine you place A, in how many ways can this be done?
junior briar
A can be places in 8 different spots
solar barn
Alright, next we place E, in how many ways can this be done?
junior briar
8 also if u put the A before the E
solar barn
yes, and lastly, in how many ways can you place U?
junior briar
wait so its just 7!/2! * 8^3?
solar barn
yes, although I think the amount of consonant arrangements is 7!/(2!2!) (since there are 2 duplicate consonants C and R)
solar barn
yes, that would be correct.
vocal sleetBOT
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Available help channel!
stoic mica
what does diagonalizing a matrix mean geometrically?
vocal sleetBOT
what does diagonalizing a matrix mean geometrically?
stoic mica
i dont understand whats its purpose
woeful valve
i dont understand whats its purpose
i dont think i can give a geomtrical explanation
but its usage is to make calcualtiıns easier
you can think it as transforming a transform to scaling
woeful valve
i dont understand whats its purpose
i only used it in taking hypercomplex variables log and exp or other functions
as using a diagonal matrix is much more easier then using the matrix normally
as you can treat each element of a diagonal matrix independantly
just makes things less painful
stoic mica
i only used it in taking hypercomplex variables log and exp or other functions
...
but the matrices are different though?
if we have a matrix A and we diagonalize it we get a different matrix
so i dont understand how working with the diagonal matrix of A and A itself is the same thing
stoic mica
you can think it as transforming a transform to scaling
and that's because the diagonal matrix of A is a matrix whose elements in the diagonal are the eigenvalues of A, right?
woeful valve
but the matrices are different though?
A = P D P-
and you work with diagonal D
and what do you to D will directly apply to A
bc ughm
math just maths there
woeful valve
and that's because the diagonal matrix of A is a matrix whose elements in the di...
ye
i guess you can say that
stoic mica
A = P D P-
the definition i have is D = P^-1 A P
stoic mica
P and D isnt unique
what is P^-1 A P
stoic mica
okay
woeful valve
they are the same thing
A is a matrix
D is diagonal
and think P as an operator
P makes matrix -> diagonal
P- makes diagonal -> matrix
stoic mica
A is a matrix
in linear transformations AB(v) means we apply B to v and then we apply A to what we got right?
so here
we have A which is defined
i dont get it
woeful valve
in linear transformations AB(v) means we apply B to v and then we apply A to wha...
?
vocal sleetBOT
woeful valve
<@854711565940293643> im kinda confused but thanks for your help 🙂
i too am confused
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Available help channel!
grizzled forge
vocal sleetBOT
grizzled forge
How do I do 21
scenic ravine
,rotate
twin meteorBOT
scenic ravine
this isn't a test, right
vocal sleetBOT
@grizzled forge Has your question been resolved?
grizzled forge
this isn't a test, right
No this is homework
grizzled forge
and then permute them
So 10P5
grizzled forge
Ok…
scenic ravine
that's NOT the same as 10P5
grizzled forge
that's NOT the same as 10P5
So do I permute or choose?
scenic ravine
I think you then get c(10,5)4!+4! as your answer
as you can permute the people at the other table in 4! ways
grizzled forge
Yeah it’s wrong
scenic ravine
I messed up the fundamental principal of counting I think, sorry
scenic ravine
yes
grizzled forge
Ok I’ll show u and u tell me if u can do or not
grizzled forge
Alr
twin meteorBOT
scenic ravine
not too sure, sorry
scenic ravine
I have a suggestion though, find the ways you can obtain x^3 using the given combinatiosn
bold scarab
How would I do 1b?
vocal sleetBOT
How would I do 1b?
shadow raft
do you know how to find the maximum of a function?
bold scarab
No…
My teacher has just been getting us to graph the function and then use g solve on the calculator to find maximums and minimums
elder scaffold
sin has a max of 1 and a min of -1
ebon rapids
You’re so fortunate the function is simple enough that if you know basic trig properties, you don’t need calculus
bold scarab
Oh my god
shadow raft
oh wait, im being stupid again
bold scarab
I think we’re supposed to learn calculus towards the end of the year
shadow raft
sin has a max of 1 and a min of -1
this @bold scarab
wary mantle
I think we’re supposed to learn calculus towards the end of the year
Then this would probably be considered pre-calculus
bold scarab
this <@1151849010248814672>
So what do I do with this information?
I’m trying to graph the function rn but it’s not appearing on my calculator
Oh my god
bold scarab
It says the answer is 10.5k grasshoppers at t=4…
I’m so cooked
And I still don’t get what maximum has to do with this
shadow raft
It says the answer is 10.5k grasshoppers at t=4…
this is correct
ebon rapids
Slow down first lol
So yes, sin(x) ranges from -1 to 1 inclusive, and that’s regardless of what x is
so sin(πt/8) still has that same range
However
In the equation, there is a coefficient of 3000 there
Which means what is the maximum now?
bold scarab
3000…?
bold scarab
Oh is it because 3000 is the amplitude/a value in the function? So that’s why it’s also the max?
ebon rapids
The former yes
Okay, so that’s the maximum sorted
Now we need to know when
Now in calculus, you would normally find the when first and then solve for the maximum, but in precalc, could go either way
If you know sin(x), for what value of x between 0 and 2π will sin be maximized?
(Note we’re in algebra, so we use radians)
bold scarab
If you know sin(x), for what value of x between 0 and 2π will sin be maximized?
I have no idea what this means
ebon rapids
Do you know the graph of sin(x)?
bold scarab
A sine wave?
ebon rapids
Yes
bold scarab
Would it be maximised at pi/2 then?
solid hornet
Not necessarily
Because of the a (pit)/8 the graph if the sine function gets squished horizontally by an amount of (pit)/8
bold scarab
Horizontal dilation?
solid hornet
Yup
So that mean it reaches the maximum earlier
And to find by how much we can use a formula
2pi/b
Actually
That only works for when it is the zero
Like the x-int.
But you can slightly change it later
My shifting it slightly back to get the maximum amount
I feel like I am over complicating this
bold scarab
Ok so what’s the b value in this case is that the pi/8?
bold scarab
I feel like I am over complicating this
Perchance
My calculator will not graph this equation for some reason
bold scarab
solid hornet
Okay
You can fix the issue
The thing is the graph does not fit on the screen
So click on Zoom
Or F2
They are the same thing
Then send a picture
Or just tell me the options
bold scarab
Wait do I graph it first and then zoom?
If I press f2 now then it just asks me if I want to delete it
solid hornet
Yeah you could
No
Don't delete it
No need
If it still works without deleting it then it is fine.
bold scarab
solid hornet
Okay
So ideally there should be a Fit option
So look for that in the rest of the options to the right
bold scarab
Wait are we trying to change the scales?