oh i havent learnt that
#help-0
stable drift
Find critical points by derivating.
pseudo ice
Hmm, you might have done, but not heard it by name?
I know that I’ve basically been asked to apply the IVT without the name itself being mentioned
stable night
Hmm, you might have done, but not heard it by name?
the only time ive heard of that is when i was learning binary search lol
gray isle
its pretty intuitive
stable night
hmm
pseudo ice
Basically find a point where you’re strictly positive, and find a point where you’re strictly negative
Provided you’re continuous in between those points, you have to take all the values “in between”
pseudo ice
Of course that’s a very tl;dr’d explanation of it, but you should have the picture
stable night
right
ocean sealBOT
stable night
LMAO
pseudo ice
That will never get old for as long as that’s your username 
stable night
okay so a negative number and a positive number and if its continous all values will exist
pseudo ice
Basically yea, any value between f(a) and f(b) will be taken
(And in fact any value between the maximum and minimum on that interval, which must be taken by continuity on a closed interval, but that’s more than we need)
woeful wind
lone heartBOT
woeful wind
how do you do 7 part b?
I am really confused by how the volume of the solid is given by that equation
I thought the volume of the solid formed would be by rearranging x as the subject of y =lnx, to get x = e^y, and then revolving that
marsh rapids
the volume of the cylinder is pi r² dh, with r = e^h (or e^y) so you're not wrong. You just didn't use the formula yet
that does explain the e^y
woeful wind
yeah thats true
but when i use the formula I get pi multiplied by the integral of e^y squared
Im not sure where the first part of their formula came from
woeful wind
im not sure how to envision the solid when its revolved around the y axis
because theres a gap between it and the y axis
marsh rapids
it's like a quarter-donut, but not in the usual sense of quarter
woeful wind
ahhh
yeah that makes sense
wait wouldnt it be a full donut?
if its revolved completely around
woeful wind
im struggling to imagine it
marsh rapids
you're already looking at a slice
woeful wind
yeah
ohh wait
i thought that x slice was revolved around the y axis, as in if you rotated the x axis arund the y axis
i didnt realize you use the shape from the y axis to the curve, and then revolve that
I know i sound lost but i just started this topic half an hour ago so im still getting to grips with it lol
marsh rapids
i thought that x slice was revolved around the y axis, as in if you rotated the ...
you rotate the x axis around the y axis yes. The that makes x the radius and y the height
marsh rapids
the volume of the cylinder is pi r² dh, with r = e^h (or e^y) so you're not wron...
hence here pi r² dh = pi x² dy
with x = e^y
now integrate over all heights, and you've got an integral in y
woeful wind
hence here pi r² dh = pi x² dy
that does make sense, but does the radius of the cylinder change at various points in the cylinder?
or i guess im trying to ask if itsd a regular cylinder
marsh rapids
it's not a cylinder, it's an ln shaped quarter donut
the cylinder is the infinitesimal approximation of the slice
so its radius changes as a function of y yes
marsh rapids
with x = e^y
as shown here
woeful wind
ahh ok
marsh rapids
it's not a cylinder, it's an ln shaped quarter donut
there's something about this sentence that I just love lmao
marsh rapids
you don't need meth when you got math
woeful wind
hahah
so is a reason for using integration
being that the radius of each cylinder slice
constantly changes
marsh rapids
yes
woeful wind
ahhh that makes sense
marsh rapids
you can't call it a cylinder, but you can call it a pile of infinitesimal cylinders
marsh rapids
with an error that becomes negligible when the cylinders get finner
woeful wind
that makes a load of sense
so you basically chop the big shape into near infinite cylinders
and then just sum tem all
that is smart
whoever came up with that
marsh rapids
Newton and Leibniz independantly, say most math history books. Though Euclid and Archimedes already had the idea I think
woeful wind
to think they came up with this
marsh rapids
a lot of people
woeful wind
with hardly anywhere near as much tech as we do
marsh rapids
which makes sense since it's a very basic concept
woeful wind
yeah
the part which confuses me is how, by integrating the equation of one cylinder slice, do you get an equation for the sum of all the cylinders
marsh rapids
that's integrals
marsh rapids
the part which confuses me is how, by integrating the equation of one cylinder s...
it's not "one cylinder slice"
woeful wind
or what im actually doing
marsh rapids
more like a description of a cylinder slice, based on the value of y
woeful wind
yeah
marsh rapids
replace the integral by a sigma and it becomes more intuitive if that helps
woeful wind
yeah it does
is there a reason why integrating the equation of the general slice, gives an equation for the summation of them all, given bounds for the radius
marsh rapids
is there a reason why integrating the equation of the general slice, gives an eq...
there's always a reason
marsh rapids
there's always a reason
for instance, you can use this technique to prove the formula for the volume of a sphere
woeful wind
yeah you can
it essentially is just a load of tiny cylinders
ohhh @marsh rapids the formula makes sense now. the total sum of the volume of I guess the block around the y axis is pi times the integral of 2e, which is pi times e^2 /2
marsh rapids
you didn't just take e as a variable did you
woeful wind
and then you take that away from the volume of the y revolving, which is the integral of pi times r^2
which leaves the area of the region R
no i used e because I imagined i guess a massive rectangle. of width e and height 1, revolving arond the y axis
as that would include both the revolving of the region R, and the revolving of x = e^y around the y axis
errant grail
ji guys
woeful wind
.close
lone heartBOT
lone heartBOT
Available help channel!
stiff apex
If R is a local ring with maximal ideal m, how can I prove that a ring homomorphism f:M_n(R) --> M_n(R/m) is surjective on units? I.e. for a unit A in M_n(R/m) there exists a unit A' in M_n(R) such that f(A')=A
stiff apex
<@&286206848099549185> ?
lone heartBOT
@stiff apex Has your question been resolved?
lone heartBOT
@stiff apex Has your question been resolved?
stiff apex
.close
flat remnant
if i have an item on a scale and i push the button so the number is 0
and then i move the item to the side by pushing it
the number the scale shows goes to the negatives
why is that
whole shell
if i have an item on a scale and i push the button so the number is 0
and then i...
it 0s it
so that whatever the weight of the item is
is now 0
and so when you remove it
flat remnant
No
The number goes back to 0 when i stop pushing the item
Its a physics question not a idk how my scale works question
whole shell
maybe youre inadvertedly providing support while youre pushing it?
flat remnant
The only thing i can think of
But shouldnt be the case
wind cloak
This isn't even a math question look at the manual for your scale
But generally it's done to account for the weight of containers
jagged cobalt
if you look in #old-network you could try the 'physics' server 
flat remnant
if you look in <#406129911992942593> you could try the 'physics' server <:catShr...
oh cool thanks
flat remnant
But generally it's done to account for the weight of containers
youre the 2nd person who doesnt understand my question even after i explained it
.close
woven eagle
lone heartBOT
inland oriole
how did they tell you to solve this?
woven eagle
idk
inland oriole
is this from homework
woven eagle
yes
inland oriole
Well they should have taught you something about how to solve these right?
maybe use ln
inland oriole
logarithms will not help in the slightest here.
do you know what to use then?
yeah you can't use ln
vale wigeon
yeah, i suspect that considering the remainders of both sides mod 4 can be fruitful.
woven eagle
sheesh
woven eagle
have you learned mod arithmatic
nope
woven eagle
i think im a bit too young to learn it :)
vale wigeon
wait, how old are you...?
and i wonder how you're expected to do this if not by that means
maybe just parity??
woven eagle
wait, how old are you...?
imma be 15 this year
im i a bit too young or what else
nvm
.close
lone heartBOT
lone heartBOT
Available help channel!
dim matrix
How should I solve it further?
lone heartBOT
How should I solve it further?
dim matrix
narrow kelp
Solving it means isolating x
heady pollen
$\frac{a}{b}=c \ a=c\cdot b$
ocean sealBOT
~Martin
heady pollen
why can you not?
dim matrix
bcz the value of x-3 could be a positive number or a negative number.
dim matrix
like x-3<0 and x-3>0 ?
heady pollen
yes
dim matrix
Shouldn't I make 0 on RHS first?
dim matrix
so problems like this one here can be solved just by taking the cases of denominator irrespective of sign and numerator?
heady pollen
splitting it up in different cases is the way to go
but beware, this problem actually has more to it than you might think
dim matrix
How can I figure that out?
dim matrix
are you stuck somewhere?
Actually I solved a similar question
and I'm trying to understand why the same method isn't working here.
heady pollen
lets go through it:
case 1) x-3>0
6/(x-3)<5
6<5(x-3)
case 2) x-3<0
6/(x-3)<5
6>5(x-3)
then it gets simple
and in the end there is one small thing to note
dim matrix
This one here
heady pollen
well in this task, you would also have to check both cases, no?
dim matrix
lets go through it:
case 1) x-3>0
6/(x-3)<5
6<5(x-3)
case 2) x-3<0
6/(x-3)<5
6>...
How can we take (x-3) to RHS?
heady pollen
multiply
dim matrix
But just if we are sure about the values.
heady pollen
ok i have to go now
once you have your result, you will have one with x< something and one with x> something
for the x<something you should look back at the assumption you made (x-3<0)
this means that whatever solution we get in this case, it only makes sense if it is x<a<3
if a itself is greater then 3, then that makes no sense
if this is the case, then think about what the answer is
if you can't figure it out im sure someone here can help you out
bye^^
lone heartBOT
@dim matrix Has your question been resolved?
west helm
I have a question about finding the derivative of a function. Now I used the power rule and got -.2325x^2 - .035x + 1.0251 but when I put it in a fairly reliable derivative calculator I got something completely different. Did I do something wrong or did the calculator just do it in a different way?
alpine sable
,w derivative of -0.0775x^3 - 0.0175x^2 + 1.0251x
ocean sealBOT
rotund crater
someone can tell me
lone heartBOT
someone can tell me
rotund crater
someone can tell me why is secx(sec^2x -1 + sec^2x)
rotund crater
? can show me
alpine sable
show what
rotund crater
information about tan^2 = sec^2 - 1
alpine sable
rotund crater
this ?
alpine sable
yes
nocturne iris
Hii, how do I find the nature of $\sum u_{n}$ ?
lone heartBOT
Hii, how do I find the nature of $\sum u_{n}$ ?
ocean sealBOT
lilisworld
worn fox
what do you mean by nature? and what are the limits of the sum?
nocturne iris
what do you mean by nature? and what are the limits of the sum?
yes
if convergent or not
alpine sable
did u try ratio test
nocturne iris
did u try ratio test
no i don't even know what it means 
nocturne iris
did u try ratio test
i can use comparison test, riemann series
and eventually taylor expansions
<@&286206848099549185>
tacit arch
did you try writing the numerator as a single log and then l'hopital?
nocturne iris
did you try writing the numerator as a single log and then l'hopital?
I tried changing the numerator with taylor series but how do I mae it into a single log?
tacit arch
,tex .log rules
ocean sealBOT
riemann
tacit arch
power rule and quotient rule
nocturne iris
power rule and quotient rule
i'm gonna try then
nocturne iris
power rule and quotient rule
uhm... anyway, i couldnt write it in latex but it gave me somthing that doesn't look like it's simpler
tacit arch
did you taylor expand the numerator using the log taylor series
nocturne iris
did you taylor expand the numerator using the log taylor series
only expended $\sqrt{1+n}$
ocean sealBOT
lilisworld
tacit arch
only expended $\sqrt{1+n}$
sqrt is only part of the log
you need to apply the taylor series of log on the entire argument
$\log(y) = y - y^2 / 2 + ...$
ocean sealBOT
riemann
tacit arch
uhm... anyway, i couldnt write it in latex but it gave me somthing that doesn't ...
y = your combined log in the numerator
nocturne iris
y = your combined log in the numerator
ok
tacit arch
nah
tacit arch
i don't know how you got that, but yes
nocturne iris
i don't know how you got that, but yes
i used an online program because it was too complicated for me
nocturne iris
no it's the other one, the first one was the wrong result but now it gives me this
it still doesnt look like a riemann series but maybe i did something wrong
i'll try again
tacit arch
Hii, how do I find the nature of $\sum u_{n}$ ?
it's probably easier if you used the log expansion twice on the original numerator
$\log(y) = (y-1) + o((y-1)^2)$
ocean sealBOT
riemann
nocturne iris
it's probably easier if you used the log expansion twice on the original numerat...
mmhh i didnt know we could do tht
ill do it tomorrow but thanks for the tips
uncut pelican
How does one solve after this
lone heartBOT
How does one solve after this
uncut pelican
tacit arch
,rotate
ocean sealBOT
uncut pelican
Oh, sry and ty
uncut pelican
Change the subject to a according to logarithm's definition
Tysm
sterile spindle
You're wellcome
uncut pelican
.close
queen depot
I need help it's really easy but I'm dumb
Buy 7 coffees get one coffee for free. How much do I get in discount by % ? Can someone explain step by step?
tacit arch
Discount for all 8 coffees?
Since it's a percentage, you can just make up any price for a single coffee
Just say $1 for convenience
lone heartBOT
Available help channel!
wintry zephyr
lone heartBOT
marsh rapids
Binomial numbers
wintry zephyr
Chapter is about probabilities
marsh rapids
Though if you see an exercise about them and never saw this notation you probably missed a lecture somewhere
last ether
$\binom{a}{b} = ^aC_b$
ocean sealBOT
Umbraleviathan
wintry zephyr
Combination?
marsh rapids
How do I make it look like the nCr thing
Looks good to me
ocean sealBOT
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
lunar ledge
wait nvm
keen depot
$\binom{a}{b} = \frac{a!}{b! (a-b)!}$
ocean sealBOT
strikersigmaV
wintry zephyr
$\binom{a}{b} = \frac{a!}{b! (a-b)!}$
How so I find n though is there some property I am missing?
Can't seem to resolve this aljebraically
Lemme recheck notes
peak bough
Hint: binomial coefficients are symmetric. So $\binom{n}{k} = \binom{n}{n-k}$
ocean sealBOT
Mikkel
peak bough
**strikersigmaV**
You can also solve it manually using this
peak bough
**Mikkel**
You don't really need to know a lot about binomials to use this to get to an answer
keen depot
how come you're doing a test on something you havent learned yet? that's really going to be hard.
wintry zephyr
how come you're doing a test on something you havent learned yet? that's really ...
I have learned probabilities but not binomials
peak bough
If $\binom{n}{k} = \binom{n}{n - k}$ then from the information $\binom{n}{5} = \binom{n}{7}$ you can set $k = 5$ and $n - k = 7$ and then solve for $n$
ocean sealBOT
Mikkel
wintry zephyr
I'll try
marsh rapids
Also what are options b and d ?
peak bough
Also what are options b and d ?
b) perish
d) 
wintry zephyr
Lmao
marsh rapids
Cause if it's a any integer between 0 and 4 it's also correct
wintry zephyr
**Mikkel**
So I can use this, is a:12 correct
wintry zephyr
If $\binom{n}{k} = \binom{n}{n - k}$ then from the information $\binom{n}{5} = \...
Yo
peak bough
Cause if it's a any integer between 0 and 4 it's also correct
Shouldn't $k \leq n$? 
ocean sealBOT
Mikkel
marsh rapids
nCk = 0 if n < k
wintry zephyr
Okay wtf is going on
wintry zephyr
**Mikkel**
If this is not the correct way to go about it then what?
peak bough
nCk = 0 if n < k
Huh, never seen this before
fast lichen
so it's 12
marsh rapids
And 0
marsh rapids
Cause if it's a any integer between 0 and 4 it's also correct
Because 0 = 0 is a correct equality
wintry zephyr
**Mikkel**
N-5 = 7 -->
wintry zephyr
Because 0 = 0 is a correct equality
So 12 and 0 are both correct?
marsh rapids
N-5 = 7 -->
Yes but it's not the only way two binomial coefficients can be equal
wintry zephyr
Fk
wintry zephyr
**Mikkel**
Okay meteo, assume I have a test soon and idk a whole lot, to increase my chances of guessing right should I use this?
marsh rapids
So 12 and 0
wintry zephyr
Should I use this? To increase chances?
marsh rapids
If this supposed to be a single answer exercise ?
wintry zephyr
I suppose, since there are 4 choices and we have to choose one and in this practice worksheet there are option a and d , 12 and 0
marsh rapids
If you can only choose one choose 12, if you can choose many also choose 0
wintry zephyr
Alright chief
peak bough
If you can only choose one choose 12, if you can choose many also choose 0
Do you have any papers/sites that defines nCk as 0 for k > n? I've never seen it in any of my courses, and can't find anything on it online
wintry zephyr
anyone nedd hopl
I doee
wintry zephyr
Do you have any papers/sites that defines nCk as 0 for k > n? I've never seen it...
Yo my dude know any of this sheet
wintry zephyr
Where does 2¹⁰-1 come from
wintry zephyr
The correct answer is b according to the book
marsh rapids
It's on the french wikipedia but not the English one
marsh rapids
The English one implies in the intro paragraph that it refuses to define it for n < k
peak bough
Clearly the French "people" are wrong, yet again
marsh rapids
Even though it's a very natural thing to do both combinatorially and as an extension to Pascal's formula
wintry zephyr
Yo anyone know thies
peak bough
Use $nPk = \frac{n!}{(n-k)!}$
ocean sealBOT
Mikkel
peak bough
Wait
wintry zephyr
What about this, they said correct answer is b
peak bough
When I reread the question it is phrased really odd
wintry zephyr
Where tf does 2 come from
marsh rapids
On or off = 2 states
marsh rapids
When I reread the question it is phrased really odd
Indeed
You always have to be careful with words
peak bough
Words suck
marsh rapids
I wouldn't go that far
peak bough
Remember that n! = n(n-1)(n-2)(n-3)...(1)
wintry zephyr
I have little time, that's why I am so hurried
Yes
Mikel
But that won't reduce it would it?
It's going from n to negative infinity
n specifically
Until it reaches 1
Hmmm
Hmm
Wait
n-5 would be left in den
Num**
Not den
peak bough
Think of n as some number on the number line, and (n - 5) as the number 5 before n. Then (n - 5)! is this number that is 5 before n multiplied with its predecessors. Now think of (n - 6)! as the number before (n - 5) multiplied together with its predecessors. If you have (n - 5)(n - 6)(n - 7)...(1)/(n - 6)(n - 7)...(1) you remove all the predecessors before (n - 5) of (n - 5)!
That was some word-brawling I had to do, to phrase that
peak bough
n-5 would be left in den
Yes
peak bough
Is the "3." supposed to mean that it is multiplied by 3?
I see some places using "." as multiplication
wintry zephyr
Then it's 18?
peak bough
How do you get that?
peak bough
(n - 5)!/(n - 6)! = n!/n! = 1 --> n - 5 = 1
Wait
You get n - 5 = 3 if you see it as multiplied by 3
Which gets you n = 8
I believe I have acquired an inner hatred for whoever has written your assignment with this notation
wintry zephyr
It's 8
wintry zephyr
I believe I have acquired an inner hatred for whoever has written your assignmen...
It's eastern Asia, so yea we all forcus too much on bullshit and memorizing sheet than doing actual math
Half the questions are worded like a decrypting letters from zodiac killer
peak bough
We truly need a mathematics police that standardize all notation
marsh rapids
Well actually...
wintry zephyr
We truly need a mathematics police that standardize all notation
You know what matrix A raised to theta is
marsh rapids
wintry zephyr
We truly need a mathematics police that standardize all notation
It's conjugate inverse of a complex matrix
marsh rapids
peak bough
It's conjugate inverse of a complex matrix
marsh rapids
Why would you know this and be learning combinatorics at the same time ?
wintry zephyr
Why would you know this and be learning combinatorics at the same time ?
?
Our study syllabus is a potato salad, learned matricies before calculus
marsh rapids
Feels like one is simple high school stuff and the other one is something you'd only really find in undergrad
wintry zephyr
My sister is learning integrals before limits
marsh rapids
Ok wtf
wintry zephyr
That's why students un alive hemselves
peak bough
Sometimes I dream about "The Great Standardization" where we overhaul everything from units to notation and throw everyone in jail who opposes this grand new system
marsh rapids
That's what happens when you let engineers design the math syllabus
marsh rapids
Sometimes I dream about "The Great Standardization" where we overhaul everything...
1984 flashbacks
peak bough
You call it 1984, I call it Heaven on Earth
marsh rapids
But then 2+2=5
peak bough
$\binom{n}{k} = \binom{n - 1}{k} + \binom{n - 1}{k - 1}$
ocean sealBOT
Mikkel
wintry zephyr
**Mikkel**
Imma write this property down
wintry zephyr
$\binom{n}{k} = \binom{n - 1}{k} + \binom{n - 1}{k - 1}$
Wtf they say c is correct
I got d
peak bough
How did you get d
peak bough
Yes
peak bough
That is correct
wintry zephyr
Soo d is correct?
wintry zephyr
13
peak bough
So n - 1
wintry zephyr
12
peak bough
And k?
peak bough
So (n - 1)Ck = 12C9
wintry zephyr
I still got some problems left,
wintry zephyr
So (n - 1)Ck = 12C9
You guys have helped the sheet out of me, I have to memorize formulas, properties and and study physics and memorize and do shit the whole day tommorow
The day after tomorrow is my test
Know any property for this?
wintry zephyr
So (n - 1)Ck = 12C9
?
peak bough
**Mikkel**
.
peak bough
Doesn't matter
wintry zephyr
Replace the negative signs with positive val
peak bough
**Mikkel**
Just replace n with n + 1 and k with k + 1 in this
peak bough
Just replace n with n + 1 and k with k + 1 in this
I would say the one where you do this
But it's pretty arbitrary. It's the same thing as some people like to use "a_{n}" to show the next number in a sequence, and others like to use "a_{n + 1}"
peak bough
Just replace n with n + 1 and k with k + 1 in this
What this one tells you though, is one of the "interpretations" that you can get from Pascal's triangle
Where every binomial coefficient is the sum of the two above it
Like this
wintry zephyr
wintry zephyr
Now I know that any of numbers from 1 to 9 can go into a place of a digit, there are 5 digits and numbers can repeat
So 9^5
wintry zephyr
What this one tells you though, is one of the "interpretations" that you can get...
But how would I go about finding repetition?
peak bough
You can think about it in another way
wintry zephyr
How so
peak bough
The total number of 5-digit numbers minus the 5-digit numbers that doesn't have repetitions
peak bough
No
peak bough
You have 5 digits, that can all be the numbers 0-9. This means you can have 10^5 unique 5-digit numbers in total
peak bough
0 is also a digit
peak bough
Now, if you want to know the amount of numbers that doesn't have repetitions, you can look at the first digit out of the 5. How many ways can this digit be chosen?
wintry zephyr
10
peak bough
Yes
wintry zephyr
Then 9
peak bough
Yep
wintry zephyr
10!/(10-5)!
peak bough
Yep
wintry zephyr
Yep
Q 46, 543*2
Not sure where I am going wrong
Nvm
I get it
Actually
So I understand that 4 spaces for 5 rings is 5!/1!
peak bough
4
wintry zephyr
1
peak bough
Yes. So if you look at the first ring out of the 5, you can place this in 4 different slots
wintry zephyr
Yes
wintry zephyr
There are 4 rings but 3 spaces
peak bough
4 spaces
wintry zephyr
We just placed 1?
peak bough
There can be several rings on the same finger
wintry zephyr
Ohh fk
wintry zephyr
There can be several rings on the same finger
This...
peak bough
Or the question doesn't make sense, since you can't place 5 things in 4 slots, if you can't have repetitions of slots
wintry zephyr
But you can do 5!/1! And get permutations for it but clearly thats not the answer
wintry zephyr
Or the question doesn't make sense, since you can't place 5 things in 4 slots, i...
Lemme think sboutbit
So the number of slots are 4! Once one is occupied 3 would be left
Can each slot contain all 5 rings?
peak bough
I think you are complicating it again
wintry zephyr
I am trying to think it through
peak bough
With the 5 rings, we first want to look at how many places we can place the first ring
wintry zephyr
4
wintry zephyr
3, 2 , 1
peak bough
You can place the second ring on the same finger as the first ring
So there are still 4 fingers when you place the second one
peak bough
Yes
wintry zephyr
And then 3 for 3rd
peak bough
No
You can also place the third ring on the same finger as the two former
So there are still 4 fingers
peak bough
Yes
peak bough
You don't need factorials for this
Think of having 5 rings on the table and your four fingers up
You now pick up a ring and place it at random on one of your fingers, you can do this 4 ways
You now pick up the second ring, and place this on one of your fingers, you can do this 4 ways also
The same for the next ring; 4 ways
And the fourth, and the fifth
So in total, you have 4*4*4*4*4 = 4^5 ways of doing this
wintry zephyr
If 5 rings can go 4 ways, 4 ways in 1st finger, 4 ways in 2nd finger, 4 ways, in 3rd finger, 4 ways in 4th finger, 4 ways in 5th finger. Number of possible ways 4^5
I was thinking of placements
rotund crater
someone can tell me why derivate 3x?
lone heartBOT
someone can tell me why derivate 3x?
rotund crater
this part
heady pollen
chain rule
derivative of 3x^0.5
3x^0.5=f(g(x))
with f(x)=x^0.5 and g(x)=3x
then the derivative is f'(g(x))*g'(x)
rotund crater
can ilustrate me pls
heady pollen
what do you mean
you dont know the chain rule?
that seams strange
as i said, if we have
f(x)=g(h(x))
then
f'(x)=g'(h(x))*h'(x)
that is literally everything
heady pollen
what
no
why would it
i mean
what you asked is, how does d/dx (3x)^1/2 become (3x)^-1/2 * d/dx (3x)
where do you see a csc there?
rotund crater
why 3x^1/2 was added i dont understand that part
heady pollen
hmm ok
that is not your original question
anyway
chain rule again
we have
$f(x)=\csc\sqrt{3x}$
ocean sealBOT
~Martin
ocean sealBOT
~Martin
heady pollen
we use chain rule again to take the derivative of f
maybe watch some videos on the chain rule
rotund crater
maybe watch some videos on the chain rule
you mean I should derive 3x again?
marsh ore
I’m trying to understand this explanation for denesting radicals (390-391). The technique works but I don’t understand why you can multiply each side of the equation by it’s conjugate. Could someone help shed some light on this?
gray isle
they've established that the square root can be expressed in that form in 390 (with justification),
so that manipulation in 391 is just multiplying both sides of the equation by the same value
lone heartBOT
@marsh ore Has your question been resolved?
lone heartBOT
marsh ore
.reopen
lone heartBOT
✅
marsh ore
I see that the conjugates of each side also equal each other, but why can you then multiply each side of the original equation by their respective conjugates? Is there a particular subject that would help clarify the strategy used here? I’d really like to grasp this at a more fundamental level.
lone heartBOT
@marsh ore Has your question been resolved?
marsh ore
Is this a systems of equations thing? I don’t get why you can do this and obtain a meaningful answer. I think I need to revisit an earlier topic, but I’m not sure which one.
gusty gorge
no it's not
Let's say you have a = b and c = d
then ac = bd
and the way to see this
Start with a = b.
Then we can say ac = bc, since we're doing the same thing to both sides.
We also know c = d, and therefore bc = bd, since we're just multiplying both sides by b.
Then ac = bd because of transitivity
marsh ore
I’m not getting past your first assertion that ac = bd.
I think I need to reread this with a fresh mind. That’s good food for thought for now. I’ll revisit it in the morning. Thank you all.
gusty gorge
I’m not getting past your first assertion that ac = bd.
wdym? you don't understand how I got ac=bd?
I literally gave the reasoning below
marsh ore
Yeah, I realized after reading. I thought you were making that assertion based on just a=b and c=d
gusty gorge
well yeah, I'm saying that if you know a=b and c=d, then you know ac=bd, but I gave the reasons why
alpine sable
did u account for leap years
jan has 31 days
you calculated 5 yrs and 2 months as jan 27th 2000
its an extra 6 days to get to feb 2nd
yes
you are now 27th jan 2000
not November
huh
27 -> 28 -> 29 -> 30 -> 31 -> 1 -> 2
6 arrows
You start 27th Nov 1994
go +5 years to 27th Nov 1999
go +2 months to 27th jan 2000
go +6 days to feb 2nd 2000
yes
but you are going +5 years then +2 months first
alpine sable
You start 27th Nov 1994
go +5 years to 27th Nov 1999
go +2 months to 27th jan 20...
You were wrong bec online calculators calculated it like this
I’d say its weird
there is no “wrong” or “right”
it’s ambiguous
unless theres a specific criteria or further instructions
4 days?
def not
where did 4 days come from
that would be feb 1st
not feb 2nd
this criteria is still not that specific
is it saying jan 27 to feb 27 is 1 month?
why
how many days?
thats even weirder lol
so
jan 27 to march 27 is what?
- how many days?
yeah thats just weird but clearly u know the specifications better than me
so if they match ur answer then its correct ?
well no calculator has ur specific specifications
based on this ur answers correct
assuming thats all correct
yea
yes if there are no seconds
lone heartBOT
lone heartBOT
Available help channel!
shut geyser
2x(5+10500)÷7=17 solve for x
lone heartBOT
2x(5+10500)÷7=17 solve for x
last ether
!status
lone heartBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Simplify what's in the parenthesis
shut geyser
10505?
last ether
Then multiply both sides by 7 to reverse the division
last ether
,w 119/21010
ocean sealBOT
lone heartBOT
last ether
I gotcha
lone heartBOT
Available help channel!
sinful juniper
Okay i'm doing my brother's homework and this question confused me: Daniela borrowed some money from her parents. She agreed to pay P700 at the end of the first month and P100 more each additional month for 12 months.
sinful juniper
do I solve for 11 months or 12 months
but there's 100 more each additional month for 12 months
but the first month was paid for already
?!?!?
i'm a stupid senior year student, please help 😭
alpine sable
ah
alpine sable
and whats the question
.
sinful juniper
How much does she pay in total after the 12 months?
alpine sable
so she pays 700 the first month then 800 then 900 etc right?
sinful juniper
yeah
sinful juniper
is the additional 100 for 12 months?
or 11 months because the first month was paid for already
alpine sable
is the additional 100 for 12 months?
huh
sinful juniper
fixed it
alpine sable
well is it 700 + 800 + 900... or 700 + 800 + 800...
but either way 11 months
is when you add the additional 100(s)
alpine sable
yes
alpine sable
,w sum from 1 to 12 of 100n + 600
ocean sealBOT
ocean sealBOT
sinful juniper
ohh wait something went wrong
alpine sable
okay either way its wrong
floral light
y=5+2x-x^2
x=5
lone heartBOT
y=5+2x-x^2
x=5
alpine sable
whats the question? solve for y?
floral light
I think so, it said solve the function if that changes anything
alpine sable
plug in x=5 into your first equation, what do you get?
floral light
I did that and I got 40, the main problem is that the answer booklet says -10
Since it’s a problem with whether or not it’s (-x)^2 or -(x^2) so I want to get another opinion since my teacher has said these answer booklets are occasionally wrong
floral light
Well the way I took it is
5+10+25 which gets me 40
So it’s supposed to be the 5^2 first and ignore the - before it? To get 5+10-25 instead
floral light
Alright- I was always taught that if you had a negative number squared it would equal positive since negative times negative is positive
Is it different in functions or it is just implied somewhere I missed?
alpine sable
Alright- I was always taught that if you had a negative number squared it would ...
thats true
but its
-(x^2)
not (-x)^2
if you see -x^2 you do the x^2 first then multiply by -1
median oar
Brackets are very important in maths!!!
floral light
Ah, alright
What about
x^2 -2x -3
x=-2
Would it be
4+4-3 = 5
Or
-4+4-3=-3
ocean sealBOT
hibyehibye
alpine sable
$(-2)^2 - 2(-2) - 3$
ocean sealBOT
hibyehibye
alpine sable
$4 + 4 - 3$
ocean sealBOT
hibyehibye
alpine sable
so yea the former
floral light
So in that case the answer booklet was wrong? Since the answer booklet says -3
floral light
My teacher has warned us that occasionally it is wrong
hollow finch
(-2)^2
alpine sable
,w x^2 -2x -3, x=-2
ocean sealBOT
floral light
Alright!
So if it’s a minus in front of x^2 do the x^2 first but if x equals a negative number then it’s the whole negative times negative equals positive stuff?
hollow finch
yeah i think so
alpine sable
you evaluate the x^2 first, doesnt matter what x is
hollow finch
pemdas lol
lone heartBOT
lone heartBOT
Available help channel!
autumn vortex
Is this correct?
lone heartBOT
Is this correct?
arctic raft
Is this correct?
seems right
autumn vortex
When I checked online it's given like this
arctic raft
When I checked online it's given like this
Odd numbers are 3,5,7 and 9 as well
autumn vortex
The n how can you explain the online solution.
arctic raft
online solution must be for some different question
arctic raft
no as far as I know your solution is correct
autumn vortex
👍
inland oriole
Is this correct?
Odd is any number that can be written in the form 2k+1 where k is an integer
Right
autumn vortex
Yeah
inland oriole
Lol nvm
autumn vortex
Wait lemme share the question
inland oriole
👍🏼
autumn vortex
@inland oriole
autumn vortex
Then 80 is the answer
autumn vortex
Yeah
inland oriole
Because it determines whether the number is odd
autumn vortex
Hmm
inland oriole
Cuz this is product rule stuff
autumn vortex
Hmm
inland oriole
I don’t know what that n choose k notation means for permutations only for the binomial theorem
autumn vortex
Ok then I gotta go... thanks for the help @inland oriole e
I will be closing this channel....
inland oriole
Lol
inland oriole
Ok then I gotta go... thanks for the help <@816885647125905418> e
I’ll ping you if I find an answer later
shy silo
so this is a question thats being on my mind
why do we take D as coefficient of x here ?
and also in the last its 3^x and we took log 3 how ?
lone heartBOT
shy silo
.reopen
lone heartBOT
Available help channel!
signal lichen
How does the absolute value work here? do we just plug in 0.3 and if the answer is negative just remove the - sign?
tacit arch
How does the absolute value work here? do we just plug in 0.3 and if the answer ...
|-a| = |a|
signal lichen
|-a| = |a|
so it would be like |blah(0.3)| - |blah(0)| ?
tacit arch
indeed
gritty raft
How do you do 10.C
lone heartBOT
How do you do 10.C
gritty raft
I found the maximised profit and max daily profit
But what do i do with C
What are the possible numbers of chairs that should be made in a day if the cost per chair must be equal 1200
lone heartBOT
@gritty raft Has your question been resolved?
lone heartBOT
@gritty raft Has your question been resolved?
tidal ingot
.close
lone heartBOT
Available help channel!
frigid zinc
lone heartBOT
frigid zinc
how to solve this real quick just one
alpine sable
preassure is equal to the density times g times the height
frigid zinc
ans is A
alpine sable
so take 75 cm ´times the density 13600 times 9.82
0.75 actually
and that sth epreassure of the mercury, but then there is air at the top i dont know what to do with that
frigid zinc
I thought is (9.81)(13600)(0.08)
frigid zinc
so take 75 cm ´times the density 13600 times 9.82
102000Pa , maybe I need minus something
Oh it's 1/100(13600)(10)
I forgot atmospheric pressure is 76cmHg
kk ty
.close
wheat hinge
hi
high ether
How to factorize xy-3x+2y=0
lone heartBOT
How to factorize xy-3x+2y=0
high ether
And 5x+5y-xy=0
I cant just search for roots like for quadratic equations
So is there any systematic methods of finding those factorizations?
high ether
How to factorize xy-3x+2y=0
And if you could do this one plz
minor needle
factor x or y firstly from two terms
then write down same bracket next to what you stayed with
and manipulate equation such that it won't change
gray isle
How to factorize xy-3x+2y=0
are these the original instructions
high ether
> How to factorize xy-3x+2y=0
are these the original instructions
Yes but im looking for the method
Idk how to factorize such equatons
high ether
then write down same bracket next to what you stayed with
Wdym
minor needle
look at the same example
and now let's factor 'y' firstly
5x + 5y - xy = 0
factor 'y'
y(5-x) + 5x = 0
gray isle
as a question, it doesn't make much sense
which makes me wonder if you're making adjustments to the original wording
high ether
as a question, it doesn't make much sense
I am justlooking to write it as a product
high ether
now write down the (5-x) term
I dont get this step
minor needle
we want to have common term to factor it out